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ELEMEttTS OF fiST({OttOMY fittD

AST({OLOGICAL CALCOI.fiTIOttS

V. P. Jain

Preface Predictive astrology is based on the positions of planets,

ascendant, expansion of bhavas etc. at the time of birth of a native or question. Horoscope, chalit charts and divisional charts are casted for that time. Now-a-days these are generated by use of·· computer. Sometimes mistake may appear due to programming error or scme defect in the computer, so it is very essential for an astrologer to have the knowledge to check the corrections and accuracy of horoscope and other charts.

An astrologer must have preliminary knowledge of astronomy. These days normally astrologers do not observe the planets and other celestial bodies but use the longitudes, latitudes, declinations etc. observed by the observatories or calculated by traditional methods. Astrology is an experimental science and thus a very small error may cumulate to a big difference in several hundred years. So our traditional methods require some correction (Beeja sanskara).

We have adopted the positions of exalation and deblitation for a point of time that occured long time ago. Surya siddhanta clearly states that the Sun, Moon and other planets are exalted when they are at apogee (at maximum distance from the earth) and deblitated at perigee (at minimum distance from the earth). The major axis of the orbit of the Earth (apparent Sun), Moon and other planets are revolving slowly in the direction of revolution of the planets.

The apses of the orbit of the earth complete one revolution in more than one lac years resulting in change of longitude of exaltation and deblitation of the Sun. Shri Kedar Dutt Joshi, Reader in astrology, Benaras Hindu University, has also touched upon this matter in the preface of his book Tajik Neelkanthi. These days Sun is exalted around 4th ·July every year, when its longitude is nearly 78° (18° gemini).

It is very essential that the modem astronomical knowledge be applied to the predictive astrology, which includes the affect of gravitational pull, magnitude of the light rceived on the earth, electro-magnetic effect etc. at different times according to the distance of the planets from the earth and the angle of elongation

of the planets. Effect of 11 year and 22 year cycles of Solar flares must also be suitably applied.

Tables given in the 'Talbe of Ascendants' by shri N.C. Lahiri have also been explained. Reasons for the retrograde motion of the planets have also been brought out.

Normally it is difficult for the students to understand the concept of sidereal time. The same has been explained with the help of a figure and I hope it would help the readers to grasp the difference between civil time and sidereal time. Mathematics upto X ·standard has been used so that the book can be understood easily.

My wife Smt. Kailash Jain and my sons Yogesh, Dinesh and their family members cooperated with me in writing this book.

Shri Amrit La! Jain of Pustak Bharti made available a lot of astronomical and astrological material, which helped me.

I am thankful to my teachers of Astrology Shri K.N.Rao, S. N. Kapoor and M. N. Kedar who inspired me to write on astronomical and astrological mathematics.

There may be some errors or omissions. Scholars and learned readers are requested to bring the san:te to my notice, so that they may be corrected in the next edition. SugJestions for improvement are also welcome.

V.P. Jain

7, Popular Apartment, Sector XIII, Rohini, Delhi -110085

Phones:27551029,22722152 Mob. : 9810683617

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Contents Chapter-/

History of Astronomy and Astrology 1-9

Prayer of Saraswati (Godess of knowledge), benefits of astrology, parts of astrology, Indian astronomy & astrology, some eminent Indian Astrologers, history of modern astronomy and some eminent astronomers.

Chapter-11 Definitions 1 0 - 14

Plane, Circle, Sphere, Ellipse, Great Circle, Small Circle, Pole, Axis, Shape of the Earth, Terrestrial equator, latitude, longitude, tropics of cancer and Capricorn, Terrestrial meridian, Prime-meridian, standard/· central meridian. ·

Chapter -Ill Astronomical Definitions · 15-22

Cel~stial sphere, poles, equator, ecliptic, zodiac, celestial latitude, longitude, right ascension, declination, horizon circle, zenith, nadir, verticals, celestial meridian, altitude, azimuth, prime-vertical, declination/ hour circles, hour angle, inferior-conjunction, superior-conjunction, opposition and conjunction.

Chapter-W Time -1 23-28

Units of measurement of time and distances, Light year, astronomical unit, parsec, apparent solar day, civil day, mean solar day, equation of time, L.M.T, G.M.T, sidereal day and sidereal time.

Chapter- V Time -II 29-35

Tithi, Week, lunar month, nakshatra month, anomalistic month, nodal month, solar month, amomalistic year, sidereal year, tropical year, calander year, lunar year, metonic cycle,luni-solar year, adhika (leap) masa and kshaya masa.

Chapter- VI Solar system -1 36-44

Stars, planets, satellites, solar system, Kepler's laws, Bode's law, Sun, solar flares, Earth, formation of seasons and observation of sky.

I

Chapter - VII Solar system - II 45-49

Moon, Mercury, Venus, Mars, Phobos, Deimos and asteroids.

Chapter - Vlll Solur system - Ill 50-58

Jupiter, Saturn, Uranus, Neptune, Pluto, Comets, Meteors and Meteorites.

Chapter-IX Standard time and Sidereal time 59-68

Standard time, L.M.T from Z.S.T, sidereal day and aynamsa correction.

Chapter-X Sidereal and Synodic periods 69- 74

Sidereal period, inferior conjunction, superior conjunction, conjunction, opposition, synodic period of inner and outer planets.

Chapter-XI Horoscope by Modem Method- I 75-83

Various types of charts of horoscope, ascendant and its calculation with examples.

Chapter- XII Horoscope by Modern Method -II 84-93

Calculation of longitudes of planets alongwith examples. Use of logarithmic tables and casting of horoscope.

Chapter- Xlll Horoscope by Traditional Method 94 - 101

Calculation of time of sunrise and sunset, rashiman, charkhanda, ascendant and longitudes of planets.

Chapter- XIV · Precession of Equinoxes 102 ~ 108

Physical cause of precession of equinoxes, nutation, zodiac, sayana & nirayana zodiacs, anynamsa and division of zodiac.

Chapter-XV Retrogression of Planets 1 09 - 115

Geo-centric & helio-centric longitudes, retrogression of inner and outer planets. Phase of planets, brightness of planets, Newton's law of gravitation and effect of planets.

Chapter- XVI Vimshotri Dasa 116-119

Vimshotri-dasa, antar-dasa and pratyantar-dasa.

Chapter- XVII Bhava - Spasta 120-124

Tenth Cusp, calculation of bhava sandhies and cusps.

Chapter - XVlll Divisional Charts 125- 136

Method of prepration of Shadvarga, Sapt-varga, Dash-varga and Shodash-varga Charts.

Chapter- XIX Panchanga 137-147

Calculation of Vara by Indian as well as Western methods, Tithi, examples of Adhika and Kshaya Tithi, Kama, Yoga, Use of Kama and Yoga in predictive astrology.

. Chapter- XX Phases of Moon, Eclipses and Upgrahas 148-157

Phases of Moon, nodes, Rahu, Ketu, lunar eclipse, solar eclipses, chaldean saros, combustion of planets, occultation and non-luminous upgrahas.

Chapter· XXI Rising and Setting of heavenly bodies 158-163

Daily rising & setting of planets, heliacal rising & setting, combustion of Moon and Planets. Setting limits of planets.

Chapter - XXII Stars 164-169

Names, magnitude, colour, spectrum, birth, mass, life time of stars. Galaxies and Milky way.

Chapter· XXIII I,.ongevity 170-178

Calculation of Pindayu, Amsayu, Naisargikayu and Nakshatrayu, Chakrapath haran or hani, satrukshetriya hani, astangata hani, krurodaya hani and bharans.

Chapter- XXIV Shadbala -I 179-204

Shadbala, calculation of positional strength, digba!a and kalbala including ayanbala.

Chapter- XXV Shadbala - II 205-220

Calculation of chesta bala, natural strength and drikbala (aspectual strength).

Chapter- XXVI Bhavabala 221-226

Bhava digbala, drishti bala (aspectual strength), bhavesh bala, strength due to occupancy of a planet and diva-ratri bala. lshta phala anr! Kashta pala.

Ch,apter - XXVII

Annual Horoscope 227-249

Annual Horoscope, its casting, dhruvanka table, Muntha, Dashas used in varshaphala, Vimshotri Mudda Dasha, Yogini Mudda Dasha, Patyayini Dasha, Graha BaJa, Harsh Bala, Panch Vargiya Bala, Table of Hadda Bala, Dwadash Vergiya Bala, Year Lord and Tripataki Chakra.·

Appendix-1 : Equation of time Appelt<.iix-ll: Charts of shodas-vargas Ap~endix-lll: Constants of stars Appendix-W: Table of planetary distances etc.

250 251-261

262 263

[]] Prayer of: Goddess of knowledge (Sar~swati) and spritual teachers

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What is astronomy : . Astronomy is the science dealing with heavenly bodies. It tells

about their motion, etc. Astronomy is the study of universe. We can thmk that Astronomy is Physics applied to problems outside the earth.

1.1 History of Astronomy and Astrology:

Human nature is such that he wants to know, what he sees. On seeing the sky in the night he becomes keenly desirous to know what are the sun, moon and the stars? Why do the stars.twinkle? What are the eclipses and why do they happen? Why sometimes the moon does not appear for whole of night? Why does it start appearing waxing till it becomes full and start waning till it disappears again? What are their effects on the human beings and other objects? This inquisitiveness gave birth to Astronomy and Astrology.

1.2 Jyotish started when the Primitive man saw the sun and moon. By the rising of sun , daylight spread and its heat became available that is the day started. When the sun set, the light disappeared and night began. Thus the relationship of the day and night was established with the sun. He noticed that sometimes the moon is full and seen throughout night, at other time only a part of it is visible for a portion of a night and a time comes when it is not visible for the whole night. When the moon is not visible throughout the night, he called that day as Amavasaya{New Moon). The night when the full

2 Elements of P.stronomy and Astrological Calculations

disc of the moon was visible for the whole night was named as Purnima(Full Moon). Man presumed the time interval between two Amava5Qyas or two Pumimas as a month. While gazing at the stars for a long time~· it was noticed that all the stars. are not stationary but some of them are moving with respect to fixed stars. He named these stars as planets. Jyotish was learnt much earlier than other sciences. Man could acquire the knowledge of time due to Astronomy and many branches

.of mathematics came into existence for solving its problems. The World /Universe changes under certain laws at every moment was inferred by the rising and setting of the sun, moon etc. and the repetitions of the seasons. The Astronomy together with mathematics is among the oldest of the sciences and that it is the one which profoundly influenced man's thinking everywhere.

1.3 Astrology including Astronomy is very much related to the human life and the mankind is benefited in various ways by its study, a few .of them are given below:

( 1) Corelation of day and night by the sun rise and the sun set is an astronomical phenomenon.

(2) Time concept is related to Astronomy and its units such as day, month, year etc. were formed by correlating the movement of celestial bodies. Small and large units of time and distance were invented for its calculation.

(3) Formation of seasons are due to apparent revolution of the sun.

(4) In olden times farmers used to guess the tilling time by examining the position of stars.

(5) The time of floods in the rivers or the time of their becoming dry were estimated with the help of stars.

(6) Observation of stars and measuring various angles and distances in an observatory increases eyesight. scrutinizing and discussion of the observations makes .1 man sharp-minded.

(7) There are lot of galaxies and cluster of stars containing innumer:able number of stars; among them our sun is a small ~tar and in the solar system our earth is very small. A person may be however strong and having the maximum wealth but it is not equivalent to a particle of sand in comparison to the universe. Because of this a person who studies Astronomy is diverted towards spiritualism.

(8) By studying it one knows that world is transformable. Sun rises in the morning , at noon its altitude is highest, it goes down and sets in the evening. The man correlates that he takes birth, becomes

Elements of Astronomy and Astrological Calculations 3

young and die in old age. Hence Astrology is the foundation of spiritualism.

(9) Many parts of mathematics came into existence for solving the astronomical problems. Now a days many formulae or principle are tested by Astronomical observation. Famous theory of relativity of Ein-stein was confirmed through Astronomy. ·

( 10) Long water journeys cannot be successful without its knowledge. Directions are known with its help.

(11) Solar and Lunar eclipses are found out by the astronomical calculations.Astronomy contributes to our cultural heritage. In the long run we make progress and no civilization has thrived for long without seeking knowledge for its own sake. Most Astronomers are intensively curious men and women.

Bhaskaracharya a noted Astrologer had written :

m:<f "tWi "tp:i f"'~Hil:iti'1 ~I ~<::I {;· q u.,. q f€1 c1 """'I fo q t 1"!ftt <nTtUJT{_ 11

.Meaning:

Vyakarana(grammar)is the mouth, Astrology is the eye, Niruktas ·are ears, kalpa(procedure for performing religious rituals) are ears, shiksha(education)is nose and Chhanda(verses)are feet of vedas.Eye is more desirable among the human body, Similarly Jyotish(Astrology) is one of the various branches of Vedas.

1.4 Formerly Jyotish was &~ided into three parts namely (1) Siddhanta (2) Hora and (3) Samhita which became five afterwords that is (4) Prashana and (5) Shakun were added to the three parts.

(1) Siddhanta is that divisio'n of Astrology which deals with the counting of time, knowledge about the heavenly bodies (Mass, velocity etc).lt is pure science .. Astronomy is one of the subjects in many universities as part of mathematics, astro-physics etc. It deals in the construction of astronomical instruments, observation of heavenly bodies with their help and discovering the knowledge of celestial objects. The· knowledge of Astronomy has progressed due to modem mathematics, physics etc and observations with the help of modem observatories. Now the results are more accurate.No correction in the formulae of Indian Astronomy has been done for several centuries .This is the reason that the longitudes of various planets found out by formulae differ with those of actual observed positions.

(2) H~ra or Jataka Shashtra : Hora word has been derived from the word Ahoratri(Day and Night). If the first letter A and last Tri are removed, it becomes hora. In this part the futUre of ·a native o'r

4 Elements 'of Astronomy and Astrological Calculations

jataka is judged. It can be said as the predictive part of the Astrology. A lot of independent literature on it is available.

(3) The third part is Samhita which is used for predicting natural phenomena like earthquakes, seasons, rains, famines, political and economic developments of nations or group of people, Ayurveda and fluctuations of rates of various goods etc.

(4) Horary (Prasana Shashtra) :In this part the prediction is done by the horoscope of the time of query, bodily action or gesture etc of the querist.

(5) The fifth part is Omen in which the prediction is given by carefully wah::hing the omen at the time of som·e task and query.

1.5 Indian Astrology: History oflndian aStrology is given briefly. Astrology was originated

in India. Rishies and Munis experienced the universe in their body by yoga(Yat Pinde tatt brahamada). A word circle (chakra) has been given in Rigveda which has been used for zodiac. It is estimated by the Rigveda etc. thatlndians possessed the knowledge of Astrology and Astronomy from 28,000 years at least. It is a well known fact that O(zero) is the Indian contribution which is very essential for mathematics and astronomy. One cannot dream about the progress in Astronomy without it.

1.6/ndian Astronomy:

(1) Surya Siddhanta : Surya Siddhanta is one of the oldest class of revelations. Shlokas (verses) 2 to 9 of Surya Siddhanta reveal that Asur Maya practised penance of sun god in the end of Satyuga. On being contented by his penance the sun god said nobody can bear my heat, therefore this man who is my part will teach you. The teaching of that sun part man is Surya Siddhanta. Some changes have occurred with the passage of time. This book is of great importance for Astrology. The knowledge of longitudes of Planets, Eclipses, Healical rising and setting, nodes etc. is available in it.

(2) Pitamaha-Siddhanta : Brahamagupta and Bhaskaracharaya have adopted Pitamah-siddhanta as the base of their calculations. It includes the calculations-about the motions of the sun and moon only.

(3) Vashishtha-Siddhantha : It is the improved version of Pitamah Siddhantha and includes the motion of moon and sun only.

(4) Romaka-Siddhantha : Some learned persons tell on the basis of Lata, Vashistha, Vijayanandi, and Aryabhatta thut it was writtten by Shrisena.


(5) Jyotishkarandaka : It is an original book and appears to have been written in 300-400B.C. It has given information about Ashwini and Swati Nakshataras.

(6) Surya-Pragyapati : It is an original Jain book as old as Vedanga-Jyotish.lt is written in Prakrata language. Malyagiri Suri wrote its commentary in sanskrit. Motion of the sun, its revolution , days, months, and fortnight etc. has been narrated in it. Solar system and their orbital circles have been described in it.

(7) Chandra Pragaypati : It is also a Jain treatise and writtten in Prakrata language. The motions of the Sun and the Moon have been fixed in it. The method of calculating the duration of day by the length of shadow has been given in it.

1.7 Some eminent Indian Astrologers:

(1) Maharishi Parashara : He is the Maharishi after Narada and Vashishtha. He wrote Brihata Parashara Hora Shashtra. it is a classical book of predictive Astrology.

(2) Rishiputra : He was prominent learned man and following Jain religion. According to Calatogus Catalogosum he was the son of Acharya Garg Muni. References of his worlG are given in the commentary of.Brihatsamhita in Bhattotpalli. He authored a samhita and described the predictions through omen and Nimitta (happening by chance with someone's help).

(3) J'\rya Bhatta-1 Was born in 476 A.D. He wrote the famous volume 'Arya Bhattiya' in which he described that the sun and the stars are stationary and the days and nights are formed due to rotation of the earth. He contributed lot in mathematics and astronomy.

( 4) Kalkacharya was a follower of Jainism and was a very learned man. He was a prominent asrrologer of third century. He also authored the books of Samhita and Nimitta Shashtra. Varahmihira has referred· Kalak-samhita in his work Brihatjataka.

(5) Arya Bhatt-11 : His siddhanta 'Maha Arya Bhattiya' or Maha Arya Siddhantha is a famous book. It is a valuable contribution for astrology and its theory were adopted by many astrologers after him.

(6) Lallacharya's fathers name was Bhattatrivikrama. He was born in 421 Saka Samvata. He followed the theory of Aryabhatta. His work 'Shishyavridhee' mainly contains mathematical and spherical portions. He authored 'Ratnakosha' which is a work of samhita.

(7) Varahmihira \.vas horn in 505A.D. He got the education of Jyotisha from his father Adityadasa and settled in Ujjain. He wrote

6 Elements of Astronomy and Astrological Calculations

Brihatsamhita there. Besides Brihat Samhita his other works are Laghujatka, Vivaha Patal, Yogayatra, and Samas-Samhita. His samhita is matchless. He was a very learned predictive Astrologer also.

(8) Kalyan Verma was born in 578A.D. He wrote Satawali which is very valuable contribution in Hora-Shashtra.

(9) Brahmagupta was born in 598A.D at Bhimalika. He was a learned Astrologer. He wrote 'Brahamasputa Siddhanta' and 'Khandkadyaka'. He discovered several new formulae of Algebra.

(10) Bhaskracharya was born in 1114 AD at Vijjadavida village. His father's name was Maheshwara who was his teacher also. He wrote the books 'Lilawati', Bijaganita(Algebra), Siddhanta Shiromani, Karan Kutuhal. and 'Sarvatobhadra'.Nter Varahmihira and Brahamagupta no astrologer could match them excluding Bhaskaracharya. Bhaskaracharya and Mahendra!luri told the methods of constructing the instruments for observation and their modus operandi.

(11) Ganesh : lt is said that he was born in 1517A.D. Laxmi was his m0ther and Keshava was his father. He wrote a book GrahLaghava at the age of 13 only. All the astronomical Mathematics is done with the help of numbers without using cosine and other circular measures.His several other works include Laghutithichintamani, Brihatatithichintamani etc.

(12) Dhundirajwas born in 1541A.D. He w~sson of Nrisingh Davagya of Parthapura and G,.vanraj was his teacher. He wrote a book Jatakabharnama on predictive astrology. It is a very good book in Predictive astrology.

(13) Ranganath was born at Kashi in ·1575A.D. His father's name was Walla! and mother's name was Goji. He wrote commentary on Surya siddhanta and made it safe from further interpolations.

Excluding these astrologers, Munjal,.Mahabiracharya, Bhattotpala, Sripati, Sridhara etc were among the famous Indian Astrologers.

1.8 History of Western and Modem Astronomy:

Astronomical discoveries have pr~foundly influenced man's thinking and has contributed lqt for freedom of thought. In ancient times it was the belief that the earth is in the centre of the universe and the sun, moon and other planets etc revolve around the earth as per Aristotle system and Indian system. Afterwards the position changed and the theory of revolution of all the planets and earth around the sun was evolved. The name of few astronomers and their discoveries are:-

(1) Hipparchus (190 to 120 B.C) prepared a star catalogue

Elements·of Astronomy and Astrological Calculations 7

but the same is not av(lilable. Ptolemy (Claudius Ptolemacus 180 to 120 BC) frequently cited him and describes his earlier contributions. Ptolemy obviously admired Hipparchus. Ptolemy assumed that the earth is atthe centre of the universe and each planet revolves around it with two simultaneous, uniform circular motions. The planets move around a circular path called an epicycle, while the centre of epicycle moves around a larger circular path called the deferent. The earth is at the centre of the deferent. This theory was highly successful and was used even after 1400 years of his death. By the beginning of sixteenth century A.D, with the Europe in the midst of a great intellectual Renaissance, the· heliocentric theory again ·appeared on the scene which was suggested by Aristarchus (It was also suggested by the Indian astronomers also).

(2) Nicholas Copernicus was born atTorun; Poland, in 1473. His father died when he was 10 years and he was adopted by his mother's brother who was an intellectual priest. Copernicus officially studied medicine and church law, but his passion was for astronomy and mathematics, to which he devoted all his spare time throughout his life. Copernicus sets the sun at the center of the universe <md makeS tha earth and other planets move around it. He believed that the univet:Se as well as the earth are spherical. The result of his study is summarized in the treatise 'On the revolutions of Heavenly spheres' which finally reached print the day Copernicus died in 1543.

(3) Tycho Brahe (1546-1601) was born in Denmark in 1546. He developed an early interest in astronomy and spent many nights studying the sky rath~r than the books of law. This interest was motivdted in part by belief in astrology. Tycho's brilliance was brouHht to the attention of King Fredric of Denmark, who offered him a small island. He designed and built several instruments for measuring the positions of stars and planets, which were far superior to any previous ones. In 1599 he moved to Prague under the patronage of emperor Rudolph II. ..

(4) Galelio (1564-1642) was bom in Pisa in 1564 and entered the University of Pisa in 1581 to study medicine. He soon showed a special talent for Physics and Mathematics and showed that the time period to make one swing of a pendulum depends only on its length. After several trials, in 1609 he made a telescope that made distant objects appear about 30 times nearer. When he observed the sky by his telescope ht! r .. ade astonishing discovery one after another. He discovered four Moons of Jupiter which revolve around Jupiter as it revolves ·around sun. Galelio published his 'Dialogue on the two chief World Systems' in 1632, spelling about Copernican arguments. Church banned this book and confiscated the remaining copies. He was called·

8 · Elements of Astronomy and Astrological Calculations

to Rome where he had to contradict his views under pressure. As he left· the room, he muttered under his breath.

"But the earth does move". He remained in house arrest for the remaining life at his villa in Arcetri "Dialogue concerning Two New Sciences" was his final work.

(5) Johannes Kepler (1571-1630)was bam in 1571 in · Wurtemberg. He studied at Tubingen University and was a student of

Copernican cosmology. He moved to Styria (Austria)in 1594, where he taught mathematics. He also believed in .astrology like Tycho. Styria was catholic and Kepler was a Protestant. He moved to Prague in 1600. Here he and Tycho worked tog~'<ther and Kepler began to analyse Tycho's measurements and continued even afterTycho's death in 1601. (His book commentaries on the Motion of Mars was published in 1609) in which his first two laws of planetary motion were given. A decade after this third law of planetary motion could also be found out.

(6) Sir Issac Newton (1642-1727) born on Christmas day in 1642, in England. Newton's main contribution was about the laws of motion and laws of gravitation. He constructed Reflector type Telescope which was called Newtonian telescope.

(7) Edmund Halley (1656-1742) applied the Newtonian method for calculating the orientations of the the orbits to several historical comets whose positions had been carefully recorded. He discovered that the comets seen in 1531,1607 and 1682, followed nearly the same orbit and concluded that they were one comet having an orbital period of 75 years(approximately).He predicted that it will reappear in 1758 and comet returned in 1759 after Halley's death.

After this ni'?W techniques for observing stars & planets were developed. The development of modem equipments, bigger Telescopes, Spectroscopy and photography made radical changes in experimental and observation fields.

(8) William Herche1 was a musician and an amateur astrologer. Herchel acquired the knowledge of telescopes and special type of reflecting telescopes. He used to prepare very good telescopes. On 13th 11.1arc'1 1781 he discovered a planet beyond Satuli!. Which is called He'rchel or Uranus. He discovered two moons (Titania and Oberon) of Uranus in 1787. After this he discovered two moons of Saturn.

(9) John Couch Adams (1819,..1892) was an English mathematician. He assumed that Newton's theory was correct and Uranus's erratic behaviour was due to preturbations by a hypothetical planet. Adams calculated the position. of the suspected planet and sent


his predictions to the Royal Greenwich observatory. Similar calculations were made by French man ·•urabin Leverrier'. John Galle a German astronomer along with H.L.D Arrest discovered a new planet Neptune in 1846.

(10) Asaph Hall (1829-1907) was an American astronomer. He discovered the two moons (Phobos and Deimos)of Mars in 1877.

(11) Twenty three years old Cyde Tombaugh attached to Lovell observatory, discovered the planet Pluto in the year1930.

(12) Albert Einstein was born in 1879 at Ulm (Gerrnany). Einsteins contribution to gravitational astronomy began with a small paper in 1913 and culminated in 1915 with the paper 'The foundation of the General Theory of Relativity'.

Space age started with the launching of Sputnik by Russia in 1957. Now the man made sattelites and space crafts are probing the space from the Moon, Mars etc.

[llJ Definitions

2.1 Plane:

When a plane surlace is extended, it is called a plane. It has got only length and breadth and not the width. It is a two dimensional figure. Three points which are not in a straight line, determine a plane. !ts examples are the upper part of the floor, top of the table etc.

2.2 Curved surface :

All the points of a curved surface do not lie in a plane for example surface of a cone, surface of a ball etc.

2.3 Circle:

All the points of a circle are equidistant from one point. That point is the centre of the circle. The distance of centre with any point on the circle is called radius. A straight line passing through the centre and meeting the circle at two points opposite to each other is called diameter.

2.4Sphere:

If a semi-circle is rotated around iis diameter, the three dimensional figure formed is called a sphere. All the points on the surface of a sphere are equidistant from the centre and this distance is known as

. radius. Football and Tennis balls are its examples.

2.5 Ellipse:

Ellipse is a figure of two dimensions and is like an egg. Fix two pins


on the board, loop the string tightly stretched. The figure drawn is an ellipse. In figure-1 the points F and H where the pins are fixed are the foci of the ellipse. Let the few points on the ellipse be AGBCD and E,

HC + CF = HD + DF = HE + EF = HA + AF = HG + GF = HB+ BE

It is commonly used in Astronomy.

2.6 Great Circle :

A great circle on the surface of the sphere is that circle whose plane passes through the centre of the sphere. This circle divides the sphere into two equal parts and its diameter passes through the centre of the sphere. The circle made on the suface of an apple or an orange, when they are cut from the middle, is a great circle.

In figure- 2, Cis the centre of the sphere and circle ABO is a great circle, whose diameter ACB is passing through the centre C.

It is evident that great circles on a sphere are equal in magnitude.

2.7 Small circle:

N

s Fig.-2

A plane which does not pass through the centre of the sphere makes a small circle at the surface of the sphere. As such these circles are smaller than a great circle and are called small circles. In fig - 2, circle EHF is a small circle as its diameter does not pass through the centre C.

12 Elements of Astronomy _and Astrological Calculations

2.8 Pole:

A straight line drawn perpendicular to the plane of a great circle and passing through the centre of the circle/sphere meets the sphere at two points. These points are the poles of the great circle, one is above the great circle and the other below it. In figure · 2, Nand S are the poles of great circle ADB.

Properties of a great circle and poles :

(a) Great circles passing through the poles of a great circle are called secondaries to the later circle. These secondaries cut the great circle at right angles. In figure- 2, ADB is a great circle and its poles are Nand S. The great circles Nl.S and NMS are secondaries and the angle betWeen them at L and M are right angles.

(b) Every great circle has two poles on the sphere in opposite directions.

(c) A pole has only one great circle.

2.9Axis:

Axis is a straight line passing through the poles of a great circle and its centre. In figure · 2, NCS is the axis of great circle ADB. In Astronomy axis is a line around which a planet rotates.

2.10Shapeoftheearth:

Earth is a spheroid like the orange. It is a bit flat on the poles.

2.11 Terrestrial equator:

Terrestrial equator is an imaginary great circle on the surface of the earth which divides the earth in two equal hemi-spheres and its poles are in the centre of both the flat portions. If the sphere in figure -2 is taken as earth, the circle ADB is the terrestrial equator N and S are its poles. The portion above this equator is called the Northern hemisphere and the lower one as Southern hemi-sphere. NCS is the axis of the earth and C is its centre.

2.12 Terrestrial latitude:

To find the position of a place on the earth, we require a set of coordinates which are called latitude 'and longitude.

Imagine small circles on the surface of the earth parallel tQ the equator. The centre of all these circles will lie on the axis of the earth. In figure- 3, ACB is the diameter of the equator and NCS is the axis of the earth. M is a place on the earth. EMF isoe. small circle parallel to the equator. NMRS is a great circle which intersects the small circle at M as well as the equator at Rat right angles. Angle MCR (which is in a plane


perpendicular to the equator) is the terrestrial latitude of the place ~. It is· the latitude of all places lying on the small circle EMF. The places north of the equator have their latitudes between oo to 90° (N) and those in the southern hemisphere have their latitudes between oo to 90° (S).

2.13 Tropic of Cancer:·

N

s Fig.-3

Tropic of Cancer is an imaginery line round the surface of the . earth parallel to the equator at an angular distance (latitude) of 23° 27' (N). The sun shines atthe head at mid-noon on about2lstJurie every year. The sun enters sayana Cancer sign at this time.lt is the reason of naming this line as Tropic of Cancer.

2.14 Tropic of Capricorn:

When the sun goes maximum towards south on its orbit, it shines above the head at places whose latitudes are 23° 27' (Sl and the declination of the sun becomes 23° 27' (S). This small circle at 23° 27' (S) is called Tropic of Capricorn as the sun enters the sayan Capricorn. sign. This happens about 23rd of December every year.

2.15 Terrestrial Meridian:

The great circles on the surface of the earth and passing through both the poles are the Meridians. In figure-3, NMRS and other semicircles joining the poles N and S are called terrestrial meridians of the places from which they are passing.


2.16PrlmeMeridian:

To divided the earth between northern and southern hemispheres, equator is there whose latitude is zero but for the starting point of longitudes a problem arises as to which meridian be taken as the starting pOint. In olden times the meridian passing through Ujjain used to be taken as the Prime-meridian (zero degree meridian). Now a days the meridian passing through the Greenwich observ~t01y near London, is considered as the Prime-meridian and the counting of longitudes starts from this meridian.

2.17 Te"estriallongitude :

Angle of the arc intercepted at equator between the Prime-meridian and the meridian of a place is known as terrestrial longitude of that place. If the place is in the east of the Prime-meridian the longitudes are Eastward 'E' is suffixed after the degrees of longitudes and in case of West W' is suffixed. Longitudes can be oo to 180° (E) or oo to 180° (W).

In figure - 3, G is Greenwich and NGQS is the Prime meridian. The longitudes of M is the angle QCR (E) as it is in the east of Greenwich.

2.18 Stancfard Meridian :

. EvelY couney/zone is not only spread from North to South but from East to West also. The earth rotates around its axis from West to East and completes one rotation in one day i.e. 24 hours. Therefore, the sun appears moving from East to West daily. The places which are in the east will have their mid-noon earlier than the places in the West, resulting in the difference of local time. Local time of the places in the east will be ahead of the local time of the places in the West.

A problem arises that there will be difference of time at the places east and west of a couney/zone and the time schedule of trains, Aeroplanes, T.V. etc. cannot be framed. A person travelling from east to west or vice-versa will have to adjust his watch frequently due to difference of local time. It was solved by finding out a way that in a country/zone a meridian is chosen whose local time will be followed throughout the country/zone and the wordly affairs are regulated according to it. This meridian is called the standard or central meridian of the country(zone and its local time is said to be sfandard time of that country/zone.

..

[ill] Astronomical Definitions

3.1 Celestial sphere:

If air is pumped into a balloon, its size increases gradually. Similarly the earth may be projected into the space, the surface of this projected sphere is known as celestial sphere. The centre of the earth is the centre of the celestial sphere.

It is also defined as an imaginary sphere in the sky, centered on the earth.

3.2 Celestial poles:

The place where the North and the South poles of the earth meet the projected sphere (Celestial sphere) are the celestial North and South poles. North pole is near Polaris and is directly above North pole of the earth.

3.3 Celestial Equator:

Celestial equator is defined as the intersection of the earth's equatorial plane with the celestial sphere.

Celestial equator is a great circle on the celestial sphere, midway between the poles. The place where the projected earth's equator meets the celestial sphere is the celestial equator.

3.4 Ecliptic :

The apparent annual path of the sun among the stars is known as its orbit. When this orbit is expanded and the great circle formed by its intersection with the celestial sphere is known as ecliptic.

Acually earth is revolving around the sun. The place where the plane of earth's orbit meetS the celestial ~ph'ere is the ecliptic. The plane of earth's orbit is the plane of ecliptic. Mean angle between the planes of ecliptic and celestial equator is 23° 27'. The angle between these two plains varies from time to time and is called the obliquity of ecliptic.

In figure - 4, APB is the celestial equator and EQF is the ecliptic. C is the centre. The angle between their planes or say diameters i.e. angle FCB is 23° 27'.


A

J

3.5Zodiac:

N

s Fig.-4

Our ancestors observed that the Moon and Planets were never at a great angular distance from the ecliptic. They, therefore, conceived an imaginary belt in the heavens extending about go on either side of the ecliptic. This belt is known as zodiac. Moon and other planets are found in this belt. Pluto sometimes goes out of this belt. The earth and the sun are naturally in the middle of this belt which is ecliptic.

In figure · 4 of the celestial sphere, EQF is the ecliptic; JK and GH are circles parallel to the ecliptic at a distance of go above and below it. This belt JKHG is called as zodiac. In other words the space covered by JEG moving round the celestial sphere is zodiac. Division of zodiac has been given in chapter- 14.

3.6 The definitions in 3.6 to 3.g have been eltplf.ined by a diagram in para 3.10.

Celestial longitude :

The celestial longitude of a heavenly body at any time is the angle of the arc measured along the ecliptic, from the first point of Aries to the foot of the perpendicular drawn on the ecliptic from the heavenly body.


3.7 Celestiallatitude:

The celestial latitude of a heavenly body is the angle sub tended by the perpendicular arc from the..,heavenly body to the ecliptic. The celestial latitudes vary from oo to 90° on either side of the ecliptic and letters 'N' and'S' are suffixed according to their position towards north/ south of the ecliptic.

· 3.8 Right Ascension:

The right ascension of a heavenly body is the angular distance of the arc measured along the celestial equator from the vema! equinox (movable first point of Aries) to the foot of the perpendicular drawn on the equator from the heavenly body.

3.9 Declination :

Declination of a heavenly body is the angle subtended by the perpendicular arc from the heavenly body to the celestial equator. The declination vary from oo to 90° on either side of the celestial equator and the letters 'N' and 'S' are suffixed according to their position towards north or south of the celestial equator.

3.10 The definitions in paras 3.6 to 3.9 are explained with the help of a diagram as under :

Ar---~:....._--:7'~-,L-+-----=1c

s Fig.-5

equator


In the figure- 5, ABC is the celestial equator, DEF is ecliptic, 0 is the centre of the earth/celestial sphere. N and S are celestial poles.

P and Q ar<' poles of ecliptic.

X is a heavenly body/star.

XG is the perpendicular arc on ecliptic.

XH is the perpendicular arc on celestial equator.

MandL are movable first point of Aries (vernal equinox) and first point of Libra (Autumnal equinox) .

Celestial longitude of the star = angle subtended by the arc MG

Celestial latitude of the star = angle subtended by the arc XG

.\1gnt M.>-.-'1sion (R.A.) = angle subtended by the arc MH

Declination = . ngle subtended by the arc XH

3.11 Horizon circle:

The circle where the earth and the sky appear to meet is called the Horizon. It depends on the power of the telesoope/eye of the observer, how much big is this circle. The plane of this circle where it intersects the celestial sphere is the Horizon circle.

3.12 Zenith:

The plumb line of the place when produced upwards, the point where it meets the celestial sphere is known as zenith of the place. In other words the meeting point of a straight line from the centre of the earth and passing through the observer, with the celestial sphere is zenith. It is one of the two poles of the Horizon circle.

3.13Nadir:

The point of intersection of the straight line passing through the foot of the observer and the centre of the earth, with the celestial sphere is called Nadir. It is a diameterically opposite point of zenith on the celestial sphere. It is the second pole of the Horizon circle.

3.14 Verticals:

Secondaries ta the Horizon circle are called verticals. The great circles passing th•·ou~h the Zenith and Nadir are verticals. These are perpendicular to <he Horizon.

3.15 Celestial Meridian:

A great circle on the celestial sphere passing through the observer's zenith and the celestial poles is called the observer's celestial Meridian. This Meridian intersects the horizon at two points. These points indicate


the North and South direction of the observer.

3.16 Altitude :

Altitude of a heavenly body is the angle subtended by the perpendicular arc from the heavenly body to the horizon. In other words· the angle of the arc of the vertical from the heavenly body to the horizon is the altitude of that heavenly body.

3.17 Azimuth :

Azimuth of a heavenly body is the arc intercepted on the horizon between the foot of the vertical drawn through the body and the r. ;.:;ddian i.e. North/ South point. The North or South point from where it is measured should be mentioned. If the foot of perpendicular is in the East of the North/South point 'E' should be suffixed to the Azimuth.lf it is towards west W' may be suffixed.

3.18 Prime Vertical:

The vertical circle which is making 90° angle with the celestial meridian is called Prime Vertical. It cuts the horizon at East and West points. The direction towards these points is East/West of the observer.

3.19 The definitions in paras 3.11 to 3.18 are explained through diagram.

z

s

R Fig.-6


0 is the observer at the. ce.)tre.

ZisZenith.

R is Nadir.

P & Q are North and South poles

X is a star (heavenly body)

NWHSE is the Horizon.

PZQ is the celestial meridian meeting the horizon at Sand N

S and N are the South & North points of observer.

ZERW is the Prime Vertical.

ZXHR is a vertical throuth X.

Altitude = angle of the arc HX

Aizmuth = angle of the arc SH (W) or NH (W)

measured from South point or North point.

3.20 Declination circles and Hour circles:

Secondaries to the equator (The circles passing through the North & South poles) are called Declination circles because the declination of heavenly bodies are measured along these circles.

3.21 Hour angle:

The angle which the declination circle through a star makes with the celestial meridian is called the hour angle of the star.

The time interval between two successive crossing of the meridian by a star is one sidereal day of 23h 56m 4' (in solar hours).

In the figure- 7, X is a star ...

P & Q are the North and South poles.

AB is celestial equator.

NKSJ is the Horizon of the observer.

PXH is the declination circle of the star.

DJEXK is the <;ircle parallel to the equator, in which the star appears to revolve daily due to earth's rotation. It rises when it comes at J and at maximum altitude at E and sets at K.

PZEBSQ is the observer's meridian.

PXH is the meridian of the star. It is also called the declination circle through it. '

Hour angle of the star is the angle between the meridian

Elements of Astronomy and Astrological Calculations 21 . . of the star and the observer's meridian. Here angle HPB or angle XPE is the hour angle of the star. This angle is converted into time unit also.

360° = 24 sidereal hours

15° = 1 sidereal hour

1 o = 4 sidereal minutes.

z

s

Fig.-7

For the sun it will be solar days and hours etc as the sun also moves about 1 o in a day.

3.22 Paras 3.22 to 3.25 will be explained in chapter X. Here the definitions are given.

Inferior Conjunct~on :

An inner planet (Mercury and Venus) is at inferior conjunction when it is in between the sun and the earth and its longitudes are equal to that of the sun. The planet is nearer to the earth at this time.

3.23 Superior Conjunction :

The time when the inner planet is at greatest distance (the sun is in between the planet and the earth) and the longitudes of the planet


and the sun are equal, the planet is at superior conjunction.

3.24 Conjunction :

When an outer planet (Mars, Jupiter, Saturn etc.) are at greatest·_ distance i.e. the sun is in between the planet and the earth and the longitudes of the planet and the sun are the same, the planet is at conjunction.

3.25 Opposition:

An outer planet is nearest to the earth i.e. the earth is in between the planet and the sun and the difference in longitudes of the sun and the planet is 180°, th-:? planet is said to be in opposition.

[ffi Time -I

4.1 Different kinds of units for measuring distances, weight, time etc were prevailing in different countries. Now uniformity among these units is observed in most of the countries and the units of distances and weight are mostly of multiples of 10. The basic unit of time are taken as Gregorien Calender year, Hour, Minutes and seconds etc. We shall see the various units of time which was followed in India and now prevailing in India.

(a) 6 Pran = 1 Pal (Vinadi) = 24 seconds

60 Pal = 1 Ghati (Nadi) = 24 minutes

60 Ghati = 1 day (civil day)

21,600 Pran = 86400 seconds= 1 day

(b) 100 Truti = 1 Tatpar

30 Tatpar = 1 Nimesh

18 Nimesh = 1 Kashtha

30 Kashtha = 1 Kala

30 Kala = 1 Ghati (Ghatika)

2 Ghatika = 1 Muhurta

30 Muhurta = 1 day = 60 Ghatika

(c) 60 Anupal = 1 Vipal

60 Vipal = 1 Pal 60 Pal = 1 ghati

I 22 Ghati = 1 hour

I 72 Ghati = 1 Prahar = 3 hours.

8 Prahar = 60 Ghati = 24 hours = 1 Ahoratri (1 day)

15 days :.: 1 Paksha

2 Pakshas = 1 Month i

12 Months = 1 year

~;4 Elements of Astronomy and Astrological Calculations

Western units which are now used in India.

60 seconds = 1 Minute

60 Minutes = 1 hour

24 hours = 1 day.

The basic time frame used in Surya-Sidhanta is Mahhayuga which is divided into four yugas in the ratio of 4:3:2:1 and the same are as under:

Satyuga

Treta

= 17 ,28, 000 solar years

= 12,96,000 solar years

I>.vapar = 8,64, 000 solar years

Kaliyuga = 4,32,000 solar years

Total= 1 Mahayuga = 43,20,000solaryears.

1 Kalpa = 1000 Mahayugas ·

= 4,32,00,00,000 solar years.

2 Kalpas = Brahma's one day & night (Ahoratri)

4.2 Distances of heavenly bodies (stars etc.) are very great and as such units covering large distance are :

(a) Light year : The favourite unit of interstellar distance in popi.llar science writings is light year. Light year is the distance travelled by light in one year. Light travels 1,86,000 miles (3,00,000 kilometers) in one second.

In one year light will travel

= 3,00,000 X 60 X 60 X 24 X 365.25 K.M.

One light ye~r = 9.46 X 1012 K.M.

= 5.88 x 1012 Miles

Some stars are at a distance of several light years, but the distance of most of the stars are in Hundreds, thousands and lacs of light years. If these are measured in Kilometers or Miles the number will be .very· big.

(b) As~ronomlcal Unit : Astronomical unit is equal to half of the major axis of the earth's orbit (path) i.e. half the distance of earth's Pe,rihelion plus Aphelion, which" is the average distance between sun and the earth.

One Astronomical Unit (A.U.)

= Average distance of the earth from the sun 1 = 2 of Major axis of earth's orbit

= 930 Lacs Miles


= 1496 Lac.~ Kilometers.

It is nonnally used by the Astronomers.

(c) Parsec : Parsec is the distance of a star having a parallax of one second of arc, as seen from the earth. Astronomers usually express distances of stars etc. in this unit. The angle of parallax is half of the angle sub tended by the heavenly body when viewed from the perihelion and aphelion positions of the earth.

s

Fig.-8

Twice of angle of parallax

In the above figure E1 and E2 are the positions of the earth when it is on aphelion and perihelion and S is the star. Angle E

1SEz = twice

the angle of parallax. When the star is going away from the earth this angle will become shorter and shorter. When the star is coming nearer to the earth, the angle will become greater.

The distance of 1 second of parallax corresponds to 1 Parsec. The angle of parallax is inve_rsely proportional to the distance of the star. If the angle of parallax is 0.01" the distance will be 100 Parsec and

I not

1 00 Parsec.

4.3 Apparent solar day :

The earth is rotating from west to east and as such the sun, the stars and other heavenly bodies including zodiac appear to move from


east to west. The earth is completing one rotation around its axis in one day, which is causing the rising and setting of the sun and the stars daily. It is called the diurnal motion of the sun and other heavenly bodies. The apparant solar day is defined as the time interval between two successive crossings of the meridian by the sun.

4.4 When the sun is at the meridian of a place, its hour angle is 0 (zero) and the counting of time starts. At the time of its crossing the other side of the meridian i.e. Anti-meridian (180° apart from the meridian) it is mid-night at that place and the hour angle will be 12 hours. In Astronomy the time starts from mid-noon and a day is from mid-noon to next mid-noon.

4.5 Civil day:

In Indian system, the time interval between two successive sunrises is called a civil day .(Savan Din). Now a days the time interval from one mid-night to the next mid-night is called a civil day.

4.6 Mean solar day :

The duration of days do not remain the same due to the following reasons.

(i) The earth revolves round the sun in an elliptical orbit and completes one revolution in one year. We are on the earth. The earth appears stationary and the sun appears moving and completing one revolution of the earth in one year. The angular velocity of the earth is more, when it is nearer to the sun than it is away from the sun.

(ii) The earth is moving on the ecliptic while the hour angle corresponds to the movement on the equator.

Due to above stated reasons, the change of right ascension of the sun does not remain constant and the duration of days do not remain the same. To avoid the difference in the length of days Astronomers have invented a Mean sun which is moving in a circular orbit along the equator and completing one revolution in the time taken by the actual sun moving on the ecliptic for completing one revolution. As the mean sun changes its right ascension at a uniform rate, the length of a mean solar day is constant. The hour angle is measured by the mean sun. The time taken by this mean sun between two successive transits of the meridian is known as Mean Solar Day.

4.7 Equation of time:

As already stated that the True sun's angular velocity of revolution is greatest when it is nearest to the earth and shortest when it is farthest from the earth. At the time it is farthest from the earth longer period of time will be taken by the true sun to move the same angular distance


than the mean sun and the mean sun goes ahead of the true sun. When the earth is at the perihelion shorter time will be taken by the true sun than the mean sun in moving the same angular distance. True sun moves on the ecliptic and the Mean sun on the equator. Due to these reasons there is difference between the time of transits of the meridian by them.

The interval of time between the transits of the meridian by the True sun and the Mean sun is known as the equation of time. Equation of time is usually denoted by 'E', Right Ascension by 'R.A.' and hour angle by 'H.A.'

H.A. of True sun = H.A. of Mean sun + E

Note :In olden text books the equation of time has been defined byE = Hour angle of Mean sun- Hour angle of True sun.

Apparent noon is the time when the true sun is on the meridian of a place and it is in the middle of apparent sunrise and sunset. Mean noon is the time when the Mean sun crosses the meridian and it is 12 local Mean time.

The· time of apparent noon is calculated by adding half of the duration of day (Dinman) in the time of the Sun rise.

Apparent noon = (Time of Mean Sunset -time of Mean sunrise)+ 2 + time of

Mean sunrise. It can also be found out by adding the 'E' in the time of local

mean noon. Table of Equation of time has been given in Appendix I.

Example:

Find out the time of apparent noon at Delhi on 1st August.

E for the first August is + 6

Sunrise at Delhi on 1st August Sunset at Delhi on 1st August

Vishwa Vijay Ephemenies Pan chang

5:46l.S.T. 19:081.S.T.

5:42 I.S.T. 19:13 I.S.T.

(a) According to Indian Astr.ology the sunrise or sets when the centre of the disc rises or sets.

Apparent noon = (Sunset- Sunrise)+ 2 + Sunrise = (19:8-5:46)+2 + 5:46 = 13:22 + 2 + 5:46 = 6:41 + 5:46 = 12:27 I.S.T.

(b) According to Ephemeries the sun rises or sets when its upper


limb rises or sets.

Apparent noon = (19:13- 5:42) + 2 + 5:42 = 6:45 + 5:42

= 12:27l.S.T. (agrees with (a))

(c) Mean noon on 1st August at the standard/central meridian = 12 l.S.T. Mean noon at Delhi on 1st August= 12:0 + 0:21 = 12:21 I.S.T., E for first August is + 0:6

Apparent noon at Delhi on 1st August = 12:21 + 0:6 = 12:27 I.S.T.

Which agrees with (a) and (b)

4.8 Local Mean time:

The time counted from the instant when the mean sun crosses the Anti-meridian of a place is the local Mean time or the time from the crossing of the meridian by the mean sun + 12 hours.

4.9 Greenwich Mean time:

Local mean lime of Greenwich observatory near London is known as Greenwich Mean time (G.M.T.).lt is also known as universal time.

4.10 Sidereal day:

Definition :The time interval taken by the fixed stars to complete a revolution round the pole is called a sidereal day. This revolution is due to rotation of the earth around its axis. It has further been explained in para 9.4.

4.11 Sidereal nme :

The reference point for sidereal time chosen in practice is called the Vernal Equinox. The hour angle of the Vernal Equinox is called the sidereal time (S. T.)

~ Time -II

5.1 Tithi (Lunar day)

The moon completes one revolution round the earth with respect to a fixed star in 27.3 days and sun appears to complete a revolution in 365.25 days. The moon moves much faster than the sun. After the conjunction of the Moon and the Sun, the time taken by the Moon to go ahead of the sun by every 12° is the period of one Tithi each. The average time of a Tithi is 23 hours 37 minutes and 28 seconds. It shall be explained in detail in the chapter of Panchanga.

5.2Week: There are seven days (days and nights) in a week and the names

of these are related to the names of the planets. The names of the days of a week have been kept systematically and not arbitrarily.

Moon

Ven

Fig.-9

In Indian Astrology a civil day is the time interval from one sun rise to the next sun rise. It has been divided into 24 equal horas or


hours. The names of the week days are kept on the basis of the lord of the first hera of the day. The first hera of a day starts from sun rise and remains for one hour. Hora'slords are according to their sidereal periods. Write down the names of planets in their decreasing order of their sidereal periods in a circle. Sun may be taken in place of earth.

Sun is in the centre of the solar system and the only star in it. We cannot imagine life in the solar system without it. Let us start from Sunday. Lord of first hera is Sun. Counting in the anti-clockwise direction, the second hera will be of Venus, Ill hera of Mercury, IV hera of Moon, V hera of Saturn, VI hera of Jupitar, VII hera of Mars, VIII hera will be of Sun again. Proceeding likewise the XV hera and XXII hera will be of sun, XXlll hera of Venus, XXIV hera of mercury and XXV hera which is the I hera of next day will be of Moon. The name of the next day is kept after Moon ie Chandravar (Monday) or Somvara.

Now starting from Monday the I hera is of Moon, II hera of Saturn, III hera of Jupiter, IV hera of Mars, V hera of Sun, VI hera of Venus, VII hera of Mercury and VIII hera of Moon again. XXV and XXII horas are of Moon, XXIII hera of saturn, XXIV hera of Jupiter and XXV hera which is the I ho~:p of next day is of Mars. The name of day next to Monday is kept after Mars (Mangal) as Mangalvara. Proceeding like this the names of other week days have been kept.

Lord of first Hora

Ravi (Sun) Soma (Moon) Mangal (Mars ) Budha (Mercury) Brihaspati (Jupiter) Sukra (Venus) Shani (Saturn)

5.3Month:

Name of the day

Ravivara-Sunday Somvara-Monday Mangalvara-Tuesday Budhavara-Wednesday Brihaspativara-Thursday Shukravara-Friday Shanivara-Saturday

There are several types of months. When the ancient man noticed the new Moon, phases of the Moon and full Moon, he described the time interval from one new Moon to the next new-Moon or from one full Moon to the next full Moon as one month. It is the natural phenomena which occurs after a fixed interval of time, it was known earlier than the other types of months.

5.4 Lunar Month :

When the longitudes of the sun and the Moon are equal, it is the · end of Amavasya (New Moon) and the Pratipada starts. The time period between two consecutive New-Moons (Amavasyas) is called a lunar


month. It is named as Amant Masa ( 31""1R!l!m) in Sanskrit. When the sun and the Moon are in opposition i.e. the difference between their longitudes is 180°, the full Moon (Pumima) ends. The time intetval between two successive full Moon (Pumimas) is also known as a Lunar Month. Such lunar months are called Purnimant (~).The time period of both the above types of the months is 29.5306 solar days, which is also the synodic period of the Moon. In Maharashtra, Gujarat, Andhra Pradesh, Karnataka, West Bengal etc the Amant month (from the end of one Amvasya to the end of next Amavasya) is followed, while in Uttar Pradesh, Madhya Pradesh, Orissa, Rajasthan and NorthWestern Part of India Purnimant is in vogue.

The names of the months are the same i.e. Chaitra, Vaishakha, Jeyshta, Ashadha, Srawana, Bhadrapada, Ashvina, Kartika, Margsira, Pausa, Magha and Phalguna. The difference is that the Purnimant starts a fortnight earlier than the Amant. New Samvata starts on the same day. It starts on the 1st day of 2nd fortnight of Chaitra in Pumimant and in Amant the new Samvata starts from the 1st day of Chaitra.

5.5 Nakshtra Masa (Sidereal Month) :

The time inteiVal taken by the Moon in completing one revolution of the Earth with respect to .a fixed star is called a sidereal Month. It is equal to 27.321 mean solar days.

5.6 Anomalistic Month :

The time inteiVal taken by the Moon to move from one Perigee to the next Perigee is known an Anomalistic Month. It contains 27.5546 Mean Solar days.

5.7 Nodical Month:

Moon's nodes (Rahu and Ketu) move the retrograde motion and their backward motion is nearly zoo per year.

The time taken by the Moon to move from one of its Node to the same Node again is called a Nodical Month. It is of 27.2122 Mean Solar days.

5.8 Solar Month:

As per Indian Astrology, when the centre of the sun enters from one Rasi to another Rasi, it is called the Sankranti of the later Rasi. The time inteiVal between two successive Sankranties is a Solar Month.

When the sun is nearer to the earth, its anguh:lr velocity becomes more than the time it is away from the earth. Due to this reason the time taken by the sun in crossing a Rashi (30°) differs with that of other

32 Elements of r'.stronomy and Astrological Calculations

Rashi. When the angular velocity is faster the time taken by it to cross 30° (a Rashi) will become shorter i.e. a solar month will be of shorter duration. It is concluded that the solar months are not of equal time period. Average time of a solar Month is 30.44 Mean solar days.

5.9 Anomalistic year:

It has already been stated that the earth is revolving around the sun in an elliptical orbit. The apsides of the orbit of the earth is slowly moving in the plane of ecliptic and completing one revolution in more than 1,00,000 years i.e. its perihelion is having a slow motion of 11" per year approximately.

The time taken by the earth from one perihelion to the successive perihelion is called an Anomalistic year. An anomalistic year is of 365.2596 Mean solar days.

This year is slightly longer than the sidereal year.

5.1 0 Sidereal year :

The interval of time taken by the earth in making one revolution of the sun with respect to a fixed star is known as sidereal year. A sidereal year consists of 365.256 days (nearly 365 days 6 hours 9 minutes and 10 seconds).

5.11 Tropical year (Sayan year) :

Tropical year is the time interval between two successive passages of the sun across the sayan first point of Aries (Vernal Equinox). Vernal equinox is not a fixed point on the zodiac but it is moving backwards by an average of 50".3 every year. Due to the above reason, it is shorter than the sidereal year by the time interval takenby the sun to move a distance of 50".3 arc.

Tropical year = 365.2422 Mean solar days.

(365 days 5 hours 48 minutes and 45 seconds nearly)

5.12 Calander year:

In 1582 A.D. Pope Gregory reformed the Julian Calander.lt is in vogue the~e days. It is lengthier by only 27 seconds from the ~pica! year. In about 3300 years, there will be a difference of one day. Calander year= 365.2425 Mean solar days.

400 Calander years = 400 X 365 + 97 days (97 is the number of leap days)

400x365+97 = 365 +I!_ da s. 1 Calander year = 400 400

y


= 365.2425 days.

After 400 years the same day of the week will come on the same date.

5.13 Lunar year:

Twelve lunar months make a lunar year. Lunar year = 12 X

29.531 = 354.372 Mean solar days.

5.14Metoniccycle:

Mitan observed in 433 B.C. that the time interval betwen 2'35 lunar months and 19 solar years (228 solar months) is nearly the same with a slight difference of one hour.

19 solar years = 228 solar months

= 19 x 365.25 = 6939.75 days

235 Lunar months= 235 x 29.531 = 6939.785 days

5.15 Thus we notice that in every 19 years or228solarmonths, there are nearly 235 Lunar months. There are 7 lunar months more than the solar months in 19 solar years.lf we follow only the Lunar year Deepawall which usually fall in November (beginning of Winter season) will come 7 months earlier i.e. in April after 19 years. The festiva:s etc. will have no relation with the seasons.

5.16 Luni-solar year:

3 As stated above, there is a difference of about one month in 24

years between solar months and Lunar months, which accumulates to 1 year in about 33 years. Both type of years were followed in olden days in India. One of it has been mentioned in Rigveda and the other in Atharveda. Seasons are according to solar years and festivals or religions rites are performed according to Lunar months. To remove this anomaly and correlate the Lunar years with the solar years, Luni-solar year was formed. In such a year normally there are 12 Lunar months but after every two or three years one Lunar month is added which is called 'Adhik Masa' or 'Mala Masa'. !1ence every third or fourth year consists of 13 months. Such a month is not increased arbitrarily but there is a principle behind the addition of a month.

The principle is when two Amavasyas fall in a solar month (between two consecutive sankranties), there will be two Lunar months of the name of that solar month. That Luni solar year becomes of 131unarmonths and the difference between the two ,ypes of years is adjusted.


5.17 Example of Adhik Masa (Mala Masa) :

Amavasya is ending at 15" 57m on 17th September, 2001 and the sun is in Virgo sign oo 43'. The next Amvasya is ending on 16th October, 2001 at 24" 53m i.e. on 17th October at 0" 53m and the Sun's Nirayana longitude is Vergo sign 29° 37'.

Both of these Lunar months ended when the sun was in Virgo (between the Sankranties of Virgo and Libra) and solar month was Ashwin. the two Lunar months were, therefore, named Ashwin.

In Amant system Ashwin Lunar months are from 18th September to 16th October, 2001 and the second month from 17th October to 15th November, 2001. The first month (18th Sept. to 16th Oct.) is called Mala Masa or Adhik Masa and the other is termed Sudha Masa (Pure Masa) bf name Ashwin.

Purnimant months start a fortnight earlier. In this system Sudha Masa Ashwin Krishan Paksha (Dark half) was from 3rd Sept. to 17th Sept. 2001.

Ashwin Adhika Masa (Mala Masa) was from 18th Sept. to 16th Oct. which is the same as in Amant system. the next fortnight (17th Oct. to 1st November) of Sukla Paksha (Bright half) was Sudha Ashwin Masa.

5.18 Kshaya Masa ( ~lim)

In case there are two Sankranties in a Lunar Month (from the end of one Arnavasya to the end of next Amavasya), a Lunar Month of the name of solar month which is between the two Sankranties is missed (Kshaya). Such a phenomenon can happen during four months (Kartika, Margshirs, Pausha and Magha) November to :=ebruary. It happens or.ly when the Amavasya ends a few minutes earlier than the Sankranti during these months. The reason has been explained in para 5.20. When so ever a Kshaya Masa occurs, it isa pre-condition that there will be two Adhika Masas in that year (Chaitra to Phalguna). One Adhika Masa will be within two to three months earlier than the Kshya Masa. Such an Adhika Masa is known as Sansarp Masa(m:rf lim). The other Adika Masa occurs within two to three months after the Kshya Masa and this Adhika Masa is called Malimlucha( 4fctR;lT.l "ll!B). In ephemeries or Panchangas first Ashik Masa (Sansarp Masa) and Kshaya Masa are not exhibited normally. Only the second Adhik Masa (Malimlucha) is shown there.

Example:

It happened in the year 1982-83. The ending time of Amavasya (the starting time of a Lunar month) and the Niryana longitudes ofthe

Elements of Astronomy and Astrological Calculations · 35

Sun are given below :

Date Starting of Lunar month Longitudes of the sun

Hour Minute s 0

17-9-1982 17 39 5 0 41 } 17-10-1982 5 34 5 29 41 15-11-1982 20 40 6 29 03 15-12-1982 14 48 7 29 28 14-1-1983 10 38 8 29 51 13-2-1983 6 02 10 0 07 } 14-3-1983 23 13 10 29 57

Notice that the Makar sign of sun is missing in the above figures. The Lunar month corresponding to it has been missed (Kshaya).

5.19 TwoAshwinmonthsstartedfrom 17th September and 17th October, 1982, Kartika from 15th November, 1982, Margshirsha from 15th December, 1982 Pausha from 14th January, 1983 and Magha was missed. Two Phalguna Masas started from 13th February, 1983 and 14th March, 1983. But in Ephemeries or Panchangas only one Ashwin was shown and the missing month was also included. They showed as, Ashwin from 17th September, 1982, Kar';ka from 17th October, Margshirsha from 15th November, Pausna from 15th December, 1982, Magha from 14th January, 1983 and two Phalguna masas from 13th February and 14th March, 1983. Kshaya Masa occurs after 19 years or about 141 yeras.

5.20 Why Kshaya Masa occurs?

When the sun is nearer to the earth its angular velocity increases and it moves fast. At the time the sun is farthest from the earth, its angular velocity is slower than the average velocity. The sun is nearest to the earth in early January and farthest in early July. It is the reason that.the solar months from November to February are shorter than the Lunar Months. When the Amavasya ends a few minutes earlier than a Sankranti during these months, there is a possibility of Kshaya Masa.

MJ Solar System - I

6.1 Solar system consists of the planets revolving around the Sun, Moons (satellites), Asteroids, Meteors, Meteorites, comets, dust of planets or asteroids and gases etc. lt is a very small portion of Cos-Mos. We live in it is the reason for its importance. Before describing the solar system, something about the stars, planets and setellites may be known.

6.2Stars:

Stars are the heavenly bodies which are self-illuminated and appear stationary. Our sun is a small star smong these stars. Every constellation is a group of stars. Details about it will be given later.

6.3 Planets:

Planets appear like stars in the sky. The difference between the stars and the planets is that the planets do not have their own light but appear shining due to reflection of sun's light by them. Stars twinkle while the planets do not twinkle but resemble with a plate when seen by a telescope. Stars are stationary while the planets revolve round the Sun. Mercury, Venus, Mars, Jupiter, and Sahtm are visible by the unaided eye and the Uranus, Neptune and Pluto could be seen after the invention oftelescope.

6.4 Satellites (Moons) :

Moons are those heavenly bodies which revolve around the planets. Now-a-days lot of man-made satellites are revolving around the earth but here only the natural sattelites will be considered.

6.5 Solar system :

As has already been told that the solar system consits of the sun, planets, satellites, comets, minor planets (Asteroids), Meteors, Meteorites, dust, gases etc.

Sun is the only heavenly body in the solar system which is selfilluminated and the rest simply reflect the light of the sun. The orbits of the pl<.:nets are elliptical and the sun is at one of their focus. The other focus is empty.


Nine planets Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto are known till now. Out of these, Mercury, Venus, Mars, Jupiter and Saturn are visible by the eyes but Uranus, Neptune and Pluto could be seen after the invention of telescope. Uranus was discovered in 1781,Neptune in 1846 and Pluto in 1930 with the help of telescope.

Names and symbols of the planets and the sw.:

0 Sun Ravi,Surya

D Moon Chandra

'0 Mercury Budha

Q Venus Sukra

d Mars Mangala, Kuja

¥ Jupiter Brihaspati, Guru

"' Saturn Sani

!;I Uranus or Herschel lndra

~ Neptune Varuna

~ Pluto Yam a

Q Ascending Node

or Dragon's head Rahu

es> Descending Node

or Dragon's tail Ketu

ffi Earth Prithivi

The orbits of the planets are shown accordi,1g to their distance from the sun in figure-10::_·:....-------

Fig.-10

38 · · Elements of Astronomy and Astrological Calculations

The planets (Mercury & Venus) whose orbit is within the orbit of the earth are known as inner planets. The planets whose orbits are greater than the earth's orbit or the earth's orbit is in between their orbits and the sun, are called outer planets or the superior planets.

Extra saturnine planets :

The planets (Uranus, Neptune and Pluto) whose orbits are greater than the orbit of saturn and saturn's orbit lie between their orbits and the sun are the extra-saturnine planets.

6.6 Kepler's laws :

Johannes Kepler (1571-1630) was a German Mathematician and Astronomer.ln 1609 he published commentaries on the motion of Mars, in which two general statements were made which are called the first two Kepler's laws of planetary motion. Nearly a decade after he found third relationship in planetary motion which is now called the Kepler's third law of planetary motion. These laws are :

1. The planets move around the sun in elliptical orbits, with the sun at one of the focus.

2. A straight line between the moving planet and the sun sweeps out equal areas in equal inteiVals of time.

3. The ratio of the squares of the periods of revolution of any tw,o planets is equal to the cubes of their mean distance from the sun. Most of the astrologers are conversant with the first law but only a few know the reason of change in angular velocity which is explained with the help of figure - 11.

Equal time

Fig.-11


S is the centre of the sun and a planet is moving in an elliptical orbit ABCD around the sun. The sun is at one of the focus of the orbit and the other focus is empty. W"len the planet is near the Apehelion (farthest point from the sun) it moves from A toBin time 't'. When it is near the perihelion (nearest point from the sun) it moves from C to Din 't' time. The law states that the areas ASB = CSD = a2. As lines AS and BS are greater than the lines CS and OS, the angle x (angle CSD) will be greater than the angle y (angle ASB), which are covered by the planet in time'!'. Therefore, the angular velocity of the planet will be lesser at A than that at C. It is one of the reasons of difference in change of longitudes of the planets in equal times.

Third Law : According to it the square of the periodic times of the planets are to one another as the cubes of their mean distances from the sun.

Let rand r1 be the semi-major axis of two planetary orbits, and T, T

1 the corresponding orbital periods, then by third law

r3 r3 -=-l-T2 T~

The earth is also a planet and its mean distance from the sun = 1 A.U and time period of one revolution = 1 year. Therefore, for other planets T2 = r'l where T is in earth years and r in Astronomical Units.

6.7 Bode's Law:

J.D. Tityas found out in 1772 some information about the distance of planets from the sun, which were arranged by J.E. Bode and the same is-numbers 0, 3, 6,12;24, 48, 96, 192, 384, 768 which are double of previous ones. Add 4 in them so that the distance of the earth, which is the third planet in order of distance from the sun may become 6 + 4 = 10.lf we continue by dividing each of these numbers by 10, we obtain the series of numbers in the last column of the table given below. These distances become in Astronomical units (A.U.)

Planet Average distance Bode's Law of planet-sun number

Mercury 0.39 0.4

Venus 0.72 0.7

Earth 1.0 1.0

Mars 1.52 1.6

Asteroids 2.2 to 3.1 2.8

·to Elements of Astronomy and Astrological Calculations

Jupiter 5.2 5.2

Saturn 9.54 10.0

Umnus 19.18 19.6

Neptune 30.1 38.8

Pluto 39.4 77.2

Bode's Law gave a reasonable respresentation for the planets upto saturn known upto 1772. Mathematicians noticed that the distance between Mars and Jupiter is much more. According to this law, there should be a planet in between them but actually no planet was there. The Astronomers concentrated their telescops at the place, where they estimated the orbit of a planet. They watched carefully and found lot of small planets nearby that belt. It was thought that there should have been a planet at that place at the time of the formation of solar system but due to unknown reasons it changed into small planets (Asteroids). Uranus could also be discovered after nine years after the publishing of Bode's Law.

6.8 All the planets excluding Pluto are slightly inclined with the ecliptic, which causes wobbling motion of the other planets and their orbits. Their orbits also revolve in their plain. The period of revolution of the orbits is very great. In the case of the earth it is more than one lac years.

6.9Sun:

The sun occupies a unique and vital position in our lives. Without it we cannot think of any life on our mother planet, the e::~rth. The places which do not get the solar light and heat, become very cold and the temperature at those places go below -170°. It is an ordinary star, one of thousands of millions in our milky way galaxy. A thing which sets it apart from the other stars is that it is orbited by a number of planets.

The sun contains about 99.9 per cent of the entire mass of the solar system. All the planets, moons, asteriods etc. have only one-tenth of one per cent mass of the solar system. the sun is almost a perfect sphere of ~.ot gases and its diameter is 13,60,000 kilometers (8,65,000 miles). At its equator it takes approximately 25 earth days for rotating once. The sun probably contains about 92 per cent of hydrogen and 7.8 per cent helium atoms and the rest 0.2 per cent atoms of other elements. It is a big thermonuclear furnace where energy is produced in it by conversion of hydrogen atoms into helium atoms. It loses mass at the rate of four million tons per second. One should not be afraid of it as it will continue to radiate heat and light for billions of years.


Ordinary white light photographs of the sun reveal the dark patches of sun-spots. The sun-spot activity follow a cycle of about 11 years. In five or six years, the number of sun-spots is reached to minimum and begins to build again until maximum sun-spot is reached again. The polarities of its magnetic field reverse every 11 years. The whole cycle is of 11 x 2 = 22 years. In 22 years it is back to the original position.

Solar flares :Sun-spots generate electricity and this force is some time discharged in a huge arc which are known as solar flares. In other words enormous release of magnetic energy that erupt periodically from the sun's chromosphere are solar flares.

The flare emits large quantities of short-wave length X-radiation, which reaches the earth quickly and this produces the sudden ionospheric disturbance which disrupts transmission of short wave radio signals and the earth's magnetic field can also be affected.

Solar storms : Exceptional solar flare activity can have startling effect on the earth. In March 1989 solar flares deluged the earth with charged particles. They caused power surges in electric supply grids in the northern United States and Canada, resulting in burned out transformers and black-out in cities.

6.10 The Earth:

The Earth is the third planet according to distance from the sun. It is spherical but a bit flat on the poles. Its rnean distance from the sun is 1498Iacs kilometers (930 lacs miles). At perihelion its distance from the sun is 914 Lacs miles, while at aphelion it is 946lacs miles. Its orbit is elliptical and the eccentricity of its orbit is 0.0167. Its density is 5.52 times of water. Its equatorial diameter is 7926 miles and the polar diameter is 7900 miles. Its equator is inclined at an angle of 23° 27' with the plane of its orbit. It is revolving around the sun at a mean speed of 29.79 K.M. per second. The sidereal period is 365.256 days. It takes nearly 23 hours 56 minutes 4 seconds to complete one rotation with respect to a fixed star. Its mass is 5.976 x 1()24 K.G. The atmosphere of the earth main_ly contains 77.6% of nitrogen and 20.7% of oxygen ..

If we divide the circumference of the earth 25000 miles by 360° 25000 1

we get 1° = 36()" = 6910 = 69.1 miles. The distance between 1° longitude at equator is 69.1 miles. In case we move 69.1 miles from east to west or vice versa the difference 1n longitudes will be 1 o only. As we move towards the pole this distace of 1° longitude will become shorter and shorter. ·


If we move 68.704 miles from the equator along the meridian, there will be a change of 1° latitude. As we will be moving towards north/south the distance of 1 o latitude will become more and more as the earth is flat on the poles.

Distance of 1 o latitude as different places is as under :

oo latitude 68.704 miles

zoo latitude 68.785 miles

40° latitude

60° latitude

80° latitude

68.993 miles

69.230miles

69.386miles

The seasons: The ancients noticed that the sun was lower in the ·sky during winter than in summer and deduced that the seasons have an astronqmical cause. The seasons arise from the obliquity of the earth's axis to the plane of its orbit (66° 33') or the obliquity of the ecliptic to the plane of equator (23° 27'). The hemisphere which is inclined towards the sun gets more heat and has summer season while the other hemisphere which leans away from th.:! sun gets lesser heat and has winter season. It is explained by the figure - 12.

The earth is revolving around the sun and completing one revolution in a year. There are four positions. N and S are north and south poles. LineNS is the axis of the earth, AB is the equator, CD and EF are tropics of Cancer and Capricorn, LM and PQ are arctic and antarctic circles.

~ ~

Fig.-12


Position (1) winter solstice (Left side of figure 12) :In this position the earth is at winter solstice and the southern hemisphere is inclined towards the sun. It happen on 22nd/23rd December when the sun is vertical to the Tropic of Capricorn EE At this time the days are longer than nights in the southern hemisphere. This period coincides with the middle of 6 months long days· at the South pole.

The reverse is in the case at the northern hemisphere which is leaning away the sun. It will be winter season and nights are longer than the days in this hemisphere. To an observer at N this period coincides with the middle of 6 months long night.

Position - 3 Summer solstice (right side of figure) : Here the conditions are reversed. The sun is vertical at the Tropic of Cancer and the Northern Hemisphere is leaning towards the sun. The days are longer than nights and summer season is there. It is middle of 6 month long days to an observer at N. In southern hemisphere it is winter season and nights are longer than the d3ys. At the south pole it is the middle of 6 months long night.

Positions 2 and 4 : The earth is at Vernal and Autumnal equinoxes respectively and the plane of equator passes through the sun. Therefore, the line of demarcation of light and darkness passes through the north and south poles. The days and nights are equal through out the world.

6.12 Seasons are not formed according to the distance of the sun only but the deciding factors for the earth are the following :

Fig.-13


(a) In summer season the days are longer than the nights i.e. the sun remains above the horizon for more than 12 hours. The earth gets heat from the sun for a longer tirrie and the time for radiating the heat received by earth is short.

(b) In the summer season the sun shines more straight than the winter season.

In figure-13 imagine two cones AB and CD (three dimensions) formed by the sun at the earth. The angle of these cones ASB and CSD are equal. The area covered by the cone SAB at the surface of the earth is shorter than that of cone SCD. The sun is radiating the heat equally in both the cones. But due to shorter area the surface AB will get more heat per unit area than the surface CD. Hence AB will be more hot than CD.

6.13 Observation of the sky:

The earth is like a sphere and one can see only half the sky which is above its horizon. The other half cannot be seen as same is hidden by the earth. Therefore, an observer's view of the sky differs with respect to his position on the earth. If he is on the North pole his horizon coincides with the equator and he will be able to see the sky above the equator and the lower hemisphere of the sky will be invisible. The north (pole star) will be above his head. As he moves towards the equator, the position of horizon goes on changing. When he is at 10° latitude, the polar star will be inclined at 10° from his horizon. At equator his horizon coincides with great circle passing through celestial North and South poles. The polar star will be seen at his horizon. As the observer moves towards south of the equator, the southern polar star becomes visible and the northern polar star disappears. The angle of southern polar star with the horizon will be equal to the southern latitude of the place of observer.

lVIII Solar system - II

7.1 Moon:

Moon is the only satellite of the earth. Its sidereal period is 27.32 earth days and it is also called the Nakshatra month. Its synodic period (from the end of one Amavasya to the next) is 29.53 days which is also known as average lunar month. Moon's mean distance from the earth is 384,402 kilometers or 238,855 miles. The duration of its nodical month (time interval taken by it in moving from one node to the same node next time) is 27.21 days. It mass is 81st part that of the earth.

Since olden times man observed the moon very carefully and the duration of a month was linked from the end of one Amavasya to the end of next one. Tables of its movement were widely used by the sailors. Moon's diameter is 3,476 kilometers or 2160 miles. Apollo mission:>, showed it to be an ellipsoid with three different diameters. The longest diameter is pointed towards the earth, and shortest is along its polar axis. Moon's orbit is an ellipse with the earth at one focus. Its orbit is inclined about 5° 15' to the plane of earth's orbit (ecliptic).

The moon rotates once on its axis in 27.3 days, therefore always keeps the same face towards the earth. Until1959 the other side of the moon could not be seen, after that man-made satellites circling the moon have revealed its entire surface to us. Before 1958 we had seen 59% of the surface of the moon and that too due to inclination of its axis on its orbit.

7.2 Mercury:

Mercury is the closest planet to the sun. Its mean distance from the sun is 580 lacs (58 millions) kilometers or 360 lacs miles. At perihelion its distance from the sun is 45;865,000 km (28,500,000 miles) and at aphelion it is 69,680,000 km (43,300,000 miles). It revolves around the sun with a velocity of 170,000 km per hour (105,600 miles per hour). If this velocity would have been slower, the sun's massive gravitational pull would drag it to blazing extinction.lts nearest distance from the earth is 45,000,000 km (28,000,000 miles). Its diameter is 4,878 km (3,031 miles). At perihelion (nearest to the sun) it receives sun's light and heat ten times more than the moon. The average


temperature on the sunlit side is 350°C (660°F). Average temperature on the dark side (where it is night) is - 170°C (- 275°F). In mid-day when the sun is at the zenith, the temperature reaches up to 430°C. Mercury's one ciay (from one sun rise to next sun rise) is equal to 176 earth days. It causes vast difference between the temperature of the day and night.

Mercury has no moon like Venus. Eccentricity of its orbit is 0.206. Its orbit is elliptical and differs much from a circle. Eccentricity is obtained on dividing the distance between the foci by the length of the major axis of the orbit. In circle both the foci are at the centre and the ecentricity becomes zero. It appears to oscillate from one side of the sun to the other side like a pendulum in every four months. It is never seen at a distance of more than 28° longitude from the sun.

Until1965, astronomers believed that Mercury kept the same face turned permanently towards the sun as the moon keeps the same face towards the earth and the mercury rotates on its axis in 87.97 earth days. In 1965, using the 305 meter disk of the radio telescope, astromoners proved that mercury had a rotation period of 58.65 ± 0.25 earth days. The period of its revolution round the sun is 87.97 days, which is Mercury's year. Its period of rotation is two-thirds of its revolution period. The time interval between successive sun rises is ·called a day, therefore Mercury's one day is equal to its two years. Its orbit is inclined 7o to the ecliptic which is much more than other planets except Pluto. Mercury's shape is nearly spherical.

At perihelion, Mercury travels faster than when it is farther out in its orbit due to sun's increased gravitational force. For a short time the angular velocity of revolution becomes very large and may compensate for, or even exceed its angular velocity of rotation on its axis. For an observer on the surface of Mercury at the equator, there will be a period of about 8 days, which occurs about mid-day with respect to Mercurian day of 176 earth days, the path of the sun is very peculiar. During this period to the observer standing on Mercury, it would seem as if the sun had slowed down, stopped and actually gone backwards for some time. When Mercury's angular velocity of revolution becomes slower sun would slow down once again, stop and resume its usual motion in the sky ..

Mercury displays phases like the moon and it has been dealt in para 15. 7. An Italian astronomer Giovanni Zupus was the first to notice the phases of Mercury in 1939. It is easy to see Mercury when its angle of elongation is maximum, which happens at the time it is becoming retrograde or direct from retrograde motion. About thirteen times every century, Mercury's orbit brings it directly between the Sun and the Earth. Mercury is surrounded by a thin layer of helium gas which is so little


that amount collected from 6.4 km (4 miles) diameter sphere would be just enough to fill a child's balloon. Its surlace is mostly composed of silicate rocks. Its density is 5.44 or say that it is 5.44 times heavier than water.

It is also called the evening star and morning star. Due to its proximity with the sun, it can be seen some time before sun rise or some time after sunset. There had been some astronomers, who could not see it during their whole of life time. Copernicus was one of them because in his country (Poland), the sky was clouded in early morning and early night by the fog formed due to river. As mercury remains within 28° of the sun, so it is not seen more than 28° above the horizon and remains much below the zenith.

7.3 Venus:

Venus i~ the second planet in order of distance from the sun. Its orbit is nearly circular. The eccentricity of its orbit is 0.007 which is very near to zero. Its orbit is inclined to the ecliptic at an angle of 3°.39. It is the nearest planet to the earth. Its radius is 6,050 km while that of the earth is 6,378 km. Its mean distance from the sun is 10,82,00,000 km (1082lacs km). At perihelion its distance from the sun is 1074lacs km and aphelion it is 1094lacs km.lt receives nearly twice as much radiation from the sun as reaches the orbit of the earth. The surlace of venus is completely hidden by clouds, the upper layers of which are made of droplets of sulphuric acid in aqueous solution. The strong reflection of sunlight by its clouds makes it the third brightest object in the sky after the sun and the moon.lt reflects 76 per cent of the light received from the sun. The dense atmosphere of the Venus at the level of 50 to 70 km, rotates 60 times faster than the solid planet. Its equator is inclined to the ecliptic at an angle of 1-78° which leads to nearly undetectable seasonal effects. Its sidereal period is 224.7 days and synodic period is 583.92 days. One day of venus or the time interval between one sunrise to the next sunrise equals to 117 earth days. It takes 243.01 days to rotate once round its axis. The rotation is retrograde. The planet reaches its greatest brilliance in the evening sky every 584 days.

7.4 When observed in visible light by telescope from the earth Venus looks like a verY bright slightly yellow disc. It appears most bright when its angle of elongation is 40° and it is said that in dark nights its light casts shadows. It also oscillates like a pendulum about the sun. It is never more than 48° away from the sun. It can be seen upto 5 hours before the sunrise or 5 hours after the-sunset (when it is 48° away from the sun). As its angle of elongation decreases the time interval before and after the sunrise and sunset also decreases. As it

48 Elements of t'.~tronomy and Astrological Calculations

goes more away from the sun than the Mercury goes away from the sun, it is easy to be seen. When its longitudes are more than the sun, it is seen in the evening in the western sky. it is seen in the eastern sky in the morning, when its longitudes are less than that of the sun. Venus has also phases like Moon and Mercury.

7.5Mars:

It is fourth planet in order of distance from the sun. Its average distance from the sun is 2279 Lacs km. It's distance at perihelion is 2067 lacs km and at aphelion 2491 lacs km. The eccentricity of its orbit is 0.0934. Its path is much more eccentric than that of the earth. Its nearest distance from the earth is 350 Lacs miles and appears most bright planet excepting the Venus. When it is farthest from the earth, it resembles with a star. It has certain phases. When its angle of elongation is 90•, it is most gibbous and appears bright also. At that time the smallest portion of its illuminated surface is towards the earth.

Mars equatorial diameter is 6796 km. Its mass is 6418 x 1()23 kilograms. Its density is 3.94 (earths density is 5.52) which is threefourth that of earth. Its rotation period about its axis is 24.6229 hours, which is slightly longer than that of earth. Its sidereal period is 669 Mar's days or 687 earth days.ln summer reason its temperature remains between- 100• C to o• C. Its magnetic field is very weak which is 2 per cent that of the earth.

The colour of its surface is red. Astronomers have always considered Mars as a second earth. In fact these two planets have many features in common.ln Indian Astrology Mars is called the son of the earth. Mars has volcanoes which are inactive now a days. Large volcanic discharges are found on the Mars.lt has two satellites : Phobos and Deimos. They are very near to the planet, and are difficult to observe from the earth. They revolve around Mars in circular orbits in the equatorial plane of the planet. Their period of rotation is equal to the period of their revolution and as such they present the same face towards Mars.lt appears that formerly these were asteroids, which were captured by the Mars gravitational force of attraction and became Mars satellites.

7.6Phobos:

Among the two moons of the Mars, Phobos orbit is nearer to the planet. It is 5,800 miles away from the Mars. Phobos is ellipsoid 28 x 22 x 18 km. Its albedo is less than 6 per cent. Its revolution period is 0.319 days which is much less than the period of rotation of Mars.


7.7 Deimos:

It is an outer and smaller satellite. Its distance from the planet is 14,600 miles and completes one revolution of the planet in 1.26 days. Its shape is also ellipsoid (16 x 12 x 10 km).

7.8 Asteroids:

Minor planets are called asteroids, whose diameter is very small. These are found in the space in between the orbits of Mars and Jupiter. It was on 1 January, 1801 that the Sicilinn astronomer Guiseppe Piazzi discovered Ceres, a minor planet with a diameter of 1000 kilometers at a distance of about 2.8 astronomical units from the sun.lt is far smaller than the smallest planet Mercury of the solar system. Until that time, the great distance between the Mars and the Jupiter had been embarrassing the Astronomers. As per Bode's Law, there should have been a planet in between them, but there was none. The orbit of Ceres corresponds exatly to that of the missing planet. There are about a hundred very small asteroids (a few kilometers in diameter) whose orbit cut across to that of the earth. The number of asteroids is very large. More than 40,000 asteroids were known upto 1985. Eccentricity of the orbits of many asteroids can reach upto 30°. It appears that due to their light mass and small escape velocity, they have no atmosphere. Rotation period of numerous asteroids have been found out and it is between 2 and 24 hours. Presence of satellites around a few asteroids such as Metis has been felt.

The similarities between the asteroids and meteorites have been noticed. It appears that asteroids are the most likely parent bodies of meteorites.

lVIII! Solar System - Ill

.1 Jupiter:

Jupiter is the fifth planet is order of distance from the sun. Mighty 1piter is the most massive planet in the solar system, containing more Jan 70 per cent of all the mass ouside the sun. It is more than 300 mes massive than the earth. There is not much difference in the :;uatorial and polar diameters of the earth but in the case of jupiter the :;uatorial diameter is more than 88,000 miles (142, 796 krn) and the olar diameter is less than 84,000 miles or 1,34,000 krn. Jupiter is blate because of its very rapid rotation. The planet is rotating about vo and half times faster than the earth. It takes 9.841 hours for Jmpleting one rotation. The other reason for flatness on the poles is 1at it is not a solid and rocky planet but it is composed of hydrogen, elium and other gases. Due to rapid rotation the equatorial part bulges ut and become bigger. Its density is 1.314. Its atmosphere contains 81 ar cent of hydrogen, 17 per cent helium and small amount of ammonia, 1ethane, water vapour etc. Its mean distance from the sun is 7783lacs ilometers, sidereal period is 11.862 years, c:nd eccentricity of the orbit 0.0485.

The great red spot is the most famous single feature of the Jvian atmosphere. Generally orangt; red, it changes hut? and ccasionally disappears, leaving a clearly recognizable oval region called ~d spot hollow. It drifts slowly with respect to the surrounding atmosphere .

.2 Satellites of Jupiter :

Sixteen satellites were known at the end of 1985 but it is likely 1at several satellites have evaded deletion. The four large satellites (lo, uropa, Ganymede and Callisto) were discovered by Galileo in 1610. hey are revolving around the planet at a distance of 4.2lacs kilometers > 19 lacs kilometers, with circular orbits in its equatorial plane. lanymede's diameter is (5,262 kilometers) bigger than that of Mercury ~.878 kilometers). Callisto diameter is 4,800 kilometers which is slightly 1ort of Mercury's diameter. The four small satellites are also revolving 1 circular orbits in the planet's equatorial plane. There are also eight, nail, distant satellites, which move in inclined and eccentric orbits. he eight outer satellites of the planet have many features in common


with the Trojan asteroids. Their surfaces em: very dark, reflecting less than 5 per cent of the light. Their dimensions vary from 10 to 80 kilometers and their orbits are strongly perturbed by the attraction of the sun. There is a possibility that these eight small satellites might have been asteroids and were captured by Jupiter. Last four satellites are revolving with a retrograde motion at a distance between 210 lacs kilometers to 240 lacs kilometers.

8.3 Rings of Jupiter:

The rings of Jupiter were discovered on 4 March, 1979 by Voyager-1 probe. The density of these rings appears to be about a billion times less than that of saturn's rings. These are situated so close to the bright disc of Jupiter, they had never been observed from the earth.

8.4 Radiation of energy:

The best measurements and calculations indicate that Jupiter is radiating over twice as much energy per second than the planet is receiving from the sun. It appears that the energy is generated by the planet and Jupiter is self-luminous and can be considered as a very cool, dim, small star contraction always produces heat. This contraction of Jupiter is nearly 1 kilometer per year. The planet is radiating some of its original heat also.

8.5Satum:

Saturn is the sixth planet in order of its distance from the sun. It was the most distant planet to be recognised by early sky watchers. They saw a dim body, yellow in colour, moving sluggishly. Due to its slow movement its name was kept Shanishchar in Indian astrology. The word shanishchar is the combination of two words Shanah + Char, which means slow moving. It is a huge planet of great beauty. Its flattened, glowing orb is encircled with shining rings and has large family of moons. Its mean distance from the sun is 14,270 Lacs kilometers, velocity in the orbit is 9.64 kilometers per second, sidereal period 29.4577 years, synodic period is 378.09 days, equatorial diameter is 1,20,000 kilometers, eccentricity of its orbit is 0.0556 and inclination to the ecliptic 2°.49; Its mass is 95.147 times that of the earth which is more than other planets except Jupiter. Its density is 0.69 C'S compared to that of water, which is the least leaving Pluto. Saturn is less dense than water. It would .float if it could be dropped in an ocean ofwater.lts volume is second largest in the solar system and is 744 times of that of the earth. Saturn is far away from the earth and is difficult to be recognised. Many times it appears like. a star but on seeing it with the help of a powerful telescope or a binocular, it is


recognized easily due to.its rings. When its rings are slanting, they can be seen easily. It so happens every 15 years or twice in its revolution period.

The planet is most luminous while at opposition. It is composed of hydrogen and helium like Jupiter. It is surrounded by the bright rings. There are 21 moons revolving the planet. The planet turns on its axis very rapidly and its rotational period is 10 hours 39 minutes. Due to rapid rotation it becomes flat (more flat than Jupiter) on the poles. Its flatness is 30 times more than the earth. It rotates on the poles once in 10 hours 14 minutes and on equator in 10 hours 39 minutes. The reason for this difference is that it is mainly composed of gases and not rocks.

8.6 Rings within rings:

Modem images show that saturn's ring is made up of a large number of individual concentric rings. They appear like a playing record or a compact disc. These rings are made up of millions of fragments of ice etc. The rings which are nearer to the planet, they revolve more rapidly round the planet. These rings are so thin and transparent that the stars could be seen scmetimes through these rings. Formerly it was thought that the saturn is the only planet having rings but now it has been revealed that the Jupite; ;;_nd Uranus are also having rings. The particles of these rings are revolving in elliptical orbits round the planet following the Kepler's laws. Their time period of revolution varies from 7 hours 46 minutes to 14 hours 27 minutes.

8.7 Magnetic field, atmosphere and energy:

The earth's magnetic field is created by currents in the outer core of liquid nickel-iron. Saturn's powerful magnetic field is believed to be due to movements in its metallic liquid hydrogen layer.

Its abnosphere contains 92.4 per cent of hydrogen and helium 7.4 per cent. Methane and ammonia have been detected and there are minute traces of acetylene and hydrogen cyanide. Planets abnosphere extends over 1,000,000 kilometers (625,000 miles). The winds that blow round saturn's equator are ten times stronger than the average hurricane on earth, travelling 1600 kilometers per hou.r (1000 miles per hour). Both Jupiter and saturn radiate more heat energy than they receive from the sun. Saturn radiates three times as much heat energy as it receives, so it must have an internal source of energy. ·

8.8 Moons of satum:

Saturn's 21 moons (satellites) have been discovered so far. The first moon Titan was discovered by Christiaan Huygens on 25 March,


1655. It is second moon in size after Jupiter's moon Ganymede in the solar system. Its diameter is more than 5000 kilometers (3000 miles) which is bigger than the Mercury. Titan has nitrogen rich atmosphere. Titan has no magnetic field. Its surface temperature is -180°C. Phoebe is the most distant of the planet's moons, orbiting 1,29,50,000 kilometers (80,47,000 miles) from the planet once evezy 550 days. It is spherical and its diameter is 220 kilometers. Its direction is retrograde, the opposite of all the other satellites. Due to this reason, it is thought that it might have been an asteroid and the direction of its revolution was retrograde. Most of the new satellites of saturn have been added to the list by the Pioneer and Voyager sightings.

8.9 Uranus:

Uranus is the seventh planet in order of distance from the sun. It is almost two and a half times smaller than saturn, the planet is just visible to the naked eye. Unknown to the ancients, for whom saturn marked the edge of solar system. Uranus was not discovered until 13 March, 1781. Its average distance from the sun is 28,696 lacs kilometers (17 ,830 lacs miles).lts equatorial diameter is 52,290 kilometers (32,000 miles) and average temperature (cloud:;) is- 140°C. Though the Uranus, Neptune and Pluto are far away from the sun, yet they are locked into the gravitation pull of the sun. They are vezy far from the warmth and light of the sun.

8.10 No planet could be discovered evenafter the two centuries of the invention of the telescope. Willian Herschel was a professional musician and an enthusiastic amateur astronomer. He obsetved (with a telescope of 16 centimeters diameter) an object which was not like a star and moved slightly in six months. No planet was added to the ancient list until then. Some astronomers used to call it by the name of Herschel but Johann Bode, suggested that is was more ·fitting to carzy on the tradition of naming planets after characters from Graeco-Roman mythology. He proposed to call the planet 'Uranus' the father of Saturn, just as Saturn had been father of Jupiter and Jupiter had been father of Mars. After that Herschel became full time astronomer and telescope maker. He discovered two satellites Titania and Oberon in 1787. The infolJTiation collected from the earlier sightings showed i~larities in Uranus's orbits. This led to the discovezy of Neptune.

8.11 Its nearest distance from the earth is 27,200 lacs kilometers (1,690,000,000 miles) or the distance traversed by the light in 2 hours 45 minutes.lts sidereal period is 84.0139. years, synodic period is 369.66 days. Its one day is of 17 hours 12 minutes in earth hours and density is 1.19 with that of water. Its equator is inclined at an angle of98° to its axis. This means that, instead of spinning in a relatively upright position


it rolls round the sun. All the other planets revolve round the sun while they are spinning on their axis.

It takes 84 years to complete one revolution of the sun. For 42 years one pole of Uranus receives some degree of sunlight, while the other pole is in darkness. For the next 42 years their positions are reversed. The equatorial regions experience two winters and two summers in each Uranian year.

8.12 Earth's magnetic axis is inclined to the spin axis by 11 ".6 but the magnetic axis of Uranus is inclined at 60" to the spin axis. It misses the centre of the planet by more than 8000 kilometers. The planet's strong magnetic field is somehow generated within the liquid mantle, perhaps by th-:J movement of solid elements in it. Uranus appears as a blue !l'·een disc because the methane in the atmosphere absorbs the red component of sunlight. The planet contains 99 per cent of hydrogen and helium. Before the voyager encounter, there were five known moons of Uranus. Ten small and black moons could be discoverod with the help of cameras of the Voyager. Uranus has also rings like Saturn. The Uranian rings are dark, very thin, with a thickness of no more than a few meters.

8.13 Neptune:

Neptune is the eighth planet in order of its distance from the sun. Its average distance from the sun is 4,500,000,000 kilometers (45,000 lacs km) or 2,800,000,000 miles (28,000 lacs miles).lts nearest distance from the earth is 43,500 lacs kilometers (27,000 lacs miles). Average temperature of its cloud is- 210"C. Its diameter across equator is 48,600 kilometers (30,200 miles) which is slightly less than that of Uranus but its density is more.lts mass is 17.23 times that of the earth.lts density is 1.69. It has P-ight moons. The length of its day is 16 hours 3 minutes. The length of its year (5idereal period) is 165 earth years. it has not completed one revolution of sun since it was discovered (1846 AD) and will complete one revolution in 2011. Neptune was the first planet to be discovered by mathematical calculations instead of by eye. It was registered as a star in 1795 by a French astronomer named Lalande. On 23 September, 1846 Johann Galle and Heinrich d'Arrest using Levenier's calculations; searched the relevant area of the sky and found the new planet. The Berlin astronomers called the new planet 'Neptune' after the god of the sea in classical mythology.

8.14 Satellites of Neptune:

Willian Lassell discovered its moon (Triton)within a month of the discovery of the planet. In May 1949, Gerard Kuiper discovered its another moon called Nereid. Triton is intensely cold at- 236°C.


It is one of the three moons in the solar system which hav~ an atmosphere. The other two are Jupiter's moon 'lo' and saturn's moon Titan.

When Voyager-2 reached near Neptune in August 1989, discovered six small unknown satellites, ranging from 30 to 300 ltilometers (20 to 200 miles) in diameter. All of them revolve in the equatorial plane of the planet. They are dark and irregular, because they are too small to have enough gravity to pull them into spherical shape.

The images sent by Voyager-2 revealed that the planet was brilliant blue globe marked wlth deeper blue features and streaks of white clouds. Neptune has internal heat source. It is at huge distance from the sun and receives only a thousandth of solar energy of that received on the earth. Neptune is a dark and cold planet and appears greenish disc from the earth. Its magnetic axis is at an angle of 60° to the spin axis. Three of its rings· are in its equatorial plane.

8.15 Pluto:

Tiny pluto is the ninth planet in order of its distance from the sun. The diameter of this small planet is 2,300 kilometers (1,430 miles) which is smaller than our moon. It is the smallest and lightest planet in the solar system. lt follows an extremely eccentric orbit and takes 248 years to complete one revolution. Eccentricity of its orbit is 0.250. Its average distance from the sun is 5,900,000,000 kilometers (37,000 lacs miles).lts nearest distance from the earth is 5,800 million kilometers (36,000 lacs miles). Average temperature of clouds is - l50°C. The temprature on its surface is- 2l6°C and it has no atmosphere.

Pluto was discovered on 18 February, 1930 as a dot on a photographic plate while a search was going on since the discovery of Neptune in 1846. There had been a considerable element of luck in discovering it.

Pluto has one moon, known as Charon.lt is the largest satellite in the solar system judged in proportiop to its planet, its diameter is 1,200 kilometers (750 miles) which is 40 per cent that of Pluto. Charon orbites Pluto at a distance of20,000 kilometers (12,500 miles) in the equatorial plane of the planet. Its orbital period is 6.4 days exactly equals the axial rotation period of Pluto.

Combined mass of Pluto and Charon is about one five hundredth of the mass of the earth.

8.16Comet:

Until 18th century changing appearance of comets was quite


unpredictable. Their appearance had been regarded with fear and superstition as fearful comets heralding great catastrophes. But mainly by the work of Johannes Kepler, Isaac Newton and Edmund Hallery, it was realised that the apparently strange motions of comets obey the same laws of motion as do the planets. They travel in elliptical orbits and the sun is at one focus. The orbits of comets are more elongated and more eccentric than those of the planets. Comets, generally appear suddenly in the sky, remaining visible for some weeks, or months, during which time they approach the sun with great velocity: they then recede from it, and finally disappear from sight. Orbits of some comets are shown in figure 14 ..

Fig.l4. The central nucleus is believed to be solid and composed of "ices"

(frozen metl.ane, ammonia, water, carbon dioxide etc.). The coma is a spherical cloud of gas and dust centred on the nucleus. The tail of a comet is created by solar photons and the solar wind, which blow material out of the coma. Coma and tail me between 1 and 10 million times larger than the nucleus. It is the motion of solid nucleus that defines its orbit. This nucleus is cold and naked at aphelion but as it reaches near the sun, the temprature of the surface rises, the ice evaporates and the resulting gas escapes into the surrounding space trailing all the dust particles in a gigantic tail many tens of millions kilometers long. This dust cloud is the luminous phenomenon.


When they reach perihelion, each time they lose a substantial part of their mass. They are consumed between a hundred/a thousand passages of the perihelion. The comets whose orbital period is short, do not last long. According to experts most of the comets do not last for more than 100 approaches to the sun. The periodical time of Encke's comet is 3.3 years and is losing brightness slowly. There exist comets whose orbital period is very great, and their life is not more than 10 million years which is very much short of the age of solar system (4.6 X 109 years). The motion of some comets is direct and of others retrograde while all the planets are orbiting in the same direction.

A comet is usually named after its discoverer. There are two types of comets (i) Periodic (ii) Non-periodic.

8.17 Periodic Comets;

The motion of periodic comets can be calculated and the dates of their return predicted.

Halley's Comet : The most famous comet is undoubtedly Halley's comet. Its mean orbiting period is 76 years which can be more or less by 2.5 years due to attractions of the planets. Its present period is 76.09 years. Its orbit has a perihelion of 0.5872 astronomical units and an aphelion of 35.33 astronomical units. It is moving in retrograde direction. When the english astronomer was of 26 years only, he was puzzled to see it in 1682. He requested Issac Newton, who was working on the force of attraction of the planets and their orbits, to get his discovery published. Halley adopted Newton's laws for the calculation of 24 comets. He found that such a comet was seen in 1531 and 1607 and those were the same comet. He made a forecast that it will reappear in 1759. This comet was visible on 25 December 1758 and his forecast proved correct. It was last seen in 1986 and will return in 2061.

Encke's Comet : It is the known comet whose period is least. Its periodic time is 3.3 years. At perihelion it is closer to the sun than Mercury. Its motion is direct and losing brightness slowly.

8.18 Non-Periodic Comets:

The orbit cf non-periodic comets are very big ellipses and they go much away from the sun and escape from solar system. Their orbit takes the shape of parabolas and they are not visible in the solar system. Some of these are captured by the attraction of the planets and revolve around them. Number of non-periodic comets is much more than the periodic comets.


8.19 Meteors:

The space between the sun, planets, satellites, COJllets etc. in the solar system is not empty but there are dust particles,,big rocks, gases etc. The minute bodies such as dust particles etc. moving-with great velocity upto 45 kilometer per second, when they enter the earth's atmosphere, the heat developed by the resistance of the air is sufficient to consume them and they appear a streak of light in the sky. they are also called shooting stars.

8.20 Meteorites:

These are relatively larger bodies, big rocks _etc. which are not completely consumed by the resistance of the air of the atmosphere of the earth. On reaching the earth's surface, they produce craters and go deep into the earth. It is estimated that meteorites of mass more than one kilogram were part of asteroids. No forecast of their entry into the atmosphere of the earth can be made.

[!R] Standard time and

Sidereal time

9.1 Standard time:

Local mean time of two places having different longitudes will not be the same. In case latitude of two places is the same, the sun will rise earlier at the place which is in~e east due to diurnal motion of the earth from west to east. Sunrise does not depend on the longitudes only but also on the latitude of a place dcte to obliquity of the ecliptic. If a place is in the north and the sun's declination is also north, the sun will rise earlier than the places in the south, inspite of the longitude being the same. But the time of mid-noon or midnight will be the same for all places having the same longitude.

The earth completes one rotation in one day = 24 hours = 1440 minutes

360° moves in 1440 minutes 1° moves in 1440 + 360 = 4 minutes

' If all the cities in a country follow their local mean time, there will

be difficulty in the day to day work of the country. To overcome such difficulti~1 a meridian is chosen in a country/zone, which is called centraV standard meridian. Big countries like U.S.A., Canada, Australia etc. are divided into several time zones. The local mean time of the central/ standard meridian of the zone/country is followed throughout the respective zone/country and such a time is called the standard time of that zone/country.

The central meridian of a zone/country is normally chosen in a multiple of 7o 30' longitudes so that time difference from that of U.T. (G.M.T.} is multiple of 7o 30' X 4m = 30 minutes.

The centraVstandard meridian of India is 82° 30' (E) longitude. It passes through a place near Varanasi. The L.M.T. of this meridian i!. the Indian standard time (l.S.T.) which is followed throughout India.

9.2 L.M.Tfrom Z.S.T.:

The following details are required for .finding out the L.M.T. of a place from zonal standard time (Z.S.T.)/standard time of a

60 · Elements of Astronomy and Astrological Calculations

country.

(a) Terrestriallongitt¥J.e of the place.

(b) Z.S.T of the zone/country in which the place is situated

(c) Longitude of Central Meridian.

L.M.T. from Z.S.T. is found out as under :

Step - I Find the difference between the longitudes of the place and that of central meridian.

Step - 11 Multiply this difference by 4 minutes per degree. The product of degrees by 4 represents minutes and minutes by 4 give seconds.

Step -11/lf the place is in the east of the central meridian, time calculated in Step - II is to be added to the standard time. In case it is in the west of the central meridian, the time of step - ll is to be subtracted. The net result will be the local time.

9.3 Example -1:

India's central meridian is 82° 30' (E). Find out the L.M.T. of Chennai at 9:35AM l.S.T. Chennai's longitude is 80° 15'.

Solution:

Step -I Difference between the central meridian and local meridian = 82° 30'- 80° 15' = 2° 15'

Step- 112° 15' X 4 = 8"'60' = gm o· Step -III As Chennai is in the west of the central place. Required

L.M.T. = 9h: 35"' - Qh: 9"' = 9h : 26"'

Example-2:

Find out the L.M.T. of Bhubneshwar at 6:25PM (l.S.T.). Using Lahiri's table of Ascendants (page - 101). L.M.T. correction for Bhubneshwar has been given + 13"' 20' and longitude is 85° 50' (E).

Solution: "' (a) L.M.T. = l.S.T + correction

= 6h : 25"' + 13"' : 20' = 6h : 38"' : 20' PM.

(b) Step -1 Difference in longitudes = 85° 50'- 82° 30' = 3° 20'

Step - 11 3o 20' x 4 = 12"' 80' = 13'" 20'

Step- lli As Bhubneshwar is in the east of central place the step II time will be added.

L.M.T. = 6h : 25"' + Qh: 13"' : 20' = 6 : 38 : 20 PM

which agrees with (a).


Example-3:

Find out the L.M.T and I.S.T. of Washington D.C. (U.S.A.) at 9:35PM (Z.S.T.). Longitude of Washington is 77° 4' (W) and time zone is- 5h.

(a) The longitude of Central Meridian = 5 x 15 = 75° (W)

As the time zone is minus, the place is west of Greenwich. So the longitude has been suffixed with 'W'.

Ste~?J~.I Difference in longitudes = 77° 4'- 75° = 2° 4'

Step -112°4' x 4 = 8"': 16'

Step -Ill L.M.T = 9" 35m O•- Qh 8'" 16'

= 9h 26m 44' PM

As Washington is in the west of central Meridian the correction of step II has been deducted.

(b) At page 111 the L.M.T. correction from Z.S.T. has been given as - sm 16'.

L.M.T. = 9h 35m- Qh Sm 16' = 9h 26m 44'. P.M.

It is the same as in (a).

(c) To find .out I.S.T. :

Time zone of I.S.T. is + 5h : 30m

Time zone of Washington is - 5 hours.

Difference in time = 5h: 30m--{- 5h) = 5h: 30'" + 5"

= 1Qh: 3Qm

As India is in East of Washington the difference will be added to Z.S.T.

I.S.T. at that time = 9h 35m + lQh 30'"

= 19" 65m = 20h 5m PM

= Sh Sm AM of next day.

(d) Washington's L.M.T. is 21" 26m 44'

Step -I Difference in longitudes = 82° 30'- {- 77o 4')

= 82° 30' + 77° 4• == 159° 34'

Step - II Time difference = 159° 34' X 4 = 636m 136'

= 10" 38'" 16'

Step · Ill J.S.T. = 21 h 26m 44' + 1Qh 38m 16'

= 32h 5m

= Sh Sm AM of next day {as at c)

6Z Elements of Astronomy and Astrological Calculations

Example-4:

Find out the L.M.T of Melbourne (Australia) of 4 AM Z.S.T. The longitude of Melbourne is 144° 59' (E) and time zone is + 10 hours (Page 111 ofTable of Ascendants) and L.M.T. correction from Z.S.T. is -20m 04', also find I.S.T. at this time.

Solution:

(a) L.M.T. of Melbourne = 4h: om: 0'- 0h :zorn: 4' = 3h : 39m : 56' AM

It is the directed method when we know the L.M.T. correction from Z.S.T.

(b) The time zone is+ 10 hours

:. longitude of central meridian = 10 x 15 = 150° (E)

which is in the east of Melbourne

Step -1 Difference in longitudes = 150°-144° 59' =so 1'

Step - II Time difference = 5o 1' x 4 = zorn 4' As the place is in the west of central meridian, it is negative

=- zom 4' Step - Ill LMT = 4h : om : O• - 0h zorn 4'

= 3h : 39m : 56' (as at a))

(c) For finding I.S.T.

Time zone of India = + Sh: 30m

TimezoneofMelboume = + 10h: om Difference in time zones = 10h : Om- Sh : 30m

= 4h: 30m

I.S.T. is lesser than Z.S.T. of Melbourne as Indian central meridian is in the west.

:. l.S.T. = 4h: om- 4h: 30m= 1Jh: 30m PM is 11:30 PM of previous night.

(d) Difference between Melborne's L.M.T. and l.S.T.

= 3h : 39m : 56' AM - 11 h : 30m PM

= 4h: 9m: 6'

This difference is used for finding out the city correction for sidereal time.

9.4 Sidereal day:

The earth rotates on its axis from west to east and completes one rotation in a day. Due to this diurnal motion of the earth, the sun and

~


other planets appear to rotate from east to west daily.

Sidereal day is defined as the time interval required by the earth to complete one rotation about its axis with respect to a fixed star. It is of constant length as the rotation of earth on its axis is uniform. It is of about 23 hours 56 minutes and 4 seconds in solar hours.

or

The time interval taken by the movable first point of Aries (Vernal squinox) from the time of its first transit of the meridian to the next transit.

;J/.5 The earth completes one revolution of the sun in one year. The earth rotates around its axis once in a day. The same part of the earth appears approximately 365 + 1 = 366 times in front of a fixed

365x24 star. The length of a sidereal day =

366 hours approximately.

The length of a sidereal day is approximately 23 hours 56 minutes and 4.09 seconds approximately. This concept is explained below with the help of figure - 15. ·

X

Fig.-15 Earth is in the centre and sun appears revolving around the earth

and completing one revolution in one year. S1 .and S2 are the positions of the sun at noon on Day 1 and Day 2. X is a fixed star. 0 is the observer on the earth and C is the centre of the earth.

OS1 and X are in a straight line at noon on day 1. The earth is rotating and when it comes again at 0 the star and the sun are not in a straight line but the sun has moved to S

2 (approximately 1 o ahead). The


sidereal day is the time taken by the earth in completing one rotation and coming again in front of the fixed star while for the completion of a solar day it will have to rotate 1 o (approximately) more and the same part of the earth will then be in front of the sun.

Therefore a solar day is longer than a sidereal day. One sidereal day is divided into 24 sidereill hours, one sidereal hour into 60 sidereal minutes and one sidereal minute into 60 sidereal seconds.

24 solar hours = 24 sidereal hours + 3 sid. minutes + 56 sid. sec. (approx.)

6 solar hours = 6 sid. hours + 59 sid. sec.

1 solar hour = 1 sid. hour + 10 sid. sec.

6 solar minutes = 6 sid. minutes + 1 sid. sec.

(a) Amount by which the sidereal time is more than solar mean time is the table IV correction in the Table of Ascendants.

· (b) On about 22nd/23rd March nearly at local noon the vernat equinox is at the celestial meridian of all the places. After that its transit time goes on increasing by 3m 56•/57• ~very day, which accumulates to 24 hours in year. If the sidereal time is zero at noon on 22nd March, it will become Oh 3m 56•/57• on 23rd March and will go on increasing every day. This has been tabulated and given at pages 2 and 3 in table 1 of the table of Ascendants. This table shows the sidereal time of the central meridian of India (82°30' E) at noon in the year 1900 A.D.

(c) While reviewing the table II at pages 3 and 4 of the table of Ascendants, it reveals that the sidereal time is decreasing by 56 or 57 seconds every year. The reasons is that a year is taken of 365 years in place of 365.2422 days. In the leap year the month of February becomes of 29 days instead of 28 days. Therefore, one day's sidereal time difference with the solar time i.e. 3m 56'/57' are added to the last figure and the same is applicable for the 1st March of that leap year.

(d) Table lil of the table of Ascendants deals with the city correction. The reason is explained below :

Table I gives the sidereal time of the central meridian at noon. The timing of the noon at different places will differ. If a city 'A' whose time difference from I.S.T. is + 4 hours. Its noon will be 4 hours early than central meridian of India. For 4 hours the table IV correction is 39'. So- 39' will become the table Ill correction of 'A' (city correction). In 24 hours the sidereal time increases/decreases by 3m 56'. As the noon at 'A' is early, the sidereal time will decrease. If the noon is later than the central meridian of India, the sidereal time will increase.

(e) Aynamsa correction : Table of Aynamsa correction is at page 6 in the Table of Ascendants. The Ascendants for different northen latitudes were tabulated by taking 1938 as the base year, at that time


the Aynamsa was 23° (Difference between sayana Aries and Nirayana Aries). As will be explained later the sayana Aries preceeds by 50" (approximately) every year. The Aynamya increases by 50" every year. Due to this the Aynamsa· correction is 1' every year for five years and Nil in the sixth year.

9.6 Sidereal time is the hour angle of the vernal equinox. When the vernal equinox is at the meridian of a place, the sidereal time is zero at that place. It is expressed in 0 to 24 hours and no AM or PM is suffixed.

Calculation of sidereal time for epoch :

Step- I Convert the Z.S.T./S.T. to L.M.T. of the place.

Step - II Find out the difference of the L.M.T: from the local noon (12 noon). It is known as time interval (T.I.). Convert the solar time to sidereal time by adding the table IV correction, which will be the increased T.l. (Time Interval).

Step - Ill Note down the sidereal time at 12 noon of the date of epoch at 82° 30' longitude from table I. It is the Indian sidereal time.

Step - IV Apply the correction for place or city correction to the step Ill figures. For important cities it has been given in table of Ascendants at pages 100 to 111. This can also be found out by the method explained in9.5d.

Step- VApplythe year correction (Table II page 4) to the sidereal time arrived at in step IV.

Step Vlln the sidereal time found out in step V add the increased T.l. of step II if the time is of afternoon, if it is for forenoon deduct the increased T.l.

9.7 Examples of Sidereal Time Calculation:

What is the sidereal time at Delhi at 8h 30' PM I.S.T. on 6th Februray, 1978?

Solution:

Delhi's latitude is 28° 39' (N) and longitude 77° 13' (E), L.M.T. correction (-) 21m 8' and sidereal time correction +3" (page 102 of table of ascendants).

I.S. T. at the epoch

L.M.T. correction

Delhi's L.M.T.

= = -

=

8h

0 21 8

8 8 .52


It is of afternoon,so it the difference in time from noon called T.l.

Table IV correction = +0 1 20

Increased T.l. = 8 10 12 (A)

Indian Sid. Time (Table I of table of Ascendants) at noon on 6th February = 21h 3m 45'

Delhi's city correction (p-102) = + 0 0 3

Year's correction for 1978 (p-4) = +0 0 25

Delhi's sid. time on 6/2/78 at noon = 21 4 13

As the increased T.l is of afternoon it is to be added (A) = + 8 10 12

Sidereal time at epoch = 29 14 25

subtracting 24 from it or 5 14 25

Example-2:

What is the sidereal time at 6h 40m AM on 5th September 1985 at Kolkata.

Answer:

I.S.T. at the epoch = 6h 4Qm 0'

L.M.T. correction (p-111) = +0 23 30

L.M.T. = 7 3 30

- - 12 0 0

T.l. = difference from 12 noon = 4 56 30

Add table IV correction = + 0 0 48

Increased T.l. = 4 57 18 (A)

Note :It is negative as the T.l. is of before noon

Indian sidereal time at noon 5th Sept. (p-3) = 10 55 38 City (place) correction (p-10 1) - - 0 0 4

Year's correction for 1985 (p-4) = + 0 1 37

Sid. time at noon at Calcutta on 5th Sept. 1985 = 10 57 11

Increased T.l. negative as the time of epoch is before noon (A) = 4 57 18



Example-3:

Find the sidereal time of Tokyo on 8th October, 1981 at 11:28 AM (Z.S.T.)

Answer:

Tokyo's longitude is 139° 33' (E), time zone = + 9 hr.

Local time correction + 18' 12" from Z.S.T.

Sidereal time (City) correction from that ofi.S.T.=- 37" (p-111)

Zonal time at epoch

L.M.T. correction

L.M.T. at epoch

Difference of time from noon (T.I.)

Table IV correction

Revised T.I.

Indian sid. time on 8th Oct. at noon

City's correction

Year's correction for 1981 (p-4)

Sid. time of Tokyo at noon on 8th Oct. 1981

Revised T.I. is to be substracted (A)

== lP 28m 0' AM

== + 0 18 12

= 11 46 12

- 12

== 0 13 48

= + 0 0 2

= 0 13 50 (A)

== 13 5 44

= -0 0 37

= + 0 1 30

== 13 6 37

as the time of epoch is before noon== - 0 13 50

Sidereal time at epoch == 12 52 47 If the city's (place) correction of Tokyo is not given can be cal~ulated

as under: We have to find the difference in time of I.S.T. and that of Tokyo

and that = (139° 33'- 82° 30') x 4 == 57° 3' X 4 = 228m 12' == 3h 48m 12'

Table IV correction for this time is - 38 sec. The difference of 1 second is due to rounding of figures and- 'J7 sec is nearest.

Exampl~-4:

Find the sidereal time of Munich (Gerrnany) at 12h 10m noon on 3rd February, 1988.

Answer:

Longitude of Munich is 11 o 35' (E), time zone = + 1 hr.


Local time correction from Z.S.T. = - 13'" 40'

City's sid. time correction = + 0 46'

(p-149 of Lahiri's ephemeries 2001)

Z.S.T. at epoch = 12" 10"' ()<

L.M.T. correction -0 13 40

L.M.T. at epoch is before noon - 11 56 20

- 12

Difference from noon (T.I.) = 0 3 40

Table IV correction = 0 0 0

Increased T.J. = 0 3 40 (A)

Indian sid. time at noon on3rdFeb. = 20 51 55

City's correction = + 0 0 46

Year's correction for 1988 (p-4) = -0 1 14

Sid. time of Munich at noon on3rdFeb, 1988 20 51 27

Increased T.I. is to be sub. as of (A) = -0 3 40

As L.M.T. is before noon sidereal time at epoch = 20 47 47

City's correction can also be found out as under :

Difference in I.S.T. and Munich L.M.T.

= (82° 30'- 11° 35') X 4 = 70° 55' X 4 = 280m 220'

= 283m 40' = 4h 43m 40'

Table IV correction of this time difference = + 46 sec.

Munich is in the west of Central Meridian of India. So it is positive.

Sidereal and synodic periods

10.1 Sidereal period (Nakshatra Kala)

Sidereal period of planets is the time taken by them in completing one revolution of the sun with respect to a fixed star. In respect of moons, it is the time interval taken by them to make one complete revolution of the planet (of which they are moons) with respect to a fixed star. Similarly the time period taken by the Asteriods to make one complete revolution of the sun with respect to a fixed star, is their sidereal period.

10.2 Synodic period of inner planets (Mercury and Venus) is the interval of time that elapses between two conjunctions of the same kind, whether it may be inferior conjunction or superior conjunction.

In the case of superior planets (Mars. Jupiter, Saturn, Uranus, Neptune, Pluto). Synodic period is the time interval between two conjunctions or oppositions.

Though the definitions of inferior conjunction, superior conjunction, conjunction and opposition have been given in Paras 3.22 to 3.25. yet the same are explained with the help. of digrams.

10.3 Inferior conjunction

When an inner planet (Mercury or Venus) is in between the sun and the earth and the longitudes of the Sun and the planet are the same, the planet is called at inferior conjuction. Mercury's case is taken for example.

Zodiac

Fig.-16


In figure 16 sun is in the centre, the inner circle is the path of Mercury and the outer circle is orbit of the earth. At a time when the earth is at E, the Mercury is at M1 and S the centre of the sun. The observer is at E. E M

1 S is a straight line The longitudes of the sun and

the mercury are same as that of A. At this time the mercury is at inferior conjucti9n.

10.4 Superiorconjunction

When the sun is in between the inner planet and the earth. The longitudes of the inner planets and the sun are equal, at that time the planet is at superior conjunction. Let the case of Mercury be· considered.

In figure 16 when the observer is atE (on the earth), Mercury and the centre of the sun are at M2 and S respectively. ESM2 is a straight line so that the longitudes of the sun and the Mercury are equal as they both appear at A in the Zodiac.

Now the Mercury is at superior conjunction with the sun.

10.5 Conjunction

Conjunction and opposition are related to the outer planets. Let us select an outer planet for exhibiting it with the help of a diagram and it may be Jupiter. In figure 17, E is the observer at the earth, Sis the centre of the sun and J

1 is the position Jupiter at any tim<;!. ESJ

1 is

zl

Zz Fig.-17

a straight line. The longitudes of Jupiter and the Sun are the same as that of Z

1 at Zodiac. The sun is in between the Jupiter and the earth

and the planet is at conjuction with the sun or say simply conjuction.


10.6 Opposition

As earlier stated the opposition is for the outer (superior) planets. At the time of opposition the difference in the longitudes of the planets and the sun becomes 180° and the earth comes in between them. So that the sun, the earth and the planet reach in a straight line.

In figure17 at any moment letS be the centre of the sun, J 2 the position of Jupiter and E the observer at the earth and the straight line meets the Zodiac at Z

1 and Z

2• The longitude of the sun is equal to

longitude of Z1 and and the longitude of Jupiter at J2 are that of;. The

difference in longitudes of Z1

and Z2 is 180°. Now the planet is at opposition (with the sun). It is called opposition as the sun and planet are on the opposite sides of the earth.

10.7 Synodic period:

The definition of the svnodic period has already been given in pa.: 10.2 and now it is explained with the help of figures.

Synodic period of inner planets :The Mercury and Venus are the inner planets and let the Mercury be selected for the example. Mercury completes one revolution of the sun in 88 days and the earth in 365.25 days which are their sidereal periods also. The angular velocity of the Mercury is more than that of the earth.

Fig.-18

N

8.. ~-

In figure 18, Sis the centre of the sun, inner most circle is orbit of Mercury, the middle one of the earth and the outer is the Zodiac. The Mercury and the Earth are revolving around the sun in the direction of


arrow and the longitudes of the Zodiac are increasing in the same direction.

At any moment let the earth be at E1 the Mercury is at M1 such that E1 M1

Sis a straight line or say the mercury is at inferior conjuction. The Mercury and the earth are moving. When the Mercury comes again at M

1 after completing one revolution, the earth is not at E

1 but has

moved ahead. The Mercury, the earth and the sun are again in a straight line when the earth reaches at~ and Mercury at M2 after completion of one revolution the planet is again at inferior conjunction. The time period taken by the Mercury in completing one revolution and moving from M

1 to M2 or the interval of time taken by the earth in moving from

E1

tc ~ is the synodic period of Mercury. Now we consider it with respect to the superior conjunction.The Earth is at E

3 Mercury is at M

1 such that E

3SM

1 is a straight line. The sun is in between the Mercury

and the Earth and the longitudes of the Sun and the Mercury are equal. It is the time of Mercury's superior conjunction. The earth and the Mercury start moving. When Mercury reaches at M2 after completing one revolution the earth reaches at E

4 at that time the earth the sun and

the Mercury are again in a straight line or say the Mercury is again at superior conjunction. The time interval taken by the Mercury during those two superior conjunctions or by the earth in moving from ~to E4 is the synodic period of the Mercury.

10.8 Synodic period of outer planets :

Outer planets are Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Any planet can be selected for example and let us take Jupiter. Jupiter's sidereal period (time period of one revolution of the sun) is 12 years and that of earth is one year. Hence the earth's angular velocity is 12 times faster than that of jupiter's.

Example:

In figure 19 the sun is in the centre. The small circle is the orbit of the earth and middle circle is the orbit of the Jupiter. The outer circle is the Zodiac. The planets are moving in the direction of arrow and the longitudes are also increasing in the same direction indicated by the arrow on the outer circle.

First of all we consider through opposition. At a time when the earth is at the E

1 and Jupiter is at J

1 such that the J

1 E

1 S is a straight .

line. At this moment the earth is in between the sun and the .Jupiter. Jupiter's longitude is that of point L

1 at the Zodiac and the sun's longi

tude is equal to that of L3. L1 L, is a straight line and difference in their longitudes is 180°. Hence they are in opposition. Now the earth and the Jupiter start st0r: movinf! further. S E: J .. becomes a straight line when


Fig.l9

N 8.. o;· n

the earth reaches at E2 (after completion of one revolution) at"' the Jupiter is at J

2• Jupiter is again in opposition. The time interval tnken by the jupiter is moving from J 1 to J2 is the synodic period of t!-le Jupiter.

I~ ow we consider the synodic period of the jup!ter by its conjunction with the sun (called conjunction only). At any time the earth is at E

1 and Jupiter is at J

3 such that E

1 S J

3 is a straight line. The sun is in

between the earth and the jupiter. The longitudes of the sun and the Jupiter are the same as that of point L3 on the Zodiac. At this time the Jupiter is in the conjunction with the sun. The Earth and the Jupiter start moving. The earth completes one revolution an~ reaches at E

1 again but the jupiter is not at J3 but has moved further. When the earth reaches at Ez and the Jupiter at J

4, the conjunction of the of jupiter with

the sun occurs again i.e Ez S J 4 becomes a straight line and the longitudes of the sun and the Jupiter are the same as that of L4 a point on the Zodiac. The time period taken by the Jupiter is traversing the arc J

3 to J 4

is the synodic period of the Jupiter.

The definition of the synodic period of inner as well as outer planets is summarised as under :-

The time interval taken by a planet in moving from one type of conjunction/opposition to the same type of conjunction/ opposition again is the synodic period of that planet.

The relation between sidereal period and the synodic period of the planets is :-


E = Sidereal period of earth in days

P = Sidereal period of planet in days

T = Synodic period of planet in days

Therefore the angle moved by the earth and the planet in one day are 360°/E and 360°/P respectively

Inferior planet :

360° 360° 360° 360° :. -P--E=T where T is the angle gained by the

planet in one day.

I I I I I I or p -E = T or p = T + E where E = 365.2422 days. Tis known

as the synodic period. Hence P can be found out.

For Superior planet :

360° 360° 360° 1 1 1 -----=--or-=---

E P T P E T

i:lS the angle moved by the earth in one day is more than that of the planet.

[R!] Casting of Horoscope Modem Method - I

11.1 Horoscope is a diagram of the heavens for a particular time. The sign rising in the east is called the Ascendant. It is the middle of the first Bhawa. There are different ways in which the position of the heavens is depicted.

11.2 Type - I :

The following type is in vogue in the northern and north-western part of India. The number of sign rising in the eastern horizon at epoch (sign of Ascendant) is written in the top middle portion. The number of signs are written in the anti-clockwise direction in successive houses. After the 12th sign, 1st sign is written. Thus numbers 1 to 12 are written in 12 house. Leo is the 5th sign, so number 5 is used to represent Leo. In the following horoscope of 4th September, 2001 at 5:30AM, Leo (5) is the ascendant. Numbers 5, 6, 7 ........ 12, 1, ........ 4 denote the signs. Name of planets are written in the sign in which they are seen at that time. ·

11.3 Type -II:

It is the second type of diagram in which the horoscope is prepared and is used in Bengal, Orissa and the nearer places to them. In this type


also the signs are in ascending order in anti-clockwise direction. The places of signs (Rashies) are fixed. Asc short form of Ascendant is written in the house which is the sign of Ascendant. The names of signs are written in brackets for the sake of knowledge and in practice the same are not written.

Jupiter

(Taurus) Saturn (Pisces)

(Aries)

--------~----------------~--------

(Cancer) Venus

·,(Leo)

Asc.

11.4 Type - Ill :

(Libra)

(Capricorn)

(Sagittarius) Ketu

(Scorpio)

The following type of horoscope is used normally in the southern

(Taurus) (Gemini)

(Pisces) (Aries) Saturn

Rahu Jupiter

(Aquarius) (Cancer) Moon Venus

~ (Leal ~

(Capricorn) As c.

~ Sun

A

(Sagittarius) (Virgo) Ketu (Scorpio) (Libra) Mereu !)I Mars


part of India. Places of the signs are fixed and their numbers are not written like the horoscope of II type. The word Asc is written in the house in ~., uch sign of the Ascendant falls and that house is marked by · a pair of slanting lines. The ascending order of signs is in the clockwise direction. The names of signs have been shown within brackets for information only and actually the same are not written.

11.5 Type - IV :

The following type of horoscope is commonly used by Western Astrologers and some Maharashtrian Astrologers. This is a circular chart showing divisions of 12 rashies (signs) and 12 bhavas and their upper and lower limits also. Planets are indicated by their symbols. In western astrology the cusp of Ascendant is taken as the starting point of 1st Bhawa while in Indian Astrology it is the mid-point of 1st bhawa. Horoscope may be casted in any way but this method of casting is more scientific as the limits of signs and Bhawas are shown in one diagram and becomes easier for predication.

11.6 Signs in Zodiac :

The constellations or stars etc. appear to move from east to west due to diurnal motion of the earth. Ecliptic and zodiac also appear to move from east to west and complete one revolution of the earth in 24 hours. When the zodiac moves from east to west; the increase in


longitudes is in the reverse direction (west to east). Let any moment zoo longitude is rising in the east, the setting in west will be nearly 200° and at meridian the longitude will be nearly 290° or Tula (Libra) is in the west, Makar (Capricorn) at the meridian and Mesha (Aries) in the east. At that time cancer will be nearly at ante-meridian.

11.7 Ascendant:

The sign along with its degrees and minutes that is rising on the eastern horizon of a place at any moment is the ascendant of that time and place. It can also be defined that at any instant the longitude of the intersecting point of the zodiac and ecliptic is the ascendant of the event occuring at that time, at that place. It is the mid point of 1st Bhawa in Indian Astrology while in western astrology it is the starting point of 1st Bhawa.

The Ascendant can be found out by two ways namely (1) modem method ana (2) traditional method. It is easier to calculate Ascendant by the modem method, so it will be dealt first.

11.8 Calculation of Ascendant :

The following information is required :

(a) Time of event/birth

(b) Table of ascendant preferably of N.C. Lahiri

(c) Ephemeris (showing longitudes of Chitra Pakshiya Aynamsa)

(d) Latitude and longitude of the place of event/birth

(e) Central meridian of the zone/country.

Latitudes, longitudes, L.M.T. correction from I.S.T. and sidereal time correction of major Indian cities are given at pages 100 to 107 of the Table of Ascendant. The above information about the principal cities of foreign country is given at pages 108 to 111.

Time zone (for other country/zone) is the time difference between . their standard time and G.M.T. Please go through the last page of the

table of ascendant, carefully for summer time correction etc.

The following steps are required to calculate the ascendant.

Step -I: The standard time is converted into L.M.T. (local mean time) and then the sidereal time at that instant is found out.

In case the name of the place of event does not appear in the book, the L.M.T. is found out by the difference of longitudes of that place and the central meridian.

Step -II : Local mean time is converted into sidereal time.

Step - Ill : The page where ascendant for the latitude of the place are given, is opened. In case exact latitude is not available, page


nearest to the latitude of the place is used. ln case one want to be more precise, one can find out by proportional method between the two ascendants one behind and the other later. Ascendants are given after 4 sidereal minutes duration. For example ascendant for sidereal time 2 hours 15 minutes and 20 seconds is to be found out for a place at 22° (N) latitude.

Sidereal time Ascendant

2h16'" = 3' 16° 6'

2h12'" = 3 15 13

Difference in 4 minutes = 0 0 53

Difference in 1 minutes = 0 0 13.25

Difference in 3 minutes = 0 0 39.75

Difference in 20 seconds = 0 0 4.42

Difference in 3'" 20' 0 0 44.17 or 44 rounded.

Ascendant at 2h 15'" 20' = 3' 15° 13' + 0' oo 44' = 3' 15° 57'

Step -IV: Aynamsa correction for 1998 (suppose the event is of 1998) (from p-6 of table of Ascendants)

= H 0' 50'

Ascendant 3 15 7

or 15° 7' of Karka (Cancer)

11.9 Example -1 :

Find out the ascendant of a native born atRohtakon 31 October, 1964 at Sh 5'" PM (l.S.T.).

Solution:

Page 105 of table of ascendants reveal the following for Rohtak

Latitude = 28° 54' (N), Longitude = 76° 34' (E)

L.M.T. correction = - 23'" 44', Sidereal time correction for Rohtak = +Om 4' (X)

I.S.T. 8h 5'" 0' L.M.T. correction -0 23 44

L.M.T. at epoch (by adding) 7 41 16

Table IV correction (p-5) +0 1 16

Time interval

(sidereal time after noon) = 7 42 32 (Al)


Sidereal time on 31st Oct. at 12 noon = 14 36 25

City correction (X) = + 0 0 4

Sidereal time at Rohtak at noon on 31st Oct. = 14 36 29

Year correction for 1964 (p-4) = + 0 1 58

Sidereal time at Rohtak at noon on 31/10/64 = 14 38 27

As the time of birth is of afternoon, so add (A) + 7 42 32


There is no table for 28° 54' (N) latitude. The nearest latitude is 29° (N) and as such table of 29 (N) at page 49 is used in the present case.

Asc. for 22" 20m = 1' 26° 33' (B)

Asc. for 2211 24"' = 1 27 31

Difference in 4m = 0 0 58

59' is nearly equal to 1m So difference for 1"' = 0 0 14 (C)

Asc. for 2211 20m 59' = B + C = 1' 26° 33' + 0' 0° 14'

= 1' 26° 47'

Aynamsa correction for 1964 (p-6) = - 0 0 22 ------

Required Ascendant

or26°25'ofTaurus

Example-2:

= 1

(From the example-2 of sidereal time para 9.7).

26 25

Find out the ascendant of a native born at Kolkata at 6h 40m AM. (l.S.T.) on 5 September, 1985. Latitude of Kolkata is 22° 35' (N).

Solution:

Page-101 of the table of ascendants reveal the following information:

Latitude = 22° 35' (N), Longitude = 88° 23' (E)

L.M.T. correction = + 23'" 30'; City correction or correction to S.T. = - 011 Om 4'

Sidereal time at birth (para-9.7) = From p-36 of Table of Ascendants


Ascendant for 6 hours = 5' 7" 0'

· Ascendant for 5h 56m = 5 6 5


Difference in 1m = 0 0 13.75

Difference in 7" = 0' ()" 2' (Approx.) (A)

By deducting (A) from the Asc. of 6h

we get the Asc of 5h 59m 53' = 5' 60 58'

Aynamsa correction for 1985 =(-)0 0 39

Ascendant at epoch = 5 6 19

as five signs have passed and sixth is running so Ascendant is 6° 19' of Virgo.

Example-3:

Find out the Ascendant of a n~tive born at Tokyo on 8 Oct. 1981 at 11 h 28"' AM (Z.S.T.)

Solution:

Its sidereal time has already been calculated in example- 3 (para 9.7) and is 12h 52m 47'.

Latitude ofTokyo is (p-111) = 35° 40' (N)

Longitude = 13go 33' (E)

Aynamsa correction (p-6) = -0" 36'

Table of Ascendant at page 56 is for 35° (N) latitude

Table of Ascendant at page 57 is for 36° (N) latitude

Asc for 12h 52"' from page 56 = 8' ZO 45'

Asc for 12h 52m from page 57 = 8 zo 9'

Difference in 1 o latitude = 0

36x40 Difference in-40: latitude =

60 = 24' (A)

0 36'

As the ascendant is decreasing from 35° (N) to 36° (N), we will deduct (A) after finding it for 35° so that it will be for 35° 40'.

(p-56) Ascfor 12h 56"' at 35° (N) = 8' 3° 39'

Asc for 12h szm at 35o (N) = 8 2 45



Difference in 47' 54 47 = -x- = 11' (approx) 4 60 .

Asc for 12h 52m 4 7' = 8· 2° 45' + o• oo 11 •

= 8 2 56

Deduct(A) = -0 0 24

= 8 2 32

Aynamsa correction = -0 0 36


or Saggitarius 1 o 56'

Tables of Ascendants for southern latitudes are not readily available, so the table for northern latitudes are used. Correction of ±12 hours is done in the sidereal time and ascendant is calculated for the revised sidereal time from the tables of Northern latitudes. After arriving at the ascendant correction of ±6 sign Is carried out. The net result will be ascendant of the southern latitude.

Example - 4 :of southern hemisphere

Find out the ascendant of a native born at Cape Town on 3 Feb, 1980 at 8h 27m AM (Z.S.T.)

Solution: (p-llO)Time zone = + 2hours.

Latitude = 330 56'(5)

Longitude = 18° 29'(E)

L.M.T. correction from Z.S.T. = - 46m 4'

Correction of Z.S.T. from I.S.T. = - 3h 3Qm

Correction of sidereal time = + om 42'

Time of birth (in Z.S.T.) = 8h 27m 0' L.M.T. correction = -0 46 4

L.M.T. = 7 40 56

As the time is of before noon so = - 12 0 0

Time interval (difference from noon) = 4 19 4

Table IV correction = 0 0 42

Increased time interval = -4 19 46 (A)

(As the time is before noon so minus sign has been shown against it.)


it.)

Sidereal time for 3 Feb. noon = 2()h 51m 55'

1980 year correction = -0 1 29

City correction = + 0 0 42

Sidereal time for noon of 3 Feb. 1980 at Cape Town = 20 51 08

(A) = -4 19 46


As the place is in southern hemisphere, either add or deduct 12h from it.

Deducting 24 hours of a sidereal day we get = 4h 31m 22'

At page 55 table for 34 o (N) are given from that

we have Ascendant for 4h 32m = 4' 18°

Ascendant for 4h 28m = 4 17

29'

39(8)

Difference in 4'" = 0 0 50

Difference in 3m 22' = 0 0 42

Adding it in B we get Asc for 4h 31m 22' = 4' 17° 39' + 0' 0° 42'

= 4' 18" 21'

Aynamsa correction = - 0 0 35

Ascendant = 4 17 46

Adding6sign for ascendant at epoch at Cape Town= 10' 17° 46'

or 17° 46' of Aquarius.

!XIII

Horoscope Modern method -II

12.1 Ephemeris by l..ahiri will be used. These days most of the Panchangas are based on the Almanacs which are prepared with the help of modem astronomy and obsetvatories and the sayana longitudes are converted into Nirayana longitudes. We shall adopt the longitudes as per l..ahiri's epl,emeries. Daily position of longitudes at 5:30AM (l.S.T.) are given in the one year's ephemeris. While the position of every two days are shown in the condensed ephemeris of 5 years or of 10 years of all the planets except Moon and the Mercury for which daily positions are exibited and monthly position of true Rahu are given. Daily position of Moon at 5:30PM (I.S.T.), position of Mercury at 5:30PM (I.S.T.) on every Sunday and Wednesday, weekly position of other planets and mean Rahu for 1st day of each month at 5:30PM (I.S.T.) have been given in the condensed ephemeris for the year 1900 to 1941. The position of longitudes of the planets is of 5:30 AM (I.S.T.) or 5:30PM (I.S.T.) (which is 0 AM or 12 noc.n universal time or G.M.T.). ·

These longitudes are geo-centric ones e.g. these are the longitudes of places in the zodiac, where the planets are seen by an obsetver at the centre of the earth. The distances of the planets from the earth is much more in comparison to the radius of the earth. So the longitudes obsetved by an obsetver at the surface of the earth are taken as obsetved irom the <:entre of the earth becnuse there will be negligible difference. The longibJdes in these ephemeris are according to Indian standard time, so the time of foreign countries/places is to be converted into Indian standard time and for that Indian time the positions of the planets are found out.

The positions of planets are calculated by interpolation, in case the time of birth etc. is in between the two given positions. Log tables can also be used to find out the positions for intermediary time. The following procedure is adopted in finding out the longitudes of the planets

Step I : Find out the arc moved by the planet in 24 hours and note whether the planet is direct or retrograde.

Step II : Find out the time elapsed from the time for which the position or planets are given.


Step III : Find out the arc the planet shall move in the time of step 11 by proportion or logarithms.

Step W : If the planet is direct add the arc of step Ill in the 1st position, and deduct if retrograde.

Step V : Rahu's longitudes are' given monthly in condensed ephemeries. Rnd out by proportion for intermediary position. True Rahu is normally considered. Ketu is always at 180° or 6 sign distance from Rahu. ·

In this way the planetary position at epoch is found out and used for casting the horoscope.

12.2 Use of Log Tables :

Logarithms (log) tables are given at page 156-157 in Lahiri's ephemeris for the year 2001. These table are included in every Lahiri's ephemeris. Columns are for hours or degrees. On the left and right sides are the minutes of hours & degrees. The rows are minutes. If we are to find out log of 2h 30m or 2° 30', see the column below2 and row of30', the meeting point is the required log (0.9823). The columns where there are four digits and no decimal is incorporated, decimal may be presumed on the left hand side of the digits. For example log of 6° 10' or 6h 10"' is 5902 as per tables but actually it is 0.5902. Logs are added for multiplication (here we are concerned with multiplication and not division). After addition anti-log is to be found out but anti-log tables have not been provided, so we use these log tables for anti-log purposes. We have to see the nearest figures in degree and minutes of the figure received after addition of logs. This is the magnitude of the arc by which the planet has moved in the partial time. In case the difference in motion in 24 hours is less than 4' or 5', logs should not be used and find out by oral method.

12.3 Example of casting of horoscopes by modem method :

Exampe -I:

Cast a horoscope of a native born on 25 September 2001 at 10:25 AM (I.S.T.) at Delhi.

Answer:

Time of Birth = 1Qh 25m 0' (l.S.T.) L.M.T. correction = -0 21 8

L.M.T. at birth = 10 3 52 As it is before noon, so deduct from 12 = - 12 0 0

Time Interval (T.l.) = 1 56 8 Table IV correction = 0 0 19


Increased T.I. = 1 56 27 (A) Sidereal time (S.T.) at noon on 25 September = 12h 14m 29' City correction (p-1 02) = + 0 0 3 Year correction for 2001 = + 0 2 8 Sid. time at noon on 25 Sept. 2001 at Delhi = 12 16 40 As the time of birth is before noon, so deduct (A) = - 1 56 27

Sid. time at epoch = 10 20 13 Latitude of Delhi is 28° 39' (N) and its table of Ascendant is at

page48. Ascendant (Asc.) for 10 hour 24 minute = 7' 40 7' Ascendant (Asc.) for 10 hour 20 minute = 7 3 16


51 13 663 Difference in 13' = -x-=-- = 0 0 3

4 60 240 Adding in Asc. of lQh 20m we get = 7' 3° 16' + 0' oo 3'

= 7' 3° 19' Aynamsa correction for 2001 (p-6) = - 0 0 53

Ascendant = 7 2 26 Time of birth is 10:25 AM of 25 Sept, 2001 which is in between

5:30 AM of 25 Sept. and 26 Sept. Difference in time = 10:25- 5:30 = 4h 55m.

Moon Sun Mercury Venus Mazs Jupter Saturn True Rahu

R::.sitional . . ' . . ' .. ' ' . ' .. ' ' . ' ' . ' .. ' 5:30AM 26-9-01 8 27 6 596 6 4 05 4 12 7 8 15 41 2 19 35 I 21 06 2 8 01 25-9-01 8 14 58 58 07 6 3 30 410 54 8 15 06 2 19 29 I 21 05 2 8 01

Motion in 0 12 8 0 0 59 0 0 35 0 I 13 0 0 35 0 0 06 0 0 01 000 24h1S.

Logof24h!S 0.2962 1.3875 1.6143 12950 1.6143 2.3802 - -Motion p-156-157

Logof4h!S 0.6885 0.6885 0.6885 0.6885 0.6885 0.6885 - -55 min.

Total 0.9847 2.0760 2.3028 1.9835 2.3028 3.0687 - -Nearest fig. in 0.9852 2.0792 23133 !.9873 23133 3.1584 - -log table Anti-log or 2° 29' ()" 12' ()" 07' ()" 15' 0" 07' ()" 01' - -motion in 4h 5,5111 Fbsitionon 8 14 58 58 07 6 3 30 410 54 8 IS 06 2 19 29 I 21 05 2 8 01 2S-9-0I

R::.sitionol 8 17 27 58 19 6 3 37 411 09 8 IS 13 2 19 30 I 21 OS 2 8 01 Planers at epoch


In case any planet would have retrograde motion, the motion in 4 hours 55 minutes should be substracted from that of 25-9-01. The longitudes of Rahu are the same on 25-9 and 26-9 and the motion of saturn is 1' in 24 hours so motion in 4 hours 55 minutes is nearly nil, which can be calculated by interpolation.

Motion in 4 hours 55 minutes can also be found out as under, we take the example of sun.

Motion in 24 hours = 59'

Motion in 1 hour

55 11

Motion in 4h 55m or 4 60

.

= 59+24

= 59 X 295 =l2' 24 60

which agrees with the figure derived by the log method. In this way the required motion is found out. Ascendant has completed 7 Rashis and is in the 8th one. The same way Rashis of other planets are known. Ketu = Rahu + 6 sign

HereKetu

Horoscope is as under :

Example-2:

=

Ketu Moon Mars

2' +6

8

v

A

8"

0

8

Sat

Mercury

01'

0

01

Jup Rahu

Venus

Sun

Calculate the planetary position of example - 2 in para 11.9 and cast horoscope.

Solution:

Date of birth = 5 Sept 1985


Place of birth

Time of birth

Latitude of Kolkata

= Kolkata

=6:40AM

= 22°35' (N)

Ascendant as per para 11.9 Example- 2 is Kanya 6° 19'. The time of birth is in between 5:30 AM of 5 Sept and 6 Sept. And the difference from 5:30AM = 6:40- 5:30 = 1 h : IQm

Motion in 24 minutes = half of the motion in 48 hours.

For the convenience of the students, we shall be adopting the logarithm table of 24 hours only. The two days, 3 days, 4 days or 7 days motions are converted in one day motion.

Moon Saturn Jupiter(R)

Rlsition of Planet .. ' ... .. '

at 5:30AM

6-9-1985 I 3 10 6 29 13 9 14 40

5-9-1985 0 21 22 - -4-9-1985 - 6 29 05 9 14 50

Motion in - 008 (-)0 0 10 48hours

Motion in 0 11 48 004 (-)0 0 5 24hours

Logol24 0.3089 2.5563 2.4594 hour motion

Log91l hour 1.3133 1.3133 1.3133 IOminutes

Total 1.6222 3.8696 3.7727

Nearest login table 1.6269 - -Ant! log or motion in I hr.IOmin. 0.034 0 0 0 0 0 0

Fbsltion of 5:30 0 21 22 6 29 09 9 14 45 AMofS-9 (Middle of 419&619)

Fbsltion of plan•ts 0 21 56 6 29 09 914 45 at birth

Longitude of Rahu on 1-9-85


Difference in 30 days


Difference in 4 days 1 hour

Mars Sun \knus .. ' . . ' .. '

4 3 46 4 19 42 3 16 53

- - -4 2 30 4 17 45 3 14 29

0 I 16 0 I 57 0 2 24

0 0 38 0 0 59 0 I 12

1.570C 1.3875 1.3010

1.3133 1.3133 1.3133

2.8919 2.7008 2.6143

2.8573 2.6812 2.5563

0 0 2 0 0 3 0 0 4

4 3 08 4 18 44 3 15 41

4 3 10 4 18 47 3 15 45

=OS 17° 21'

= 0 15 42

MercuJy .. '

4 4 56

4 3 16

--

0 I 40

1.1584

1.3133

2.4717

2.4594

0 0 5

4 3 16

4 3 21

= 0 1 39 = 99'

~ 3' (Approximately)

99x4 3xl =--+-=13'

30 24 (approximately)

As Rahu's motion is retrograde, deduct it from the position of

1-9-85 = o· 17° 21'- os oo 13' = o· 17° 8'


Ketu's position = 0' 17° 8' + 6' oo 0' = 6' 17° 8'

Moon Rahu

Venus

Mars Jup (R) Sun

Mercury

Sat v

Ketu Asc,

~

Example-3:

Calculate planetary position and cast horoscope of the data given in example- 3 of para 11.9.

Solution:

Date of birth

Place of birth

Zonal time of birth

Time zone

l.S.T. from Z.S.T.

= 8 October, 1981

=Tokyo

= 11 hours 28 minutes AM.

= + 9 hours

= -3h30m

Ascendant as per ex-3, para 11.9 = Saggitarius 1 o 56'

Time of birth in J.S.T. =; 11:28-3:30 = 7:58AM

The position of planets given in ephemeris is according to I.S.T., so these will be calculated for 7:58AM (I.S.T.)

Difference from 5:30AM= 7:58-5:30 = 2:28

This is the time in between 5:30AM of 8-10-81 and 9-10-81

(Logs of retrograde planets are added and the motion is deducted)


Fbsition ol planets Moon Merrury Sat at 5:30AM (R) .. ' .. ' .. '

10-10-81 - - 5 19 42

9-10-81 9 22 52 6 9 50 -8-10-81 9 10 03 6 10 06 5 19 28

Molion in 48 hrs. - - 0 0 14

Molioo in 24 hrs. 01249 (-)0016 007

Log ol duration 02724 1.9542 2.3133 of24 hrs

Log of 2" 28' 0.9881 0.9881 0.9881

Total 12605 2.9423 3.3014

Nearest lug in reble 12607 2.8573 3.1584

Anti-log 0 1 19 (-)0002 0 0 01

Fbsition at 5:30 9 10 03 6 10 06 5 19 28 onB-10-81

Fbsition at bir1h 9 11 22 6 10 04 5 19 29




Jup M"" Sun

.. ' .. ' .. '

5 26 15 3 29 50 5 23 00

- - -5 25 49 3 29 39 5 21 02

0 0 26 0 0 11 0 1 58

0 013 005.5 0 0 59

2.0444 2.4198 1.3875

0.9881 0.9881 0.9881

3.0325 3.4079 2.3756

3.1584 3.1584 2.3&12

0 0 01 0 0 01 0 0 06

5 25 49 3 29 39 5 21 02

5 25 50 3 29 40 5 21 08

= 3'5°42'

= 3 2 15

= 0 3 27 = 207'

lkn

.. '

7 7 32

-7 5 16

0 2 16

0 1 8

1.3258

0.9881

2.3139

2.3133

0 0 07

7 5 16

7 5 23

57 207 Difference in 7 days 3 hours = 8 x 31 = 4 7' (approximately)

3 1 57 as7- = 7- =-

24 8 8 Longitude of Rahu at epoch =· 3' 5° 42'- 47' = 3' 4° 55'

Longitude of Ketu of epoch = 3' 4° 55' + 6' = 9' 4° 55'

Mars Rahu

Moon Ketu

v Sat Asc, Ven Mer Jup

(R) Sun A


Example-4:

(West of India and Southern hemisphere)

Date of birth = 5 January, 2001

Time of birth = 11 hours 30 minutes PM (Z.S.T.)

Place of birth = Rio-de-Janeiro (Brazil) from p-111 ofTable of ascendants. Time zone (-) 3\ latitude 22° 54' (S); longitude 43° 12' (W).

L.M.T. correction from Z.S.T. = + 7'" 12'

l.S.T. correction from Z.S.T. = +81' 3Qm

correction of Indian sidereal time = + 1'" 23'

Solution:

Zonal Time = 11: 30 : 0 P.M.

L.M.T. correction = + 0:7 : 12

L.M.T. (T.l.) = 11:37: 12 (The time is of afternoon) Table IV correction = 0 : 1:54

Increased time interval = 11:39:06 (A)

Indian sidereal time = 18h 57'" 35' on 5-1-2001 at noon

City correction = +0 1 23

Yearcorrectionfor2001 = + 0 2 08

Sidereal time of P.O.B. at noon = 19 1 06

Add (A) = + 11 39 06

Total = 30 40 12

As the sid. time is more = -24 0 0 than 24 hours so


Place of birth is in southern hemisphere and the tables of ascendants for southern latitudes. is not available with us. So the tables of ascendants for nothern hemisphere will be used. 12 hours will be added in the sidereal time and 6 signs (Rashis) will be added/substracted from the ascendant. The net result will be ascendant of this place.

Sidereal time after adding 12 hours= 18h 40'" 12'

Latitude of Rio-de-Janeiro is 22° 54' (S) which is near to 23°, Tables of 23° latitudes is used.


Ascendant for 18 hours 44 minutes= 11' 210 37'

Ascendant for 18 hours 40 minutes= 11 20 18


Difference in 1 minute = 0 0 19.75

Difference in 12 seconds = 0 0 4

Ascendant for 18h40m 12' = 11'20° 18' + 4' = 11 20 22

Aynamsa correction (p-6) = -0 0 53

Total = 11 19 29

Correction for southern latitudes = -6 0 0


Time of birth = 1P 3Qm O• PM (Z.S.T.)

l.S.T. correction from Z.S.T. = + 8 30 0 [5:30-(-3:0)]

= 20 0 0 PM (l.S.T.)

or 8 AM of next day viz 6-1-2001

Time difference from 5:30AM . = 8h- 5:30 = 2:30

longitudes Sun Moon Memuy Venus Mars Jupiter Sa tum True at 5:30AM (R) (R) Rahu

• 0 ' • 0 ' • 0 ' • 0 ' • 0 • • 0 ' • 0 • • 0 •

7-1-2001 8 22 53 I 13 25 9 0 14 10 9 39 6 14 34 I 7 54 I 0 30 2 21 40

6-1-2001 8 21 52 0 29 17 8 28 35 10 8 34 6 13 59 I 7 58 I 0 32 2 21 40

Motion in 0 I 01 0 14 08 0 I 39 0 I 5 0 0 35 --{)004 --{) 0 2 -24hours .

Log of 1.3730 0.2300 L1627 1.3454 1.6143 - - -241hmotion

Logof2'300 0.9823 0.9823 0.9823 0.9823 0.9823 - - -

Total 2.3553 12123 ·2.1450 2.3277 2.5966 - - -Nearest log 2.3802 1.2139 2.1584 2.3133 2.5563 - - -in table

Antilog 0 0 06 0 I 28 0 0 10 0 0 07 0 0 4 0 0 0 0 0 0 0 0 0

Position at 8 21 52 0 29 17 8 28 35 10 8 34 6 13 59 1 7 58 I 0 32 2 21 40 5:30AM on 6-1-2001

Planetaty 8 21 58 I 0 45 8 28 45 10 8 41 6 14 03 I 7 58 I 0 32 2 21 40 position at epoch

Longitude ofKetu = 2'21 o40• + &0°0' = 8' 21°40'


Moon Jupiter Rahu Saturn

Venus

Sun v Mercury Mars Asc,

Ketu ...<::

lXIII I Casting of Horoscope

Traditional Method

13.1 Casting the horoscope by traditional method is different from that of modem method. Longitude of sun at the time of rising is the longitude of lagna at that time because the rashi rising at the eastern horizoo at that time is the same. In this method the ascendant at epoch is found out by adding the Rashimans in the ascendant at the time of sunrise (longitude of sun at sunrise). The duration of time elapsed since sunrise is called lshatkaal. For calculating the Ascendant, we require (1) time of sunrise of the day of birth, (2) longitudes of the sun at the time of sunrise and (3) the Rashimans of that place.

13.2 Palbha is required for knowing the Rashiman of a place. A table of Palbha is given in para 13.6. Charkhandas of that place are calculated from the Palbha. These Charkhandas are added/substracted in the Rashiman of the equator (0° latitude). Those are explained in paras 13.5 to 13.8.

13.3 Calculation of time of sunrise and sunset:

Sun appears to move on the ecliptic which is inclined at an angle of 23° 27' with the equator. Earth revolves from west to east around its axis which is perpendicular to the plane of equator and passes through the centre of the earth. Due to above reason the time of sunrise and sunset differ on the places having the same longitude but different latitudes. The solar disc takes 7 to 8 minutes in rising or setting. Sunrise or sunset is reckoned at the time when the centre of sun is on the horizon, in the Indian astronomy. The timings relating to the visibility of the upper limb of the sun on horizon is considered the time of sunrise in modern astronomy. The sun's complete disc takes 7 to 8 minutes in crossing the horizon. Half of the disc will take 3.5 to 4 minutes. Thus the sunrise is 3.5 to 4 minutes later and sunset earlier in Indian astronomy than the modem one. The timings of sunrise or sunset differ with the sun's declination. The time of sunrise and sunset at any place is nearly the same on the same dates of Gregorian calander every year.

Timings of sunrise and sunset on different dates for latitudes 0°,


10°, zoo, 30° and 35o have been given in the Lahiri's ephemeris for Z001 at pages 94-95. The sun rise or sunset of a place is calculated by interpolation of the data given in the ephemeris.

13.4 Example :

Calculate the time of sun rise and sun set of Hyderabad on 3 June, ZOOZ. Latitude of Hyderabad is 17° Z6'·(N).

In Lahiri's ephemiris for Z001 (p-94) and for ZOOZ (p-93) time of sun rise and sun set are given in L.M.T.

Date Sunrise Sunset

1/6

5/6


Difference in Z days

100

5h:38"'

5 :38

0:0

0:0

zoo 5h:Z0"'

5 : zo 0:0

0:0

100 zoo 18h: 18"' 18h:36'"

18 : 19 18 :37

0:1 0: 1

0:0.5 0:0.5

= 0:1 0: 1

rounded to nearest minute.

3/6 5:38 5:20

On 3/6 difference in (20°- 10°) = 10° latitudes is 18"'

On 3/6 difference in 7° Z6' latitude = 13"'

18: 19 18:37

13'"

Time of sun rise is decreasing and sun set is increasing with the increasing of latitudes.

Sun rise sun set

Time of 3/6 of Hyderabad 5:25 18:32

Add the L.M.T. correction + 0:16 + 0:16

Time of rising & setting of sun's upper limb = 5:41 18:48

Time taken in rising or seiling the centre = + 0:04 -0:04

Time of rising and setting of the sun's centre 5:45 18:44

13.5 Rashiman (Oblique Ascension) :

Rashiman is the time interval taken by each Rashi or sign (30°) for complete rising at the eastern horizon of a place. Rashimans vary from latitude to latitude. Rashimans are always computed for the moveable


zodiac or sayana zodiac. Longitudes are converted from sayanas to Nirayanas and then Nirayana Rashi's are found out.

13.6 Palbha:

Length of shadow of 12 Angula or 12 units (say 12 centimeters} in Angula or that unit (centimeter) on sayana mesh sankranti or sayan a Tula sankranti (when the sun is at vernal equinox or autumnal equinox) at 12 apparent noon is called Palbha of that place.

Table of Palbha according to various latitudes :

Lat. Palbha Lat. Palbha Lat. Palbha Lat. Palbha

010 0.21 w 3.44 31° 7.21 460 12.43

02° 0.42 170 3.67 32° 7.50 47° 12.87

030 0.63 18° 3.90 33° 7.79 480 13.33

040 0.84 19° 4.13 340 8.09 49° 13.80

05° 1.05 200 4.37 35° 8.40 soo 14.30

060 1.26 21° 4.60 360 8.72 51° 14.82

070 1.47 22° 4.85 37° 9.04 52° 15.36

08° 1.69 23° 5.09 38" 9.37 530 15.92

090 1.90 24° 5.34 3~ 9.72 540 16.51

100 2.11 25° 5.59 400 10.07 sso 17.14

no 2.33 26° 5.85 41° 10.43 560 17.79

12° 2.55 27° 6.11 42° 10.80 57° 18.47

13° 2.77 28° 6.38. 430 11.19 sso 19.19

w 2.99 29° 6.65 440 11.59 59° . 19.97

15° 3.21 30° 6.93 450 12.00 600 20.78

13.7 Charkhanda: 10

On multiplying 'palbha: of a place by 10, 8 and ~ at separate

three places. we get the charkhandas of three Rashis of that place in 'Palas'. It is explained with an example.

Example: Find out the charkhandas of Delhi. Its latitude is 28° 39' (N)

Solution:

Delhi's latitude is in between 28° (N) and 29° (N). Palbha of these

.


latitudes are 6.38 and 6.65 respectively.

Difference of Palbha in 1 o or 60' = 6.65- 6.38 = 0.27

Difference of Palbha in 39' 0.27x3~

= 60

= 0.18 (nearly)

By adding it into 28° Palbha we get 6.38 + 0.18 = 6.56 Palbha ofDelhi.

Charkhandas of Delhi

6.56 x 10 = 65.6 = 66 Pala approximately

6.56 X 8 = 52.48 =52 Pala approximately 10

6.56 x 3 = 21.87 = 22 Pala approximately

13.8 Rashiman :

By addinglsubstracting these charkhandas in the Rashiman of oo latitude or equator, we will get the Rashimans of Delhi. Charkhandas are subtracted from the Rashimans of equator in signs Aries, Taurus, Gimini, Capricorn, Aquarius and Pisces for the places in Northern hemisphere and are added in the rest as shown in the example below. Charkhandas are added for the places in the southern hemisphere in the Rashimans of equator in signs Aries, Taurus, Gemi.ni, Capricorn, Aquarius and Pisces and subtracted in the rest of signs. Rashimans of equator as per verse ( 1) ofT riprasnadhikar of Graha Laghava are given in the example.

t'i en I <{<41 f<~ t:1 fl<tl l"~l~·rrf.Fff S<tl<{f.l ff'l q 8ftW1J: liiM i'l i;ij) •Hli!ll: 1

t\1'1lf.qol~: ;;tlllli'li;ijillWliftllfC::Jl lfG<f <li<n4of«<:~i'l ~: II ~ II

Rashi Rashimans Charkhandas Rising time at equator of Delhi of Rashis in. Delhi

Rising time in Pala Pal a Ghati Pala

Aries = Pisces 278 -66 212 :;3 32

. Taurus = Aquarius 299 -52 247 =4 07

Gemini·= Capricorn 323 -22 301 =5 01

Cancer = Sagittarius 323 + 22 345 =5 45

Leo = Scorpio 299 +52 351 ==5 51

Virgo= Ubra 278 + 66 344 =5 44

Total 30 00 -Total of 6 Rashis = 30 Ghatis, Total of 12 Rashis = 30 x 2 = 60

Ghatis


Example-2:

Latitude of Jakarta (Indonesia) is 6° 16' (S). The place is in Southern hemisphere.

Palbha of 6° = 1.26

Palbha of 7° = 1.47

difference in 1 o = 0.21

0.21 xl6 Difference in 16' =

60 = 0.06 (approximately)

Palbha of Jakarta = 1.26 + 0.06 = 1.32

Charkhandas of Jakarta

1.32 x 10 = 13.2 = 13 Pala Approximately

1.32 x 8 = 10.56 = 11 Pala Approximately

10 1.32 x 3 = 4.4 = 4 Pala Approximately

These cherkhandas will be added where they were subtracted for Northern hemisphere and subtracted where they were added in the previous example.

Rashimans of Jakarta

Rashis Rashiman Charkhanda Rashiman of Equator of Jakarta of Jakarta

Pal a Ghati Pal a

Alies = Pisces 278 + 13 291 =4 51

Taurus = Aquarius 299 +11 310 =5 10

Gemini = Capricorn 323 +4 327 =5 27

Cancer = Sagittarius 323 -4 319 =5 19

Leo = ScorPio 299 -11 288 =4 48

Virgo = Libra 278 - 13 . 265 =4 25

'Total = 30 00

13.9 Calculation of Ascendant:

Example:

We have to find out the ascendant of a native born at Delhi on 7 July 2001 at 10:30 AM (I.S.T.).


Solution:

Time of Birth = lQh; 30m AM

Sunrise = 5 : 33

On subtracting we get Istkaal = 4 : 57 = 12 Ghati 22.5 Pala

= 12 Ghati 22 Pala (nearly) (A)

Longitude of sun at sunrise = Ascendant at that time

Nirayana longitude of sun at sunrise -- 2' 21° 4' 57"

Aynamsa = +0 23 52 25

Sayana longitude of sun at sun rise = 3 14 57 22

= 3 14 57

rounded to nearest minute.

Cancer sign has risen

Balance of cancer to rise

= 14° 57' = 8 97'

30° = 30 X 60 = 1800'

= 1800- 897 = 903'

Cancer sign tahes time to rise in Delhi = 345 Pala

Time taken for rising 1800' = 345 Pala

Time taken for rising 903' = 345x903 = 173 Pala 1800

= 2 Ghati 53 Pala

Ghati Pala

Time required for completion of cancer sign = 2 53

Time required for rising of Leo sign = 5 51

Total = 8 44(B)

In case we add time of rising of Virgo sign (5 ghati 44 pala) it will be more than the lstkaal. Hence Virgo is the Ascendant but its degrees are to be found out.

lstkaai=A-B=l2:22-8:44=3:38 = 218 Pala

In 344 pa!a Kanya (Virgo) rises = 1800'

In 218 Pala Kanya (Virgo) rises = 1800x218 =

1141,

344 = 19° 1'

Sayana longitude of Ascendant = 5' 19° 1'

Aynamsa =-0 23 52

Nirayana longitude of Ascendant = 4 25 9


or Ascendant is 25° 9' of Leo.

13.10 Planetry Position :

Panchangas also give the daily position of the planets like ephemeris. Planetary position can be calculated as told in casting of horoscope by modern method. Old Panchangas do not give daily positions of planets and the same are found out by the method given below. Vishwa Vi jay Panchanga for the year 2001-2002 shall be used. We shall consider the time in hours and minutes and not in ghati, pala. Hours and minutes can be converted into ghati pala on multiplying it by two and half.

13.11 Longitude of the sun :

Horoscope at right hand side on page 61 is of 5th July, 2001 showing longitude of sun at 5:30AM (l.S.T.) as 2' 19° 11' to nearest minute. Sun moves 57' 11" or say 57' in 24 hours.

The time interval between 10:30 AM on 7 July and 5:30AM on 5th July = 2 days 5 Hours

Sun moves in 2 days 5 hours@ 57' per day = 0' 2° 6'

Longitude of sun at 5:30AM on 5 July

Longitude of sun at epoch

=+2 19 11

::: 2 21 17

13.12 Longitude of Moon:

Moon enters Uttrashadha Nakshatra on 6 July at 10:12 AM and Uttrashadha ends (enters in Shrawan Nakshatra) on 7 July at 12:49 noon.

Time for moving on Uttraskadha Nakshatra ie 13° 20' (800')

= 26h : 37m = 1597m

Time elapsed upto Istkaal since start of Uttrashadha Nakshatra

= 1 day 18 minutes

In 1597 minutes Moon moves

In 1458 minutes Moon moves

= 1458 Minutes

=800'

= 800xl458 = 730

, 1597

= 12° 10'

Uttrashadha begins at Dhanu (Sagittarius) 26° 40'.

Adding 12° 10' in it, we get Makar (Capricorn) so 50'

which is the longitude of moon.

13.13 Longitude of Mars:

Longitude of Mars at 5:30AM on 5 July = 7' 22° 47'

Elements of Astronomy and A.strological Calculations 101

In 24 hours it moves = 0 oo 11' 40"

In 2 days 5 hours it moves = 11' 40" x 2 + 2' = 25' (nearly)

The motion of the planet is retrograde.

Hence its longitude at epoch = 7' 22° 4 7' - 25' = 7' 22° 22' or Mars was at Scorpio 22° 22'

13.14 Longitudes of other planets will be found out by the method explained in para 13.13.

Precession of the Equinoxes

14.1 A constellation (Nakshatra) is a group of stars and the name of the constellation is kept after the name of brightest star in it. As the zodiac is circular, some point is to be taken as the starting point. In Indian Astrology this starting point, which is called the first point of Aries, was taken according to the Nakshatras (constellations). It is called the first point of fixed Aries and is nearly 180 opposite to the Chitra star (spica-16) in chitra constellation. In Western Astrology the intersecting point of ecliptic and the celestial equator or Vernal Equinox is taken as the first point of Aries. It so appears that before the precession of Equinox was known the vernal equi.nox (Moveable orsayana first point of Aries) was considered as the starting point of the zodiac, in Indian Astrology also.

14.2 Our Rishies and Munis observed the sky continuously for a long period and noticed that the longitudes of all the stars were increasing. It is impossibl~ that longitudes of all the stars increase by the same amount. When they tried to find out the cause of this increase, they noticed that there was no change in their latitudes but the longitudes were increasing. They concluded that the ecliptic is not moving backwards but the vemdl equinox is moving backwards and the longitudes of all the stars are increasing. This backwards motion of the Vernal Equinox is called the Precession of Equinox.

14.3 Physical cause of Precession :

The precession is almost caused by the attraction of the moon and sun on the proturberant portions of the earth at the equator. It is causing the wobbling motion of the earth like a spinning top so that the axis of the earth pointing in heavens to which it is directed (celestial pole), describes a small circle round the pole of the ecliptic (Kadamb). The north pole of the axis of the earth completes one revolution round the pole of ecliptic in 25,800 years. It is illustrated by the following figure:


North Star

(North Pole)

Ecliptic

Fig.20

Figure 20 : Moon and sun pull on the equatorial bulge tend to pull earth's equator into the plane of ecliptic and thus the earth's axis sweeps out a cone of precession and thereby makes a circle on the sky.

If the earth would have been a perfect sphere and its mass would have spread uniformly, the earth would not have wobbling motion or there would not have been precession of the equinoxes. Precession of equinoxes is mainly due to the Moon and Sun and amounts to nearly 50".35 each year with retrograde motion. The disturbing effect of the Moon is more than twice that of the sun. The ratio is 7:3 and the reason is that the moon is nearer to the earth. This retrograde motion of equinoxes is reduced byO".ll each year due to planets and it is called the planetary precession. The net amount of precession of equinoxes is 50".35- 0".11 = 50".24.

14.4 This disturbance is greatest when the attracting body reaches its greatest north or south de.dination. When the attracting body is on the celestial equator (zero declination), the disturbing effect is zero. The declinations of the Moon, Sun and Planets vary at different times resulting in the variation in the disturbing force and the precession of the equinoxes.

14.5 Nutation:

As earlier dealt that the celestial pole moved uniformly in a circle round the pole of ecliptic, if th2 attraction due to the moon, sun and planets would have been constant, but the attraction of these are not


constant and the celestial pole describes a wavy path. This nodding is called nutation: It causes the precession sometimes more and at other times less. Nutation is also caused by the variable action of the moon depending upon the positions of its nodes which make a revolution in

2 l83years.

Fig.21

In figure 21, K is Kadamb (the pole of ecliptic). CD is a small circle of diameter nearly 47° (23° 27' x 2). Pis the celestial pole wh:ch is revolving round K on the small circle CD and completing one revolution in 25,800 years. but due to variable force of attraction of the moon it is also revolving on the small elliptical orbit APB which has been shown by the wave-like figure. Its major axis AB = 18".5 is directed towards K (the pole of ecliptic) and minor axis = 13". 7 along the circle CD. The pole completes one revolution on this ellipse (which is made up of the

2 waves) in 183years. It causes in the change of position of the pole up

to nearly 9" arc on either side of the mean position of the pole. It brings change in the precession of the equinoxes.


14.6Zodiac:

Our ancients observed that the moon and other planets were never at any time at a very great angu:ar distance from the ediptic, they therefore conceived an imaginary belt in the heavens extending for about go on either side of the ecliptic. Sun, Moon and other planets are aiways found in this belt. Pluto goes out of this belt sometimes. This belt is known as zodiac and Pluto was not discovered when the concept of zodiac was imagined.

14.7 Sayan a zodiac or Tropical zodiac or Moveable zodiac:

Vema! Equinox is the starting point of the longitudes in movable zodiac. Vernal Equinox or movable first point of Aries moves backwards each year. As this first point of Aries is not stationary, this zodiac is called moveable zodiac also. Moveable zodiac is also known as Tropical zodiac or Sayan zodiac. In sanskrit sayan is made up of two words Sa + ayana meaning with movement. The longitudes that are counted from this point are known as sayan longitudes or tropical longitudes:

14.8 Fixed zodiac or Nirayan zodiac or Sidereal zodiac :

A zodiac in which the counting of longitudes starts from a fixed point is known as fixed zodiac or Nirayan zodiac. Precession of vernal equinox does not change the longitudes of this zodiac. The first point of Aries or the starting point for counting the longitudes is started from a fixed point in the constellations. The first point of Aries in this zodiac is nearly 180° opposite to the Chitra star (spica 16) in Chitra constellation. Chitra star is a fixed star as such this first point of Aries is also fixed.

14.9 Ayanamsa:

Vernal equinox or the movable first point of Aries is one of tl!e points on which the equator and ecliptic intersects.lt is the point when the sun crosses the equator while moving towards north from the south This point moves backwards by nearly 50".24 each year {opposite t.l sun's movement on its orbit). In hundreds or thous<;~nds of years 't sufficiently goes backwards, while the fixed first point of Aries does not move at all. The difference between these two first point of Aries at an~· time is called Ayanamsa at that time. Due to backwards motion of the· Sayan first point of Aries, Sayana longitudes becqmes greater than the Nirayana longitudes.

The formula becomes:

Nirayana longitude + Ayanamsa = Sayana longitude or

Sayan longitude - Ayanamsa = Nirayana longitude


According to Chitrapakshiy Ayanamsa or Lahiri's Ayanamsa both the first of Aries coincided on 22nd March, 285 AD (207 saka samvata). The Calendar Reform Committe appointed by the Govt. of India in 1952 recommended this value of Ayanamsa and Govt. of India adopted this system of Ayanamsa in 1953.

14.10 Why Aynamsa is a vexed problem in Indian Astrology :

There is a controversy on the t!me when the Nirayana first point of Aries coincided with the Sayana first point of Aries. Many eminent astrologers differ on this point and they consider their ayanamsa to be c01rect and the problem of ayanamsa becomes a difficult one. The following tables show the difference in the thoughts of eminent scientists and Astrologers:

Name of the Astrologer

Chero

G. Massey

CFagan

L>hiri

Krishnamurti

P. S. Ray

B.V. Raman

Sepharial

Time when both the first point of Aries coincided

388BC

255BC

213AD

285AD

291AD

319AD

397AD

498AD

There is no agreement in the rate at which the Vernal Equinox moves in retrograde motion. The figures adopted by various astronom€ocs are:

Aryabhata 46".3

Parashara 46".5

Varahamihira 50".0

Krishnamurti and Newcomb 50".24

Surya Sidhanta 54".0

Thus we see that astrologers adopi different Ayanamsas. Now an example of Chitrapakshiya Ayanamsa and Raman's Ayanamsa is considered. The first points of Aries coincided in 285 AD and 397 AD according to Chitrapakshiya system and Raman's system.

Difference = 397- 285 = 112 years.

Diff~rence in Aynamsas = 112 x 50".24 = 5626".88

= 93' 47" = 1° 33' 47"

There will a difference of 1 o 33' nearly in Nirayana longitudes


calculated by both the systems. A Navamsa is of 3° 20' and a Rashi is of 30°. Thus there will be a difference in 50% of Navamsa Kundlies and 5% of Rashi charts. When the Rashis .of Rashi chart and Navamsa chart differ, how can the same formulae be applied in prediction. Thus aynamsa becomes a vexed problem in l ndian Astrology.

14.11 Example of calculation of Aynamsa :

Find out Aynamsa on 1st December, 2002. Both the first points of Aries coincided on 22nd March, 285 A. D. so at that time Aynamsa was= 0

Difference from 1/12/2002 to 1/4/285 = 1717 years 8 months

= 1717.7 years.

Aynamsa = 1717.7 x 50.24 = 23° 58' 17" which is very nearto that of ephemeris which is 23° 53' 35".

14.12 Division of Zodiac:

There are 360° round a point. So there are 360° in the zodiac. These have been sub-divided in two ways (a) Twelve Rashies and each Rashi = 360° + 12 = 30° (b) 27 Nakshatras and each Nakshatra = 360 + 27 = 13° 20' = 800'.

Zodiac = 360°

1° = 60 minutes = 60'

1' = 60 seconds = 60"

The Tables of Rashi and Nakshatra divisions are :

Sl.No. Name of Rashi Indian Name Longitudes Rashi Lord

from to

1 Aries ry> Mesh 0' 30' Mars

2 Taurus ~ Vrisha 30' 60' Venus

3 Gemini II Mithuna 60' 90' Mercury

4 Cancer g; Karkata 90' 120' Moon

5 Leo Q Simha 120' 150' Sun

6 Virgo ll}l Kanya 150' 180' Mercury

7 Libra .n. Tula 180' 210' Venus

8 Scorpio m. Vrischika 210' 240' Mars

9 Sagittarius X' Dhanus 240' 270' Jupiter

10 Capricorn ':lo Makara 270' 300' Saturn

11 Acquarius ~

Kumbha 300' 330' Saturn·

12 Pisces X Min a 330~ 360' Jupiter


Sl. Nakshatra Longitudes Rashi Nakshatra

No. from to Nome from to Lard

I Asvini 00'00' 13'20' Aries 0'0' 13'20' Ketu

2 Bhami 13~ 20' 26' 40' Aries 13'20' 26'40' Venus

3 Krittika 26' 40' 40'00' Aries 26'40' - Sun Taurus - 10' 00'

4 Rohini 40'00' 53'20' Taurus 10'00' 23'20' Moon

5 Mrgasirsa 53' 20' 66'40' Taurus 23'20' - Mars Gemini - 6'40'

6 Ardra 66'40' 80'00' Gemini 6'40' 20'00' Rahu

7 Punarvasu 80'00' 93'20' Gemini 20'00' - Jupiter Cancer - 3'20'

8 Pcl.,.a 93'20' 106'40' Cancer 3'20' W40' Saturn

9 Aslesha 106' 40' 120'00' Cancer 16' 40' 30'00' Merrury

10 Magha 120'00' 133'20' l£o 0'00' 13'20' Ketu

11 Pclrvaphalguni 133'20' 146' 40' l£o 13°20' 26'40' Venus

12 Uttraphalguni 146' 40' 160'00' l£o 26'40' - Sun Vrrgo - 10°00'

13 Hast a 160'00' 173'20' Vrrgo 10'0tl' 23'20' Moon

14 Chitra 173'20' 186'40' Virgo 23'20' - Mars Libra - 6'40'

1S Svatl 186'40' 200'00' Libra 6'40' 20'00' Rahu

16 Visakha 200'00' 213"20' Libra 20'00' - Jupiter Scorpio - 3'20'

17 Anuradha 213'20' 226'40' Scorpio 3'20' !6'40' •turn

18 Jyestha 226'40' 240'00' Scorpio !6'40' 30'00' Merrury

19 Mula 240'00' 253'20' Sagittarius 0'00' 13'20' Ketu

20 Purvasadha 253'20' 266'40' Sagittarius 13'20' 26' 40' lknus

21 Uttarasadha 226'40' 280'00' Sagittarius 26' 40' - Sun Capri com - 10'00'

22 Sravana 280'00' 293'20' Capricorn 10'00' 23'20' Moon

23 Dhanistha 293'20' 306'40' CapricOrn 23'20' - Mars Acquarisis - 6''40'

24 Satbhisaj 306' 40' 320'00' Acquarius 6'40' 20'00' Rahu

25 Purvabhadrapada 320'00' 333'20' Atquarius 20'00' - Jupiter Pisces - 3'20'

26 Uttarabhadrapada 333'20' 346'4.0' PISces 3'20' W40' Saturn

27 Revatl 346'40' 360'00' Pisces 16'40' 30'00' Merrury

109

~ Retrogression of Planets

15.1 Before proceeding to analyse the retrograde motion of the planets, it is essential to know the geo-centric and helio-centric longitudes.

15.2 Geo-centric longitudes:

The longitudes of the places in zodiac where the planets are seen, in the ~ackground of the zodiac (constellations), by an observer at the centre of the earth are the longitude~ of the planets.

It is explained with the help of figure 22. Sun is in the centre of the figure, the circles from small to bigger ones are the orbits of Mercury, Earth, Jupiter and the zodiac. The orbits of other planets have not been shown. In the zodiac the degrees of geo-centric longitudes have been maked. oo is the Nirayana first point of Aries (Mesha). At any time the observer is at 0 on the centre of the earth, Mercury at M and Jupiter at J.

180" Fig.22


The Mercury is seen at M1

in the zodiac. The longitude of M1

is 315°, therefore, the longitude of mercury is 315°. Jupiter is seen atJ

1 in

the zodiac at 58° longitude, therefore, the longitude of Jupiter is 58° at that time.

The distance of planets from the earth is in crores of miles and the earth's radius is only 3950 miles which is negligible in comparison to the distance of the planets. Therefore, the longitudes of the planets as seen by the observer at the surface of the earth are taken as geo-centric longitudes.

15.3 Helio-centric longitudes :

Helio-centric longitudes are those seen by the observer as if he is at the centre of the sun. Such longitudes are never retrograde as the planets move around the sun and they will be ever increasing.

15.4 Sun and Moon are never retrograde:.

It has already been told in the solar system chapters that the earth is revolving around the sun and the Moon around the earth. Therefore, an observer at the earth (at the centre of the earth), will never see the sun and the Moon moving in backwards motion. It can be understood by the example of two persons, one standing and the other making a revolution of the 1st one. The moving person will always be seen forwarding in one direCtion, whether it may be clockwise or anticlockwise.

15.5 Retrogression of Inner Planets: .

The inner planets (Mercury and Venus) are those whose orbits are in between the Sun and the Earth's oi:bit. The sidereal periods of the Mercury and Venus are less than that of the earth. We take the example of Mercury whose sidereal period is 88 days and that of earth is 365.25 days. Due to this the angular velocity of Mercury is much faster than that of the earth. For simplicity we consider that the earth is stationary and the mercury is moving with its relative angular velocity with that of the earth.

It is analysed with the help of figure 23.

In figure 23 the sun is at the centre, earth is stationary at E. The inner circle is the orbit of Mercury, the middle one is of earth and outer one is zodiac. The arrows show the direction of their revolution and increasing of longitudes.

When Mercury was at A it was seen at A1

in the zodiac and its longitude was that of A1. When Mercury reached at B its longitudes had increased and equal to thatB1• Similarly at 0 equal to 0 1 atG equal to G1 but EGG

1 is a tangent to the .orbit of Mercury. The longitudes


Zodiac

Fig.23

were increasing upto this place or the Mercury appeared direct. After that it moved to Land was seen at L

1 in the zodiac. The longitude of L1

isless than G1.ltshows that the Mercury become retrograde afterG.lt

came to 82

and was seen at 81• Longitudes was that of 8

1 still retrograde.

After that it moved toM and H, its longitudes at those time were those of M1 and H1• Here EHH1 is again a tangent to the orbit of Mercury, after that its longitudes begins to increase. Mercury remained direct from H toG and retrograde from G to H. 8 2 sun B 8 1 is a straight line. At 8

2 Mercury is nearly in the middle of its retrogression. It is observed

that the planets actually do not move in the opposite direction but appear to move retrograde as explained above. lt may also be noticed that the planet is retrograde when it is nearer to the earth. lt may also be concluded that when the planet reaches at G or H it appears stationary as the change in lonqitudes is very small and for some time before and after G and H its rate of change of longitudes remain slow.

15.6 Retrogression of outer planets:

We take Jupiter for showing the retrogression of outer planets. Jupiter completes one revolution of the sun in approximately 12 years, while the earth completes it in one year, Therefore, the angular velocity of the earth is 12 times faster than that-of Jupiter. For simplicity we consider the Jupiter being stationary at one place and the earth inoving


with relative angular motion. It is explained with the help of figure 24.

J2

Fig.24

The st . .m is in the centre. The small circle is the orbit of the earth. The outer circle is path of Jupiter and the outer most arc is of zodiac. The arrows show the direction of revolution of the planets. The longitudes are increasing in the direction of arrow on the zodiac. Jupiter is at J. When the observer is on the earth at E1 jupiter is seen at J

1 and longitude

of jupiter is equal to that of J1

• When the observer moves to Ez, longitude of Jupiter is equal to J2 and the longitude has increased. At this time the longitudes of Jupiter and the sun are the same or Jupiter is in. conjunction with the sun. The observer moves to E

3 and E

4 the longitudes increases

to that of J3

and J4

. Here E4

J J4

is the tangent on the earth's orbit. Now the observer moves to E5 and longitudes become equal to J5 which is less than J

4• Hence the planet is said to have become retrograde. The

observer moves to E6 such that J2 J E6 S Ez are in a straight line. In this position the planet is nearly at the middle of its retrogression and irr opposition with the sun or the difference between the longitudes of the


planet and the sun is 180°, the longitude has further decreased. When the observer moves toE, and fa, the longitudes of the planet are further decrased and are equal to those of J

7 and J

8• Here J8 J E

8 is tangent to

the earth's orbit. The planet appears stationary for a few days when the observer is at E4 and fa as the rate of change of longitudes becomes very slow and for some days before and after these two positions the rate of change of longitudes remain slow.

It may be noticed that the planet or the earth !s not moving backwards but the planet appears to move in backwards motion. The planet becomes retrograde from E4 to E8 when it is nearer to the earth.

15.7 The inner planets have phases like moon. In figure 25 the inner planet appears full when it is at H. It appears more than half

0 H

A

Earth's orbit

Fig.25

114 Elements of r'\stronomy and Astrological Calculations

at D, half at C, less than half at B and not visible at A. The reason is that at H it is on the other side of the sun and the whole disc reflects the light of the sun and becomes visible while at A the dark side (which is not receiving light of the sun) is towards the earth. Similarly at B, C and D only the portion which is receiving light of the sun, is visible. ·

15.8 Phases of superior planets:

The superior planets must always appear either full or gibbous; for its orbit is outside the orbit of the earth. It appears full at conjunction or opposition. Its illuminated disc is always more than half towards the earth. The smallest portion of the planet will be seen when the sun and the planet subtend a right angle at the earth.

15.9 Brightness (Magnitude) of the planets :

The amount of reflected light received from a planet at the earth is the brightness of the planet/star. This reflected light is based on two things.

(a) If the distance of a planet from the earth is more, the light received from it will be less and the planet becomes brighter as it reaches near the earth. Brightness of light is inversely proportional to the square of its distance from the earth. If a source of light goes three times away than its earlier distance, the magnitude of light will be one-ninth of the original one.

(b) It depends also on the portion of the illuminated disc of the planet towards the earth. If more illuminated portion of the disc is towards earth, more light will be received on the earth.

15.10 Magnitude of inner planets:

We consider the case of Venus. When it is at superior conjunc· !ion, it is at maximum distance from the earth and at inferior conjunc· tion it is at the least distance. Diameter of its disc is 11" at superior conjunction and 66" at inferior conjunction or 6 times more than superior conjunction. At the time of inferior conjunction, a very small part of its illuminated disc is towards the earth or visible to the observer, while at superior conjunction the whole disc is normally visible. When. elongation angle of venus (the angle subtended by the sun and the venus at the earth) is 40°, it is maximum bright.

15.11 Magnitude of outer planets:

An outer planet is at the time of opposition appears like a full moon. The whole disc is visible and it is nearest to the earth. While at conjunction, though the whole disc is normally visible but it is at the


maximum distance from the earth its disc appears smaller also. In between these two positions, at quadrature (the angle subtended by the planet and the sun at the earth is 90°) it appears most gibbous.

15.12 Newton's Law of Motion:

Every body in this universe attracts every other body with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

MMI Foc-D2

Where M and M1 are the masses of two bodies and D is the distance between their centres. Let M be the mass of the earth and M1 of other planet which remain constant but the distance between the earth and planet changes from time to time. The force of attraction of the planet on the earth will be more when it is near and less when it is farther. The same way the changes in the radiation, electro-magnetic waves are observed.

15.13 E./feet of Inner Planets:

When the inner planets are retrograde (nearer to earth), theirforce of attraction, radiation from them, electro-magnetic force increases and as they move away, these effects go on decreasing. The reflected light goes on decreasing after a certain angle of elongation. When the planet is at inferior conjunction, the light received is nearly nil and the planet becomes stronger otherwise.

15.14 Effect of Outer Planets:

When the outer planets are retrograde, the earth is in between the planet and the sun. The planet is nearest at the middle of retrogression and its force of attraction etc. including its brightness is greatest. It may be the reason that the planets are considered as exalted, though they may be actually deblitated (as per classical text books).

lXVII Vimshotri Dasa

16.1 Casting of horoscope including the calculation of lagna at epoch has been told in previous chapters. To time the major events Dasa system, Gochara etc are used in Indian Astrology. Maharishi Parasar has narrated many types of Dasa-systems in his Brihat Parashara shastra. Vimshotri Dasa-syst~m is mostly in vogue.

16.2 Life span is considered of 120 years in this dasa system. Each planet is Lord of three Nakshatras. Its table is given below.

Sl.No. Lord Of Nakshatras Years of

Nakshatras dasa

1 2 3

1 Ketu Ashwini Magha Mula 7

2 Venus Bhami Purva Phalguni Purva Shadha 20

3 Sun Kritika Ultra Phalguni Ultra Shadha 6

4 Moon Rohini Hasta Sravan 10

5 Mars Mrigrhira Chitra Ghanishtha 7

6 Rahu Ardra Swati Shatbhisha 18

7 Jupiter Punarvasu Vishakha Purva Bhadrapada 16

8 Sa tum Pusya Anuradha Ultra Bhadrapada 19

9 Mercury Ashlesha Jyestha Revti 17

Total = 120 Years

The seriatim of Dasa is as above. The classical books give the formula to remember is Aa (Aditya or sun), Cham(Chandrama or moon), Bho (Bhaum means mangal or mars), Ra (Rahu), Ji (Jiva or Jupiter), Sha (Shanishchar or saturn), Bu (Bu!iha or Mercury), Ke (Ketu)and Shu (Shukra or Venus).

The rashi in which the moon of the native is posited is called his Rasi. similarly the nakshatra in which moon is posited is known as Nakshatra of the native. Let the moon be 6° of sigittarius(Dhanu) and in Mula Nakshatra, the Rasi and Nakshatra of the native will be called as Dhanu Rasi and Mula Nakshatra.

16.3 r'Jter sun the moon is most influencing the earth and


especially the human beings. Life on the earth cannot be imagined without the sun. The moon is the significator of mind and influence us very much. Accordingly, our Rishies and Munis based this Vimshotri dasa system on the Nakshatra of the moon.

16.4 Vimshotri Dasa and Antar Dasa periods :

One Nakshatra is equal to 13°20' = 800'. Dasa of the lord of Nakshatra in which the moon is in the horoscope is running at that time. The ratio of the Nakshatra to be covered by the moon to the whole Nakshatra (800')is the ratio of the period of Dasa balance with the whole period of that Dasa. For example, let the moon be 16°40' of Leo at the time of birth of the native. The moon was in Purva Phalguni Nakshatra and moved 3° 20' or the balance of the nakshatra to be moved was 13° 20'-3° 20'=10° = 600'. Lord of Purva Phalguni is Venus whose dasa period is 20 years.

800 : 20 : : 600 : X

or x = 20 x 600 + 800 = 15 years So the Dasa balance at birth is of Venus for 15 years. Venus Dasa

shall be followed by the Dasas of Sun, Moon, Mars, Rahu etc.

16.5 Example: Find out the dasa of Horoscope of example 1 of para 12.3 of a native born at Delhi at 10:25 AM on 25th September 2001.

Solution:

Longitude of Moon = 8' 17"27'

or the Moon has moved Purva shad a Nakshatra 17° 27'- 13° 20' = 4° 7' = 247' and its lord is Venus whose dasa period is 20 years. Balance of Purvashada to be moved =800'- 24 7' = 553'

Balance dasa period is 800: 20 :: 553: x or x = 20 x 553 + 800 = 553 + 40 years

33 = 13-40

33xl2 = 13 years + ~ months

= 13 years 9.9 months = 13 years 9 months 27 days.

:. The balance dasa is of Venus for 13 years 9 months 27 days. Now we find out with the tables in the Ephemeris at page-106.

The rasi of the native is Dhanu which falls in the first column. Against 17°20' we find in lst column == Balance of Venus 14Y' 0"' Od

yr stands for year, m stands for months and d for. days.


For 7' see proportional parts -0 2 3 under Venus (P-107)

(It is minus as the balance is reducing ).

Total = 13 9 27 (A)

Day Month Year

Date of birth 25 9 2001

Balance of Venus dasa(A) 27 9 13

Venus dasa up to = 22 7 2015 (considering a month of 30 days) Period of Sun's Dasa = 0 0 6

End of Sun's Dasa 22 7 2021

Period of Moon's Dasa = 0 0 10

End of Moon's Dasa 22 7 2031

"' on and so forth

16.6 Antardnsa (Sub-period) :

The first sub-period will be of the planet whose Dasa is running and Vi ill be followed in the seriatim as for dasas. The sub-period will be in proportion to the number of years allotted to the planet in 120 years. Sun's Period is 6 years. The sun'sAntardasa (sub-period) in sun's dasa

6 6 (6 Years)=

120 of its period =

120 X 6.

If we have to find out the sa turns sub-period in sun's dasa, it shall

be= 6x19 = 114 years= 114x12 months 20 120 120

114 4x30 = lO months = 11.4 month = 11 month -w days = 11

months 12 days. Its table is given in emphemeris at page 108.

16.7 Now we concentrate again at the end of para 16.5 and to find out dasa and antar dasa running at the time of birth.

Venus dasa ends on

Period of venus is 20 years

D M Y 22 7 2015

(-)20

.Date of starting Venus Dasa = 22 7 1995 which is before birth From tables Dasa Sub-period

Venus Venus 0 4 3


22 11 1998

Venus Sun 0 0 1

22 11 1999

Venus Moon 0 8 1

22 7 2001

Venus Mars 0 2 1

22 9 2002

The date of birth falls in the Venus /Mars sub-period so the dasa of Venus and antardasa of Mars was running at the time of birth which ends on 22 Sept 2002.

16.8 Pratyantar Dasa (Sub-sub Period) :

The way in which we have calculated antardasa in a dasa, the pratyantar dasa will be found in the same manner from the antardasa. The first sub-sub period will be of the planet whose sub-period is running. The duration of sub-sub period will also be in proportion to the period of planet to 120 years of the sub-period.

Example:

Find out the sub-sub period in Rahu's antardasa of Example 16.7 20x18

Venus dasa, Rahu's antardasa = m-- = 3 Years

3xl8 Time period of Rahu Pratyantar in Rahu's Antar = -- Yrs

120 . 54

= 120

X 12 months = 5.4 months = 5 months 12 days

3x16 48 Jupiter's Pratyantar Dasa = 120=

120 = 4.8 months = 4

months 24 days

Similarly one can proceed further :

Dasa antardasa pratyantar Dasa Day Month Year

Venus Rahu Rahu begins = 22 9 2002 Period for Rahu = 12 5 0

Venus Rahu Jupiter begins 4 3 2003 Period of Jupiter = 24 L1· 0

end of Jupiter (sub-sub period) = 28 7 2003 or beginning of Saturn's sub-sub pefod.

Similarly we can proceed further.

lXVIII

Bhava Spastha

17.1 As has already been told that the zodiac is of 360° and it has been divided into 12 rasis of 30° each. Every bhava or house is not of equal angle. So it is esssential to know the extension of a house. Some house is of 25° while the other is 35°.

Ascendant and tenth cusp are to be found out for finding the extent of the bhavas or houses. Mostly this system of division is followed. There are difference of opinion in finding out the extent of the houses. Many learned persons consider all the bhavas equal or of 30° each.lf the ascendant (Middle of first bhava) is zoo Jamini, the middle of second bhava will be of zoo Cancer, the middle of third bhava will be of zoo Leo etc. In this system there is no necessity of finding out the tenth cusp (Medium coeli or M.C.).

17.2 Tenth cusp (Dasam lagna) :

The point of intersection of the meridian of a place to the ecliptic at any time, is the tenth cusp of that place at that time. The right ascension (R.A.M.C) of that time is the sidereal time at that time It is found out like ascendant is found out from sidereal time with the help of table of the tenth house given in the table of ascendants or from 121-125 of Lahiri's ephemeris. Latitude do not make any difference. it is the same for the whole of the meridian.

17.3 Table of Bhavas :

Bhava tables are also avaible in the market, like table of ascendants, the longitudes of middle of tenth , eleventh, twelth, first, second and third bhavas are given. Adding six rasis or 180° we get the cusps of JV, V, VI, VII, Vl!l, and IX bhavas.

The point wl.ere a bhava ends and the other bhava starts is called Sandhi Ounction of the later bhavas). The extension from X cusp to I cusp consists of later half of X, eleventh, twelfth and first part of first house. This lor.gitudinal distance is divided by six . Addition of this sixth part into X cusp gives the sandhi of XI house. By adding the sixth part successively we get XI cusp, XII sandhi, XII cusp, I sandhi and I cusp. Subtracting this sixth part from 30° we get the sixth part for addition


into first cusp. On addition sucessively we get II sandhi , II cusp, III sandhi, III cusp, IV sandhi and IV cusp = lOth cusp+6 signs. Please notice that the extension of I, IV, VII, and X bhavas are always equal to 30°, while the other bhavas are more or less than 30°.

17.4 Now the division of houses of horoscope given in example-I of para 12.3 will be done. In this example the native was born at Delhi on 25 Sept 2001 at 10:25 AM (I.S.T).

The ascendant =7'2° 26' and sidereal time= 10h 20'" 13'

Solution:

(Ephemetis-2001 page- 124)

X Cusp at 10h 21 rn = 4' 100 19'

X Cusp at 10h zorn = 4 10 3

Differe nee in 1 rn = 0 0 16

difference in 13' = 0 0 3

X Cusp at 10h zorn 13' = 4' 10° 3' + o· 0° 3' = 4' 100 6'

Aynamsa correction =-0 0 53

X Cusp = 4 9 13

Longitude of Ascendant = 7 2 26 (A)

Less Longitude of X Cusp = 4 9 13

Arc of 3 bhavas = 2 23 13

Dividing it by 6 we get = 0 13 5210"

The Bhavas are :

X Cusp (Madhya) = 4' 9" 13' 0"

adding one sixth part = +0 13 52 10

Xi sandhi = 4 23 5 10

= +0 13 52 10

XI Cusp 5 6 57 20

= +0 13 52 10

XII Sandhi = 5 20 49 30

= +0 13 52 10

XII Cusp = 6 4 41 40

= +0 13 52 10


I Sandhi = 6 18 33 50

= +0 13 52 10

I Cusp (it agrees with A) = 7 2 26 0

Now add 30°-13° 52' 10" = 16° 7' 50" from I Cusp to IV Cusp.

I Cusp = 7' zo 26' 0''

+0 16 7 50

II Sandhi = 7 18 33 50

+0 16 7 50

II Cusp = 8 4 41 4D

+0 16 7 50

III Sandhi = 8 20 4g 30

+0 16 7 50

Ill Cusp = 9 6 57 20

+0 16 7 50

IV Sandhi = g 23 5 10

+0 16 7 50

IV Cusp = 10 g 13 0

Please note that X Cusp + 6 sign = 4' go 13' + 6' = 10' go 13 which agrees.

By adding 6 sign in the above we get the 7th house fro~ them.

IV Cusp = 10' go 13' 0"

VSandhi = 10 23 5 10

VCusp = 11 6 57 20

VI Sandhi = 11 20 49 30

VI Cusp 0 4 41 4D

VII Sandhi = 0 18 33 50

VII Cusp = 1 2 26 0

VIII Sandhi = 1 18 33 50

VIII Cusp = 2 4 41 4D

IX Sandhi = 2 20 4g 30

IX Cusp = 3 6 57 20

X Sandhi -· 3 23 5 10

X Cusp = 4 g 13 0


RasiChart BhavaChart

RasiChart BhavaChart

Saturn Jupiter Rahu

v VI VII

IV

Venus III

Ketu v Mars Mer Sun Moon A

Ketu Mer Mars II I Moon XII

The 11 Bhava is from 7' 18° 33' 50" to 8' zoo 49' 30" Longitude of Moon is 8' 17° 27'

Longitude of Mars is 8 15 13 Longitude of Ketu is 8 8 01

Sat Jup IX

Rahu

IX

X Venus

Sun XI

These are within the upper and lower limits of 11 Bhava, so they remained in second Bhava.

VIII Bhava is from 1' 18° 33m 50' to 2• 20° 49' 30" Longitude of Saturn is 1' 21° 5' Longitude of Jupiter is 2 19 30

Longitude of Rahu is 2 8 01


These are within the upper and lower limit of VIII Bhava. In tGsi chart, Jupiter & Rahu were already there but Saturn was in VII house. Though it appears to be in the VII house but actually it is in VIII house as per bhava chart. Rasi of Saturn will remain the same (Taurus), only the bhava has changed.

Results of planet are according to their position In the bhava, but most of the astrologers only see the Rasl chart. Readers may see as per their own experience.

lXVIII I Divisional Charts (Shodash Vargas)

18.1 Readers are well acquainted with the zodiac of 360°, Rasi of 30° and 27 Nakshatras of 13° 20'=800' each. The parts of zodiac that are formed by dividing a Rasi in equal parts differently are called Vargas. Each divisional chart (Varga Chart) is symbolic of certain aspect of human life. Sodash Vargas (Sixteen divisional charts) are of great significance. These have been described in Parashara Hora Shashtra. Some astrologers use six vargas, some seven vargas, some ten Vargas, and some Sodash Vargas.

18.2 Their names are:

Shad Vargas ie six charts are: Lagna, Hora, Drekkana, Navamsha, Dwadshamsa, Trimshamsa.

Sapt vargas or seven charts are:

These include Saptamsa along with the Shad vargas.They are Lagna (D/1), Hora (D/2), Drekkana (D/3), Saptmansa (D/7), Navamsa (D/9), Dwadashamsa (D/12), and Trimshamsa charts(D/30).

Dash Vargas or Ten Charts :They are the above seven charts plus Dashmansa(D/10), Shodashamsa (D/16) and Shashthyamasa (D/60)charts.

Shodash Vargas or sixteen divisional charts:

It includes Dash vargas along with chaturthamsa (D/4), Vinshamsa (D/20), Chaturvinshamsha (D/24), Saptvinshamsa (D/27) Khavedamsha (Chatvarishamsa) (D/40), and Akshavedamsa or Panch-Chatvarishamsa (D/45).

Here notation D/20, D/i7, etc have been used. D means division and 20 or 27 means 20 or 27 divisions of a sign. So D/20 means twenty divisions of a sign.

18.3 Different aspects of life are indicated by different divisional charts as under :

(1) Lagna/Rasi chart (D/1) :The significations of first bhava such as complexion, features, structure of the body etc.

126 · · - Elements of AStronomy and Astrological Calculations

(2) Hora Chart (D/2) :-Significations of second bhava such as wealth, family, prosperity etc.

(3) Drekkana chart (D/3) :-Significations of third bhava such as brothers, sisters etc.

(4) Chaturthamsa (D/4) :-Significations of fourth bhava such as moveable and immoveable properties, assets, education, luck etc.

(5) Saptmansa (D/7) :-Children, grandchildren etc.

(6) Navamsa (D/9):-Strength and weakness of planets, spouse etc.

(7) Dashmansa (D/ 1 0) :-Significations of tenth house, honour achievements in life and profession etc.

(8) Dwadshmsa (D/12):-Parents and their happiness etc.

(9) Shodashmsa (D/16):-Happiness, fulfillment or desires, con-veyances etc.

(1 0) Vinshamsa (D/20) :-Scientific and spritual uplift etc.

(11) Chaturvinshamsa (D/24) :-Knowledge, education etc.

(12) Saptvinshamsa (D/27):-Strength, troubles etc

(13) Trimsamsa (D/30):-Happiness and miseries in life, accidents etc.

(14) Chatvarishamsa (D/40) :-Good or bad results in general to the native.

(15) Panch-chatvarishamsa(D/45)}A·ll other indication~ ~ap-.

(16) Shasht amsa (D/601 ?mess, :~rrows, auspicious; Y ' mauspicious etc. ·

18.4 Method of preparing varga charts :

There are different opinions for preparing the varga charts and several methoods are in vogue. We shall be following the method which is folllowed by B.V: Raman, and majority of the astrologers and is described in Parashar Hora Shashtra.

Tables for the chacts are given in Appendix II. The charts can be prepared with the help of tables without calculations. Planets are to be posted in the Rasis for the longitudes in the Rasi charts.

(1) Lagna Kundli or Rasi Chart (D/1) :This is the rasi chart which is prepared for the birth/event/prashna time. Remaining fifteen charts are based on this chart. The horoscope of the native born at Delhi on 25 Sept. 2001 at 10:25 AM (I.S.T) given in example 1 of para 12.3 is taken for example.


D/1 Rasi chart Rasi chart D/1

Saturn Jupiter Rahu

Venus

Kelu ~ Moon Asc, Mercury Sun Mars .t

Note:-Longitude of jupiter is a bit more than 19° 30' so it has been taken here as 19° 31'.

(2) Hora chart : Each rasi is divided into two equal parts of 30~2=15° each. First part or hora is from oo to 15° and second part from 15° to 30°.

In odd sign or rasis {Aries, Gemini, Leo, Libra, Sagittarius, and Aquarius).

{a) Ruler of first part or hora is sun {Leo rasi).

(b) Ruler of second part or second hora is moon {Cancer rasi).

Hora Chart (D/2)

7

Asc 4 Sun Moon Mars Jupiter

5 Mer Ketu Sat Rahu Venus

128 Elements of Astwnomy and Astrological Calculations

In even signs (Taurus, Cancer, Virgo, Scorpio, Capricorn and Pisces).

(a) Ruler of first part or first hora is Moon(Cancer rasi)

(b) Ruler of second part or second Hora is Sun (Leo sign)

For example horoscopE::. hora chart is casted as on pre-page:

Ascendant is in the first part of scorpio which is even sign, the ascendant of the hora chart willl be Cancer as the first part of even signs is ruled by Moon. Mars is in the second part of saggitarius(odd sign) and ruler of this hora is moon, so it will be posted in Cancer sign. Similarly all the planets will be posted in the Hora chart.

(3) Drekkana chart (Dreshkon Chart)(D/3) ; Each rasi is divided into three equal parts of 10° each. In case a planet is in the first part or first drekkana (0° to 10°), the planet will be posted in the same sign in which it is in the Rasi chart{D/1). If the planet is in the second drekkana (10° to 20°), it will go to fifth sign from that of rasi chart {D/1). In case the planet is in the third drekkana (20° to 30°) it will be placed in the ninth sign from the sign of rasi chart.

In the example horoscope ascendant is in the first drekkana of Scorpio, so the lagna of the Drekkana chart becomes Scorpio. Jupiter is in the second part of Gemini sign, it will go to fifth sign from it or Tula (Libra) sign in Drekkana chart. Saturn is in the third drekkana of Taurus sign in rasi chart. It will be posted in ninth rasi from Taurus or Capricorn in the drekkana chart. The Drekkana chart is as under:

D/3 chart D/3 chart

Moon Rahu

Mars

Sat

!;';' Ketu Asc, Mer

Sun Venus Jup

h

(4) Chaturthamsa or Turyamsha (D/4): Each rasi is divided into four parts of 30° 7 4 = 7° 30' each. If the planet or ascendant is in the first part, it remains in the same sign, in case of second part, it goes to fourth sign, in case of third part in the seventh sign and for fourth part in the tenth sign. In the example horoscope the ascendant is


in first part , so the ascendant will remain in Scorpio sign. Venus is in second part of Leo. It is shown in fourth sign from Leo or Scorpio sign Saturn is in third part of Taurus. it is posted in seventh sign from it or Scorpio.

The chaturthamsa chart becomes:-

D/4 chart D/4 chart

Ketu Moon Mars

Sun V Asc,

Jup \fen Mer Rahu Sat .h

(5) Saptmansha chart (D/7) : Each rasi is divided into seven equal parts of 30°7 7 = 4° 17'. The remaining 1' is added in the last part which becomes 4° 18'. Parts of the odd rasis are counted from that rasi and in even rasis saptmanshas are counted from the seventh rasi in which the planet or lagna is in the rasi chart (D-1).

D/7 chart D/7 chart

Mars Moon v

Sat Sun Asc,

.h

Rahu

· Ketu

Mer If en Jup

In the example horoscope ascendant is in the first saptmansha of scorpio sign which is an ever. sign. So the ascendant will be in the


seventh sign from Scorpio that is Taurus. Mars is in Sagittarius 15° 13' (fourth saptamansha) which is an odd sign. So Mars goes to fourth sign from Sagittarius, which is Pisces. Saptmansha chart can also be casted with the help of tables in appendix II.

(6) Navmansa Chart (D/9) :Each rasi is divided into nine equal parts (Navmansa) of 30°+9=3"20'=200'. Zodiac contains 360° and 12 Rasi x 9= 108 Navmansas. Four rasis or 120° have 4 x 9 =36 navmansas. Every navmansa is givC?n one sign in seriatim, three rounds of signs are completed in 36 navmansas. Every fifth rasi will have the same Seriatim as is earlier. Thus it is seen that first navmansa of fiery signs ( 1, 5, 9 rasis) will be of Mesha (Aries), second of Taurus and so on; the last navmansa will be Dhanu (Sagittarius). The first navmansa of earthy signs (2, 6, 10 rasis) will be of Capricorn sign (Makar) because the first nine navmansa have been covered by signs 1, 5 and 9. The navmansas of watery signs (3, 7, 11 rasis) will start from Tula (Libra) and of airey signs (4, 8, 12 rasis) from Cancer navmansa. Navmansa chart can also be prepared with the help of tables in Appendix ll.

In the example horoscope the ascendant is in the first navmansa of Scorpio sign, which is of airey sign hence it goes to Cancer sign.

The navmansa.horoscope is as under:

D/9 chart D/9 chart

Sun Ketu Jup

V Asc, Sat

\len~~

Mars

Rahu Mer Moon

(7) Dashmansa chart (D/10) :Each rasi is divided into ten equal parts of 30° + 10 = 3° each. Dashmansa is counted from the same sign in case the sign is odd and for even signs it starts from the ninth rashi. Its chart is also in Appendix 2.

Ascendant is in the first dashmansa of Scorpio which is of even sign, so the ascendant of dashmansa chart will be ninth from it or Cancer sign.


Dashmansa chart of the example horoscope is :-

D/10 chart D/10 chart

Mars Moon

~

Ketu Asc, Sun

~

Rahu Sat

Jup Mer Ven

(8) Dwadshamsa Chart (D/12) :Each rasi is divided into twelve parts of 30° + 12 = 2°30'. Counting of Dwadshamsa starts from the rasi in which the ascendant or planet is posited. In the example horoscope ascendant is in the first dwadshamsa of Scorpio, so the ascendant of dwadshamsa chart is Scorpio. Moon is in the seventh dwadshamsa of Sagittarius sign. Seventh sign from Sagittarius is Gemini. Hence the moon goes to Gemini sign in Dwadshamsa chart. The dwadshamsa chart of the example horoscope becomes :


Ketu Moon Mars

Sat Jup

~ Sun Asc, Rahu Ven Mer

~

(9) Shodashamsa Chart(D/16) :Each sign is divided into sixteen parts of 30°+ 16=1°52' 30"


Twelve signs are divided into 12 x 16=192 parts and the parts are alloted signs in seriatim. The first to sixteen parts are of Aries and 17th to 32nd are of Taurus and so on. The shodashamsas of Aries start from Aries and go upto Cancer after completing one round. The 1st shodshamsa of Taurus will be of 17- 12 = 5 or Leo (next to Cancer the last Shodshamsa of Aries) and the last Shodshamsa of Taurus is of Scorpio. The first shodshamsa of ,Jemini starts from 33 - 24 = 9 or Sagittarius and of Cancer starts from 49 - 48 ~ 1 or Aries. It results that moveable (Char) rasi's first shodshamsa is Aries, fixed (sthir) rasi's shodshamsa starts from Leo and dual rasi's shodshamsa starts from Sagittarius.

In the example horoscope the ascendant is in second shodsh::~msa of Scorpio which is a fixed sign. The shodshamsa starts from Leo, the second shodshamsa is of Verga sign. Hence Verga sign becomes the ascendant of shodshamsa chart. Jupiter is in the eleventh shodshamsa of Gemini, a dual sign. The first shodshamsa of a dual sign is Sagittarius and the eleventh sign from it is Libra. So Jupiter goes to Libra sign. These can be found out from the table given in appendix ll.

Shodshamsa chart D/16

Sun Rahu Mer Ketu

Sat

Ven Mars

v Jup

Asc,

Moon,&

(1 0) Vimshamsa chart (D/20) :Each sign is divided into twenty equal parts of 30° +- 20 = 1 o 30'. In zodiac or twelve rasis the Vimshamsas are 12 X 20 = 240. In Aries the first vimshamsa is of Aries. In Taurus the first vimshamsa is (20 + 1) + 12 = remainder 9 representing Sagittarius and in Gemini the first vimshamsa is (40 + 1) +- 12 = remainder 5 or Leo sign. The Vimshamsas in {char) moveable signs starts from Aries, in fixed {sthir) signs start from Sagittarius and in dual


signs start from Leo.

In example horoscope the ascendant is in second Vimshamsa of Scorpio, a fixed sign, therefore ascendant's sign is Capricorn (second to Sagittarius}. Mars is in eleventh Vimshamsa of Sagittarius (dual sign} and as such it goes to Gemini sign (eleventh sign from Leo sign). These could be computed from the table also.

Vimshamsa chart (D/20}

Mars Mer

Sat Moon \len

V Asc. Rahu Ketu Sun/}

Jup

(11) Chaturvimshamsa (Siddhamsa) Chart (D/24) :Each sign is divided into twenty-four equal parts of 30° + 24 = 1 o 15' each. The first chaturvimshamsa of odd signs is Leo sign and for even signs it is Cancer sign.

Chaturvimshamsa chart of example horoscope is as under :


Ven

Ketu Rahu

v Sun Asc.

Mars A

Sat Jup Mer Moon


(12) Sapt-Vimshamsa (Bhamshamsa) Chart D/27; Each sign is divided into twenty-seven equal parts of30° +27 = 1° 6' 40".ln zodiac or twelve signs there are 12 x 27 = 324 sapt-vimshamsas. These are in seriatim. The fiery signs (Aries, Leo and Sagittarius) the saptvimshamsas start from Aries, in earthy signs (Taurus, Virgo and Capricorn) start from cancer, in airy signs (Jemini, Libra and Aquarius) start from Libra and in watery signs (Cancer, Scorpio and Pisces) start from cancer.

D/27 chart for example horoscope is :

D/27 chart D/27chart

v Asc. Mars Jup

A Rahu

Sun Moon Ven

Mer Sat

Ketu

·-

(13) Trimsamsa chart (D/30) :Each sign is divided into thirty parts of 30° + 30 = 1 o each. The lords in odd signs (Aries, Gemini, Leo, Libra, Sagittarius and Aquarius) and even signs (Taurus, Cancer, Virgo, Scorpio, Capricorn and Pisces) are as under :

(a) In odd signs Mais, Saturn, Jupiter, Mercury and Venus rule 5, 5, 8, 7 and 5 parts successively. The planet in odd sign will be placed in the odd sign of the above rulers in the Trimsamsa chart.

(b) In even signs Venus, Mercury, Jupiter, Saturn and Mars rule 5, 7, 8, 5 and 5 parts successively. The planet in even sign in the original chart will be placed in the even sign of the above rulers in the Trimsamsa chart.

Trimsar.1sa chart (D/30) of the example horoscope is :


D/30chart D/30 chart

v Mer Asc. Jup

h

Rahu Ketu

Sat

Moon Mars Sun Ven

(14) Chatwarishamsa (Khavedamsa) chart (D/40): Each sign is divided into 40 equal parts of30° + 40 = 45' each. In odd signs the chatwarishamsa will start from Aries sign and in even signs from Ubra sign. Chatwaishamsa (D/40) of the example chart is :

D/40chart D/40chart

Moon Jup Ven

Rahu Ketu Sat

v As c. Mer

~

Mars Sun

(15) Akshavedamsa (Panchchatvarishamsa) chart (D/45) : Each sign is divided into 45 parts each of 30° + 45 = 40' each. Akshavedamsa starts from Aries in moveable signs, from Leo in fixed signs and from Sagittarius in dual signs. Lords of moveable signs are

· Brahma, of fixed sigil.are Shahker and of du<'l signs are Vishnu. ·

Panch chatvarishamsa chart (D/45) of example chart is :


D/45 chart D/45chart

Sat Jup

Moon

.

Rahu v Ketu Asc. Mars Mer Sun Ven A

(16) Shashthlamsa chart (D/60) :Each sign is divided into sixty parts of 30° + 60 = 30' each. There are 12 x 60 = 720 shashthiamsas in the zodiac. Each sign has the first shashthiamsa of that sign. The fifth shasthiamsa of Gemini will be fifth from Gemini or Libra.

Shashthiamsa chart (D/60) of the example horoscope is :

D!60chart D/60chart

(/

As c. Ketu Mer Mars Ven

A

Sun

Sat Moon Jup

Rahu

lXIX I Panchanga

19.1 Panchanga is a sanskrit word which consists of two words 'Panch'+ 'Anga'. Panch means five and Anga means parts, Therefore, Panchanga means five parts. The same are :

1. Weekday (Vara)

2. Lunar date (Tithi)

3. Constellation (Nakshatra)

4. Karana

5.Yoga

19.2Vara:

It has been told earlier in para 5.2, that the names of weekdays were kept after the name of the lord of the first hora of the day. In Indian Astrology; the day is from one sunrise to the next sunrise. So, a Vara is also from one sunrise to the next. How to find out vara of the day by the Indian as well as Western methods is given below.

19.3lndian System:

Arahgana means one day which consists of a day and night (24 hours). The name of a week day is found out by dividing the Sristhyadi Arahgana (number of days from the beginning of the world) by seven. The remainder shows the day of the week. This number becomes very big, therefore, a short cut method is to find it out by dividing Ketki Arahgana by seven and the remainder represents the week day. Remainder seven or zero is for Sunday, 1 for Monday, 2 for Tuesday, 3 for Wednesday, 4 for Thursday, 5 for Friqay and 6 for Saturday.

Example:

At page 72 of Vishwvijay Panchanga Ketki Arahgana for Marg5hirish Krishna Ashtmi for the year 2002-2003 is 3889 (it is written above the 1st horoscope), Dividing it by 7 the remainder is 4, which stands for Thursday. It tallies with the Panchanga. Ketki Arahganas are


given after 7 or 8 days. In case the day of a week in between them is to be known, add or substract the number of days from the day for which Arahganas are given and if it is earlier, substract the number of days. As if we want to find out the day for Margshirsh Krishna Panchmi which is 3 days earlier to Ashtmi, the Ketki Arahgana will be 3889-3 =3886 and dividing by 7 the remainder is 1 which shows that the day is Monday.

19.4 Western Calender Method:

Tropical year (refer para 5.11) is of 365.2422 days. If this figure is multiplied by 100, 200, 300 or 400, we don't get the complete number of days in these years. Therefore, a calender year was adopted of 365.2425 days (which is very near to 365.2422 days).

According to Julion Calender a year was of 365 days and the years which are divisible by four without remainder will be a leap year (366 days).ln this calender an error of 3 days would accumulate in 400 years.

Hence Pope Gregory XIII, in 1582, introduced a new calender according to which the years divisible by 4 will be leap years but the centuries which are not divisible by 400 will not be leap year. Thus he rectified the e'rror of 3 days in 400 years. In this new calender years 100, 200, 300, 500, 600, 700, 900 etc are not leap years but 400, 800, 1200, 1600, 2000 etc are leap years.

According to this new calender there will be a difference of 3 days in 10,000 years or one day in 3333 years approximately.

oneyear = 365.2425days

100years = 36524.25days

400years = 146097 days

146097 days is divisible by 7 11nd leaving no remainder. So the same day will be on the same date after 400 years. The week day on 2nd January, 1601 was the same as was on 2nd January 2001 i.e. Tuesday.

In one year of 365 days the number of days more than completed weeks

= 365 + 7 = 1 day (remainder)

In 100 years of 36524 days the number of days more than completed weeks

= 36524 + 7 = 5 days (remainder)


ln 200 years, the number of days more than completed weeks

= 5 x 2 + 7 = 3 days (remainder)

In 300 years, the number of days more than completed weeks

= 5 x 3 + 7 = 1 day (remainder)

Now an example for finding out the week day is given below :

Example:

We have to find out the week day on 15th March, 1998. The number of completed years is 1997.

Remainder

In 1600 years, the number of days more than completed weeks = 0

In 300 years, the number of days more than completed weeks = 1

In 97 years, the number of days more than completed weeks = 97 + 7 = 6

In 97 leap years (complete days) = 97 + 4 = 24

Number of days from 1st January to 15th March 1998 = 74 + 7 and remainder = 4

Total =· 35

Dividing 35 by 7 the remainder is zero (Sunday). The remainder 0 or7 stands for Sunday, 1 for Monday, 2 for Tuesday, 3 for Wednesday, 4 for Thursday, 5 for Friday and 6 for Saturday.

19.5 Tithi:

the angular velocity of the Moon is faster than the sun as the Moon completes one revolution in 27.321 days and the sun in 365.25 days. When the longitudes of the sun and the Moon are same, it is the ending time of Amavasya. A Lunar month is the time period from one Amavasya to the next Amavasya or from the end of one Pumima to the end of next Pumima and it is of 29.53 days (which is the synodic period of the Moon). In this period Moon covers 360° more than the Sun and there are 30 Tithis in this period. So one Tithi is completed

360 when the Moon moves ahead of the sun by

30 = 12°.

The following table shows tithis alongwith the longitude of the . Moon minus longitude of the sun.


Sukla Palasha (Bright Halj) Krlshon Palasho (Dork Holj)

Number Nome of Longitudes Number Name of Longitudes

of Tlthl of of Tlth! of

Tlthl Moon-Sun T!thl- Moon-Sun

1 Pratipada o· to 12° 16 Pratipada 1800 to 192•

2 Dwitya 12• to 24• 17 Dwitya 192• to 204•

3 Tritya 24• to 36• 18 Tritya 204• to 216•

4 Chaturthi 36• to 48° 19 Chaturthi 216• to 228•

5 Panchmi 48• to 600 20 Panchmi 228• to 2400

6 Shashthi 60• to n· 21 Shashthi 240• to 252•

7 Saptmi n· to 84° 22 Saptmi 252• to 264•

8 Ashtami 84• to 96• 23 Ashtami 264° to 276°

9 Navmi 96• to 108• 24 Navmi 276• to 288·

10 Dashmi lOS• to 1200 25 Dashmi 2ss• to 3000

11 Ekadashi 120• to 132• 26 Ekadashi 3000 to 312•

12 Dwadashi 132• to 144• 27 ' Dwadashi 312• to 324• ' 13 Triyodashi 144• to !56• 28 Triyodashi 324• to 336•

14 Chaturdashi !56• to 168 29 Chaturdash 336• to 348•

15 Purnima 168• to ISO• 30 Amavasya 348• to 360•

The angular velocity of the sun varies from 57' to 1°1' approximately per day while that of the Moon varies from 15° plus to 12° minus per day. When they are at perigee the angula~ velocity is more and on apogee velocity is less than the average velocity. Due to this reason the

- difference between the longitude of the moon and the sun varies from 14 o to 11 o per day. A tithi changes after every 12° difference of their longitudes. When this difference is about 12° - 1 o = 11 o per day, the duration of tithi is of more than 24 hours. When this difference is about 15°- 1° = 14°, the duration of tithi becomes less than 24 hours.-A lunar month is of 29.5 days, while the average solar month time period is 30.44 days.

Due to above reasons a tithi can start at any time of the day. In case erne tithi ends at 11 AM and the other starts, which tithi should be taken for that day. Hence it was decided that the tithi at the time of sunrise (whether it may remain for a short time) should be adopted as the Tithi for the whole of the day. For example, if Chaturthi ends after one minute of the sunrise, the tithi for the day will be called ChaturthL In case tithi starts 2 minutes b-efore the sunrise and ends 5 minutes after the sunrise of the next day, this tithi will be for two days. It will be a case of gaining a tithL It happens when the Moon's


angular velocity is slower than average velocity.

Many times it happens that a tithi starts a few minutes after sunrise and ends before next sunrise that tithi is called lost (Kshaya). It happens at the time, when the Moon's angular velocity is fast.

The formula for finding out a tithi at any time is (longitude of Moon- Longitude of the sun)+ 12. The longitudes are in degrees. The quotient gives the number of tithies passed. Quotient + 1 is the tithi running at that time.

Let the Moon's longitude be 6• 10° 5' and of the sun 5• 6° 7'

The Tithi at that time is to be calculated.

6• 10° 5'- 5' 6° 7' = 190° 5'- 156° 7' = 33° 58'

(as 1 sign = 30 degrees)

gos8' Tithi at that time = 33° 58' + 12 = 2 ---u-lt shows that two tithis were completed and the third was

running at that time. The third tithi has also passed 9° 58' out of 12°.

19.6 Example of losing (Kshaya) of a tithi :

The time of sunrise at Delhi on 15th Oct, 2001 = 6:26

The time of sunrise at Delhi on 16th Oct, 2001 = 6:26

16th October, 2001 at 5:30AM


Motion in 24 hours

longitude longitude ofthesun oftheMoon

= 5' 2SO 49' 5• 17o 40'

= 5 27 49 5 2 44

= 0 1 0 0 14 56

Motion in (6:26 - 5:30) 56 Minutes= 0 0 2 0 0 35 ----------------15th October, 2001 at 6:26AM


= 5 27 51

=52852

5 3 19

5 18 15

Tithi on 15th October, 2001 (5' 3° 19'- 5' 27° 51')+ 12

= (153° l9' .:.177° 51')+ 12

= (360 + 153° 19'- 177° 51')+ 12

= (335° 28') + 12 = 27 110 2

8' 12

(As minus figure is more)

Thus 27th tithi had completed and 28th tithi was running or the


tithi of the day was Krishan Paksha Triyodashi.

Similarly tithi on 16th October, 2001

= (5' 18° 15'- 5' 28° 52') ... 12

= (11' 19°23') + 12

1°23' = (349° 23') + 12 = 29 Uo

Thus twenty-nine tithis had completed and 30th tithi was running i.e. the tithi for that day was Amavasya.

It is seen that the tithi of Krishan Paksha Chaturdashi was lost (Kshya). It can also be called that Triyodashi and Chaturdashi had come on the same day.

19.7 ExampleofAdhik tithi:

We have to find out the tithi for 28th October, 2001 and 29th October, 2001.

only

Time of sunrise

Longitudes at the time of sunrise .

Moon Sun

28th October, 2001 6 : 34 10' 23° 32' 6' 10° 48'

29th October, 2001 6 : 35 11 5 33 6 11 48

Tithi on 28th October = (10' 23o 32'- 6• 10° 48') + 12

= (4' 12 44') ... 12

0°44' = 132°44' + 12 = 11--

12 So it was Dwadshi on 28th October, which was passed by 44'

Tithi on 29th October = (11' 5° 33'- 6• 11 o 48') + 12

= (4'23° 45') + 12 = 143° 45' + 12

11° 45' =11--

12 It was also Dwadshi on 29th October and passed 11 o 45' and

the remaining period was only 15'.

Thus it is noticed that it was Dwadshi on 28th as well as on 29th October, 2001. The tithi became Adhik (more) .

19.8 Nakshatra:

Zodiac = 360° = 12 signs = 2'7 Constellations (Nakshatra).

1 sign = 360° + 12 = 30°


360 1 Nakshatra = 27 = 13° 20' = 800'

= 4 charan (Pada) or quarter

1 charan (quarter) = 200'

First quarter is from 0' to 200', 2nd 200' to 400', 3rd 400' to 600' and 4th 600' to 800'. Zodiac is divided into 27 parts which are called Nakshatras and each is equal to 13° 20' = 800'. The names are given in Para 14.12. The formula for finding out the Nakshatra is longitude of the planet in minutes divided by 800. The quotient tells the number of Nakshatras passed and the planet is moving in the next Nakshatr;:. number = Quotient + 1.

Example:

25'. Find out the Nakshatra of the Moon when its longitude is 6' 10°

6' 10° 25' = 190° 25'

Nakshatra = 190° 25' + 13° 20'

= (190 X 60 + 25) + (13 X 60 + 20)

= (11400 + 25) + (780 + 20)

= 11425+800

225 =14-

800 The moon has traversed fourteen Nakshatras and is moving in

the fifteenth i.e. Swati Nakshatra in II quarter, as the remainder is 225' which is in between 200' and 400'.

In this way Nakshatras of all the planets are found out. When the name of a planet is not mentioned, it should be understood that the Nakshatra is of Moon. ·

19.9 Kama:

Kama is related to the tithi. Each tithi has two Kamas. As already stated a tithi is the duration of time in which the Moon moves 12° ahead of the sun. The same way a kama is the time interval in which the Moon moves 6° ahead of the sun. First kama of a tithi starts with it and ends when the Moon has gained 6° over thl;! sun. The second kama ends with the tithi.

Formula for calculating Kama is:

K Longitude of the Moon- Longitude of the Sun

ama = 6

The quotient tells the number of kamas passed and number of kama running is Quotient + 1. There are 30 tithi in a lunar month. So


there are 30 x 2 = 60 kamas in that period of time. There are seven kamas that are repeated 8 times and four are non-repetitive during a Lun?or month. Total number of kamas become 8 x 7 + 4 = 56 + 4 = 60.

The names of recurring Kamas are ; 1. Bava

2. Balava

3. Kaulava

4. Taitila

5. Gara

6. Vanija

7 Vishti

Names of Kamas that occur only once in a month;

l.Shakuni

2. Chatuspada

3.Naga

4. Kinstughna

The following table shows the order in which they are related to the tithis/Month :

~ Sukla Paksha Krishna Paksha

No. Name of 1st Karna 2nd Kama Tit hi lstKarna 2nd Kama

Tithi N Name No Name Nc Name No Name Nc Name

I Pratipada 1 Kinstughna 2 Bava !6 Pratipada 31 Balava 32 Kaulava

2 I:MiJtya 3 Balava 4 Kaulava 17 I:MiJtya 33 Taitila 34 Gara '

3 Tlitya 5 Taiti\a 6 Gara 18 Tlitya 35 Vanija 36 V!Sihi

4 Chaturthi 7 Vanija 8 Vishthi 19 Chaturthi 37 Bava 38 Balava

5 Panchami 9 Bava 10 Balava 20 Panchmi 39 Kaulava 40 Taitila

6 Shashthi 11 Kaulava 12 Taiti\a 21 Shashthi 41 Gar a 42 Vanija

7 Saptmi 13 Gara 14 Vanija 22 Saptmi 43 Visthi 44 Bava

8 Ashtami 15 VJShthi 16 Bava 23 Ashtami 45 Balava 46 Kaulava f--

9 Navmi - 17 Balava 18 Kaulava 24 Navmi 47 Taitila 48 Gara

10 Dashmi 19 Taitila 20 Gara 25 Dashmi 49 Vanija 50 Visthi

11 Ekadashi 21 Vanija 22 Visthi 26 Ekadashi 51 Bava 52 Balava

12 Dwadashi 23 Bava 24 Balava 27 Dwadashi 53 Kaulava 54 Taitila

13 Tliyodashi 25 Kau\ava 26 Taitila 28 Tliyodashi 55 Gar a 56 Vanija

14 Chaturdashi 27 Gara 28 Vanija 29 Chaturdashi 57 Vishti 58 Shakuni

15 Pumirna 29 Visthi 30 Bava 30 Amavasya 59 Chatuspada 60 Naga


Example:

To find out Kama at the time of sunrise on 25th October, 200lat Delhi at 5:30AM.

Longitude of the Moon

Longitude of the sun

= 10' 23° 32'

= 6 10 48

Longitudes of Moon- Sun = 4 12 44

132°44' 0°44' Kama =

6 = 22-

6- i.e. 22 Kamas have passed and

23rd Kama named Bava was at that time.

19.10 Results of Kamas at the time of the birth of a native as per Mansagri are:

Bava

Balava

Kaulava

Taitila

Gara

Vanija

Vishthi

- Proud, religious and righteous deeds.

- Education, wealth and happiness.

- friend of friends and self-respectful.

- Owner of several houses and wealthy.

- Agriculturist and hard working.

- Gains from business.

- Expert in poisons, adulterous and bad deeds.

Sakuni - Vaidya, manufacturer of medicines and arbitrator.

Chatuspad - Devotion to god, veterinarian and cow-herd.

Nag - Doing difficult jobs, well wisher of sailors, with bad-luck and lively eyes.

Kinstughna - Get the desired and auspicious results by good deeds.

19.11 Yoga:

Yogas are 27 and their names are given in seriatim.

1. Vishkumbha 10. Ganda 19. Paridha

2. Priti 11. Viridhi 20. Shiva

3. Ayusmana 12. Dhruva 21 Sidha

4. Saubhagya 13. Vyaghata 22. Sadhya

5. Shobhan 14. Harshana 23. Shubha

6. Atiganda 15. Vajra 24. Shukla (Shukra)

7. Sukarma 16. Sidhi 25. Bhrahma

8. Dhriti 17. Vyatipat 26. Aindra

9. Shula 18. Variya~a_ 27. Vaidhriti


19.12 Formula for calculating Yoga is:

Long. of Moon + Long. of Sun Yoga = ~-=::....:...:.......~.:..:.....--.:::_-__;_

800

Example:

Yoga is calculated for,'!xample given in para 19.9.

Longitude of Sun = 6' 10° 48'

Longitude of Moon = 10 23 32

10' 23° 32' + 6'10° 48' 17' 4° 20' Yoga=- =

800' 800 =

as it is more than 12 signs so deduct 12 signs.

800

9260 460 = -- = 11 -- i.e. 11 yogas have passed and

800 800 12th (Dhruva) is running.

19.13 Qualities of a native born in the following yogas as per Man-sagari :

1. Vishkumbha - Beautiful, lucky, wise and learned

2. Priti - Loved by women, philosopher, enthusiast and hard-working.

3. Ayushmana - Self-respectful, rich, poet, long life, strong and victorious in fight.

4. Saubhagya - Minister of a king, expert in work and loved by women.

5. Shobhan - Beautiful, having wife and son and ever ready for duty.

6. Atiganda - Killer of mother and destroyer of dynasty.

7. Sukama - Strong character, loving, passionate, doing righteous deeds and virtuous.

8. Dhriti - Patience, famous, wealthy, lucky, learned, happy and virtuous.

9. Shula - Religious, Philosopher and expert to gain knowledge and wealth.

10. Ganda - Brave, sickly, strong will power and short statured.

11. Vridhi - Beautiful, having wife and son, wealthy, passionate and strong.

12. Dhruva - Long-lived, wealthy, popular, strong-minded and strong.


13. Vyaghata

14. Harshana

15. Vajra

16. Sid hi

17. Vyatipat

18. Variyana

19. Paridha

20. Shiva

21. Sidha

22.Sadhya

23.Shubha

24. Shukla

25. Brahma

26. Aindra

27. Vaidhriti

- Omniscient, popular, pleasing to the people and helpful to all.

- Very much luckly. loved by the king, obstinate, wealthy, clever in arms and wise.

- Clever in arms, wealthy, wise and courageous.

- Able to do all sort of works, generous, passionate, happy, beautiful and with grief.

- Uve troublesomely and if saved by the grace of god, he is popular and gets comforts.

- Strong, knowledge of art, story-teller and clever in music and dance.

- Knowledge of arms, making the dynasty popular, poet, generous, passionate and well-behaved.

- Well-being, self-respectful like Mahadeva and very wise.

- To give sidhi to others, makes new mantras, having beautiful wife and very wise.

- Gets mental sidhi, popular, has all comforts and loved by all.

- Beautiful face. wealthy, having knowledge and scientific knowledge, generous and respecting Brahmins.

- Knowing all arts, poet, brave, wealthy and popular.

- Very learned, perfect in religions knowledge and clever in every respect.

- King (if born in a royal family), otherwise wealthy, short-life, happy, passionate and virtuous.

- Enthusiast, strong appetite, unpopular even after doing good to others.

lxxl Phase of.Moonr Eclipses and

non-luminous upgrahas 20.1 It has already been told that the planets and satellites do

not have their own light but they reflect the light received from the sun. Moon's orbit is inclinP.d at an angle of so to the ecliptic. It is revolving round the earth and moving alongwith the earth it is revolving round the sun also. The sidereal period of the Moon is 27.3 days and its synodic period is 29.53 days. The time period between two Amavasyas is the synodic period of the Moon (29.53 days). Moon moves with faster angular velocity than the sun. Moon is at a distance of 2,39,000 miles and the sun's diameter is 8,65,000 miles and radius is 4,32,500 miles which is nearly twice the distance of moon from the earth. In case the earth is at the centre of the sun, the moon would be in middle of the centre & surface of the sun. Thus we see that the sun is very big. Its mean distance from the earth is 93,000,000 miles (930 lacs miles) and we can presume that the rays of sun are parallel for us. The moon is 400th part of the sun but the former is 400 times nearer to the earth than the latter, so the difference in diameters of their discs are nearly equal.

20.2 Phases of Moon :

The shape of illuminated surface of the moon changes from one night to the next. We st<ut from the end of Amavasya (new moon). The thin crescent seen low in the western sky just after sunset grows in illuminated area (waxes) every day. It is found more towards east each night after sunset. Half a moon is seen after the first quarter of a month. It becomes gibbous after that and reaches to full moon after a fortnight of its appearance. It starts waning and after third quarter it becomes half again and after a m~:mth Amavasya ends again.

The phases of moon ~re due to (i) the moon has not got its own !ight but reflects sun's light, (ii) it is revolving round the earth. Sun's rays always fall on half of the moon, the face which is towards sun remains illuminated and the other half remains in darkness as happens with the earth during day and night. The phases of moon are explained in the figure below.

Sun rays are coming from the left and considered as parallel.


Sun rays

----+. (1) c

Sunrays.

8

(2) B

() (3)

Fig.26

(5)

or Moon

0(4)

Earth is in the centre, the moon is revolving around the earth in the outer circle on which eight different positions of the Moon have been shown. 0 is the centre of the moon. The shaded areas of the moon and the earth are dark as the same are not receiving sunlight. AB is the diameter of the moon perpendicular to the sun rays and one side of it is receiving the light of the sun and the other is dark. COD is the line perpendicular to the line joining the centres of the earth and the Moon. Half of the moon facing the earth is visible from the earth and the portion of this half which is receiving the sunlight is visible portion of the moon imd the rest is invisible as the same is nat receivil)g light from the sun consequently not reflecting any light. ·

Now we consider the position (1) in which (AB & CD coincide) the moor. is in betwe~n the sun and the earth and its dark portion is towards the earth. So no reflection of ~tn;t's light_ is on the earth and it is amavasya.

In positions (2) and (8) the illuminated part'ofthe moon towards the earth is DOA and COB. Less than: half the portion of moon is


visible.

In positions (3) and (7) half of the illuminated part of the moon towards the earth is DOA and COB. Hence half the disc of the moon is seen.

In positions (4) and (6) more than half of the iliuminated disc of the moon towards the earth is DOA and COB. So the moon will appear gibbous (more than half).

In position (5), AB and CD coincide again and the whole of the illuminated part is towards the earth. Hence full disc of the moon will be visible and it happens on Purnima (full moon).

20.3 The planets/Moon do not move along the ecliptic but their orbits are inclined at a certain angle to the ecliptic. Because of this a planet'moon cuts the ecliptic at two points in one revolution of the sun/ planet, once going upwards and again going downwards of the ecliptic. These two points are known as nodes of the planet'moon. The point through which the planet passes in going from southern to the northern side (downwards to upwards) of the ecliptic is known as ascending node and the other point as descending node. Latitude of planet is zero when it is at its nodal point. When the planet is crossing the point of ascending node, its latitude changes from minus to plus or from southern to northern.

20.4 Rahu and Ketu: The ascending node of the Moon is called Rahu and the descending

node as Ketu. As explained in para 20.3 that there is no physical existence of the nodes and these are only mathematical points. Therefore, these are called shadowy planets (Chhaya graha). They are also called dragon's head and dragon's tail. They are of much importance in predictive astrology. The line joinii1g the nodal points is calied the nodal axis or line of nodes.

In the following figure, the orbit of the moon and the ecliptic appear to be intersecting at four points, in space (three dimentions)

(Ketu) • ~:nding

~

t Ascending Node (Rahu)

Fig.27

Ecliptic


there will be only two points of intersection of two great circles. The point where two thin lines are intersecting is Ketu (desendingnode) and where two thick lines are meeting is Rahu (ascendingnode).lbe difference between the longitudes of Rahu "'nd Ketu is 180° and they move retrograde. They complete one revolution in 18 years 220 days. Their average annual motion is nearly 19° 36' or 8" per hour.

20.5 Eclipses : ---<-

Eclipses are simply shadow effects. The moon is eclipsed when it moves within the shadow of the earth and the sun is eclipsed when the moon obstructs the light of the sun or the earth reaches in the shadow of the moon. Lunar eclipse takes place on Pumima (full moon) and solar eclipse falls on Amavasya (new moon) but these phenomena do not occur at every Amavasya or Pumima. The explanation for it is that the orbit of the moon is inclined at an angle of so nearly to the earth's orbit (plane of ecliptic). When the moon happens to be in the plane of earth's orbit on nearby at Amavasya or Pumima, solar/lunar eclipses occur.

Maximum number of eclipses possible in a year is seven (either four solar and three lunar or five solar and two lunar). The minimum number is two (boih solar) and the average is four eclipses.

20.6 Lunar eclipse:

Lunar eclipse occurs when the moon comes within the shadow of the earth. There are two necessary conditions for a Lunar eclipse and the same are :

(I) It Is the time of the end of Pumima or the moon Is at the opposition of the sun.

(II) Moon's longitudes should be equal to or nearby those of Rahu or Ketu.

As Rahu and Ketu are the nodes of the Moon, the Moon will be at the ecliptic or nearby. At this time the centres of the Sun, Earth and Moon are nearly in a straight line. The Earth obstructs the sun rays in falling on the moon. Thus the Moon's disc is obscured and lunar eclipse takes place. At the time of totality, the Moon seems to have dull red or copper colour, due to rays of sunlight passing through the earth's atmosphere, are bent so they enter the shadow and strike the Moon.

The phenomena is explained through the following figure. Sand E are the centres of the sun and the earth. Straight lines AOQ, BOR, ADN and BCN are tangents to both the sun's and earth's discs. Moon's orbit is M1MzM M}14•

The dark shaded space CDN is not receiving any light of the sun


Fig.28

as the same has been obstructed by the earth. Cone CON is in complete darkness and is called umbra. The cones RON and NCQ are receiving light from one side and not from the whole disc of the sun. These lightshaded cones are known as penumbra. The moon is moving round the earth M1 to~. M, M3 and M4 etc. As moon starts moving from~ and enters penumbra, it brightness goes on diminishing and the eclipse starts from the time it enters umbra, which ends till it crosses umbra and afteM•ords its brightness goes on increasing till the time of crossing the penumbra.

Lunar eclipses are of two types (i) Total Lunar eclipse takes place when the whole disc of the moon is within Umbra (ii) Partial Lunar Eclipse takes place at the time when ·only a part of the disc passes through Umbra.' The maximum duration of Lunar eclipse is 1 hour 45 minutes.

20.7 Solaredlpse:

Solar ecliPf ! takes place at the time when the Moon arrives in between ·the_ Sun and the Earth in such a way that it may obstruct the light of the Sun in reaching the Earth. It can happen only at the time when the centres of the Moon, Sun and Earth are nearly In a straight line. The longitudes of the moon and sun are nearly the same at that time. As has been already explained in lunar eclipse that the Earth and Sun always remain on the ecliptic, while the Moon's orbit Is inclined at an angle of so nearly with the ecliptic. So Moon is not always on the ecliptic. It is on ecliptic when it coinc:.:les with Rahu or Ketu which are

Bements of Astronomy and Astrological Calculations 153

the nodes of the Moon. Therefore, there are two necessary conditions for solar eclips£ and the same are :

(i) Moon should be at Rahu or Ketu or nearby.

(ii) Amavasya should be ending at that time.

Solar eclipses are of three types :

(i) Total solar eclipse.

(ii) Partial solar eclipse.

(iii) Annular solar eclipse.

20.8 Total Solar Eclipse :

At the time of total solar eclipse the tight of Sun is nearly hidden from the observer; and the Moon being much smaller than the earth, the solar eclipse can be visible over a very limited area (nearly 120 kilometers) at a time. It takes place at a time when the Moon comes in between the Earth and the Sun and obstructs the tight in reaching to a portion of the earth's surface. It happens when the diameter of the disc of the Moon is bigger than that of the Sun's disc.

20.9 Partial Solar Eclipse :

It is seen when the observer is in the penumbra and the Moon may not obstruct the whole disc of the Sun. At this time the centres of the Moon, the Sun and the observe~ are not in a straight tine.

20.10 Annular eclipse:

Such eclipse happens at the time when the Moon's disc may become shorter than Sun's disc or Sun may be at perigee (nearest to the earth) and the Moon at apogee farthest from the earth and other conditions remaining the same. The maximum and minimum diameters of the discs of the Sun and the Moon as seen from the earth are :

Maximum when Minimum when at perigee at apogee

Moon 33' 31" 29' 22"

Sun 32' 36" 31' 32"

The annular eclipse is explained with the figure on the following page.

No sunlight is reaching at cone DOC which has been shown as dark shaded. When the earth is in E1 position and the observer is atE, total solar eclipse will be visible to him.

Maximum period of total solar eclipse is 7 minutes 40 seconds and normally its duration is lesser.

The time when the Moon is away from the earth or say earth is


L

M

Fig.29

in ~position and the Moon may not cover the whole disc of the Sun, annular solar eclipse takes place. Sun's disc between AB will not be visible to an observer at F and the remaining circular disc (ring shape) between LM excluding AB is seen by him. Such an eclipse is called annular solar eclipse.

Take care not to view the partially eclipsed Sun directly, as considerable infrared radiation remains and eye damage could result.

20.11 Chaldean Saros:

19 synodic revolutions of node= 19 X 346.62 = 6585 days. which is equivalent to 18 years 11 or 10 days, according as there are four or five leap years in this interval. The Sun and Moon will return to the same positions relative to the nodes and therefore the eclipses will repeat in the following cycle in the same order as in the previous one. Chaldeans were enabled to foretell the occurence of eclipses.

20.12 Combustion of planets:

When any planet is near to the_ Sun. its reflected rays mix with the rays (which are dazzling) of the Sun and the effect of the rays of planet becomes very less. It is not visible due to light of the Sun. At that time the pl<:t:1et is said to be combust. Its diurnal rising and setting coincides with that of the Sun. By planets here we mean Mars, Mercury, Jupiter, Venus, Saturn, Uranus, Neptune and Pluto. Moon and Sun are satellite and star in astronomy.

20.13 When the Moon or any heavj!nly body passes between

Elements of Astronomy and Astrological Calcul~tions 155

. the observer and the Sun, the planet or fixed star is said to be in occultation. Actually in solar eclipse Moon occults the Sun and in lunar eclipse the earth occults the Moon. There are also examples of occulation. The occultation of a planet by Moon is called 'Samagama'. Moon revolves round the earth and completes one revolution in 27.3 days. During its revolution some star is hidden by the disc of the Moon and this is called 'Samagama'.

20.14 Non-luminous upgrahas:

In astronomy, upgrahas or satellites are those heavenly bodies which revolve round a planet. Here we shall be telling about the upgrahas which are merely mathematical points and these find an important place in predictive astrology. We shall discuss how they are calculated for a given horoscope.

Upgraha:

Name of upgraha - Kala Paridhi Dhoom Ardhyam or or

l Parivesh l Ardhprahara

! ! Lord of upgraha - Sun Moon Mars Mercury

Name of upgraha - Yamgantak lndrachapa Gulika Patha Sikhi or or or or

j Kodanda Mandi Vyatipata Upketu

! 1 1 1 Lord of upgraha - Jupiter Venus Saturn Rahu Ketu

20.15 Some of the upgraha are related with the longitude of the sun. They are calculated as given below. Let the longitude of sun be 25°.

(a) Dhoom = Longitude of Sun + 133° 20' = 25° + 133° 20' = 158°20'

(b) Patha

(c) Paridhi'

= 360°- Dhoom = 3600- 158° 20' = 201 o 40'

= Patha + 180° = 201° 40' + 180° = 381" 40'

= 21° 40'

(d) lndrachapa = 360°- Paridhi = 360°- 21 o 40' = 338° 20'

(e)Sikhi = lnd;:achapa + 16° 40' = 338° 20' + 16° 40' = 355o Sikhi + 30° = Sun's longitude

Note : 355° + 30° = 385° = 25° (Sun's longitude)


Sikhi355°

Dhoom 158" 20'

90" Hg.30

Rest of the upgrahas are calculated as under :

20.16 When the time of birth Is In day time :

Divide the duration of day (Dinmana) in eight equal parts. The first part of the day shall be of the lord of the vara of the day. The second part shall be of the lord of the vara of the next day. Proceeding likewise the lords of seven parts of the day will be alloted the lords and the eighth part is without any lord (Nireesh).

Example: Let the birth be on Wednesday and the duration of day (Dinmana)

be 10 hours 40 minutes. Sunrise time is 6:50AM.

Eighth part of the day= 10: 40 + 8 = 1:20

Sl.No. Part of the clay Lord Upgraha

1 Fast part 6:50 to 8:10AM Mercury Ardhyam

2 SecOnd part 8:10 to 9:30AM Jupiter Yamagantak

3 Third part 9:30 to 10:50 AM Venus lndrachapa

4 Fourth part 10:50 to 12:10 Saturn Gulika

5 Fifth part 12:10 to 1:30PM Sun Kala

6 Sixth part 1:30 to 2;50 PM Moon Paridhi

7 Seventh part 2:50 to 4:10PM Mars Dhoom

8 Eighth part 4:10 to 5:30PM without Lord -(Nireesh)

Thus it is seen that the eighth part is without any lordship. Longitudes of lndrachapa, Paridhi and Dhoom are calculated as per para 2.15 and remaining four are calculated by this method. The

Elements of Astronomy and Astrologice~l Calculations 157 . . ., . longitudes of the ascendants at the ending time of the part are the longitudes of the respective upgrahas. Some Astrologers consider the starting time insteac;i 9f endillg.time. · .

. '. ," ·· ... '

20.17 When the birth Is of night time:

The duration of the night (Ratrimana) is divided into eight equal parts and the lord of the first part of the night will be lord of the fifth day or Vara from that day. The lord of the second part of the night will be the lord of sixth day or vara from that day.

E:<ample of para 20.161s considered here:

Duration of night (Ratrimana) = 24-10: 40 = 13:20

Eighth part = 13:20 + 8 = 1 hour 40 minutes.

The fifth day from Wednesday is Sunday. So the lord of the first part of the night is sun.

SI.No. Part Lord Upgraha

1 First pe~rtof night 5:30 to 7:10PM Sun Kala

2 Second pe~rt of night 7:10 to 8:50PM Moon Paridhi

3 Third pe~rt of night 8:50 to 10:30 PM Mars Dhoom

4 Fourth part of night 10:30 to 12:10 Mercury Ardhayam

5 Fifth part of night 12:10 to 1:50AM , Jupiter Yamgantak

6 Sixth pe~rt of night 1:50 to 3:30AM Venus lndrachapa

7 Seventh part of night 3:30 to 5:10AM Saturn Gulika

8 Eighth pe~rt of night 5:10 to 6:50AM Without -Lord (Nireesh)

The longitudes of the ascendants at the ending time of the part are the longitudes of the respective upgrahas excluding those which can be calculated by para 20.15.

IXXJ,I· Rising and setting of

Planets & Stars

21.1 Why and when the planets and stars rise and set will be dealt in this chapter, There are two types of rising and setting of planets and stars.

(a) Diurnal rising and setting of stars and planets.

(b) When a planet becomes so much near to the Sun that it cannot be seen by the unaided eye due to dazzling light of the Sun. Its rays are also intermingled with that of the Sun. The planet is said to have been set in terms of Indian astrology. When that planet becomes at sufficient distance from the Sun, so that it can be seen by the naked eye, it is said to have been risen. In modem astronomy ihese setting and rising are called Heliacal rising and setting.

21.2 Daily rising and setting of planets:

The earth rotates on its axis from west to east and completes one rotation in one day. It is called the diurnal motion of the earth.

Fig.31


Due to this diurnal motion every star or planet appears to move from east to west and completing one revolution daily. When a heavenly body (star or planet) goes down the horizon of the observer, it is settiftg and when comes upwards of the horizon, it rises. Below the horizon ·the observer cannot see as the same disappears due to earth. The heavenly bodies that are above the horizon can be seen by the observer. Now the diurnal motion of the heavenly bodies is explained with reference to the figure on the previous page.

In this figure, E is the earth and observer is at 0.

AB is horizon, CD is celestial equator,

X is a star/planet,

PZQ is the meridian of the observer,

Z is zenith and P, Q are the North and South poles.

Due to diurnal motion o(the earth, X appears to complete one revolution along a small circle XMFLH parallel to the equator, in one day. When X reaches at M (a point on the horizon) it is going down the horizon, that is why it is setting. X reaches at F, at this time it is on the ante-meridian and has maximum altitude downwards.

When it comes at L, it is again on the horizon and it is rising as it comes within the visible hemisphere of the observer. By and by it reaches at H (a point on the meridian) and it is having maximum altitude afterwards the altitude tends to decline. At H the planet is said to be at transit as it is crossing the meridian. The stars which are near the pole, like S (star). S completes one revolution daily on a small circle SJJ round the pole and parallel to the equator. S never sets as it does not go below the horizon. It cannot be seen in the day due to sunlight. It is called circum polar star. Such circum polar stars can be seen during the day with the help of telescope or by other methods. In predictive astrology the diurnal motion of the planets is not considered.

21.3 Heliacal rising and setting:

Stars are considered as fixed and as such their longitudes remain the same and do not change from time to time. The planets revolve round the sun and the satellites (Moons) revolve around their planets. It causes the increase and decrease in their longitudes. When a planet is so much near the Sun that it cannot be seen by the naked eye due to dazzling light of Sun, it is said to have been set (Heliacal setting). There is difference in the diameters of the discs of the planets. When a planet reaches within a distance of certain degree of lontgitude. it sets and after going away by the same distance it rises. While calculating heliacal settings and risings celestial latitudes of the planets

160 Elements of Astronomy and Astroiogical Calculations

must be accounted for but In normal practice these are not taken Into account. It causes many times difference of several days in the heliacal rising and setting between actual observation and calculated by the setting limit of longitudes between the Sun and the planet.

Longitudes of the zodiat. increases from west to east the direction in which the planets are revolving round the Sun. At any time if the longitude at western horizon is 10°, it will be nearly 100° at the point of intersection of zodiac and the meridian of the place and nearly 190° in the eastern horizon. The longitudes of zodiac at any time are increasing from west to south to east to north. The planets visible by the unaided eye are Mercury, Venus, Mars, Jupiter and Saturn. Sun is a star and Moon a satellite of the earth are also seEm by the naked eye. But in predictive astrology Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn are considered as planets. In Indian astrology Mercury and Venus are the Inner planets while In modem astronomy Mercury, Venus, Earth and Mars are considered Inner planets as their surface is rocky and Jupiter, Saturn, Uranus, Neptune and Pluto are outer planets because they consist mainly of gases and liquids.

21 .4 Combustion of the Moon :

The Moon revolves round the earth and completes one rotation in one month. Its angular motion is much faster than the Sun. When the longitudes of the Moon and the Sun are the same, the amavasya ends. The Moon is not visible by the eye between the period in which it traverses a distance 12° behind the Sun to 12° ahead of it..It is the period of Moon's combustion. Therefore, the Moon is combust on Amavasya and Shukla Paksha Pratipada.

Moon is visible in the eastern sky, some time before the Sunrise on Krishan Paksha Chaturdashi as the longitude of the Moon is lesser · than the Sun. It is not visible during the day due to dazzling light of the Sun. After this the difference in longitude of the Moon and the Sun becomes lesser than 12° and the Moon is not visible by the naked eye. Therefore, it is said that the Moon has become combu~t in the east as it was seen last in that direction. Its longitude ·equals that of the sun at the end of Amavasya (new moon) and now onwards Moon goes ahead of the Sun. When its longitudes are more than 12° that of the Sun (after Sukla Paksha Pratipada), it can be seen in the western sky after sunset and as such it is said that it has risen in the west. When the longitude of the Moon becomes 180° (6 sign) more than the Sun, it is visible in the early night on the eastern horizon.


Moon combusts (sets) on Krishan Paksha Chaturdoshi in the east and rises in the west on Shukla Poksha Dwitiyo.

21.5 Heliacal rising and setting of direct Inner planets :

Mercury and Venus rise and set on fiXed longitudal distances from the Sun, when they are direct. They are visible in the eastern sky before Sunrise, when their longitudes are lesser than the Sun. As the portion of the zodiac having lesser longitude will be on the eastern horizon earlier than the portion having more longitude. When their longitudes are lesser than the Sun but are within the setting limit, they appear on the eastern sky before the Sun but are not visible due to twilight. After some time their longitudes become equal to that of the Sun, at that time these Planets are said to be deep combust (Pumasta). After that they gain longitudes over the Sun and when the difference crosses the setting limit, they can be seen in western sky after the sunset and are said to have risen.

Direct Mercury and Venus set in the east and rise in the west.

21.6 Heliacol rising and setting of Retrograde inner planets :

The Mercury and Venus become retrograde when they come near the earth or their longitudes go on decreasing for a period of time. When they are re~de and their longitudes are more than the Sun, they can be see~the Western sky after the sunset. But after some time their longitud r~ become within the setting limit, they cannot be seen by the unaided eye due to twilight and said to have been set. Their longitudes go on decreasing and the time when these become equal to that of the Sun, they become combust (Pumasta). After some days their longitudes become lesser than that of the sun and the planet goes out of the setting limit. Now they can be seen in the eastern sky before sunrise.

Retrograde bmer planets set In the west and rise In the east.

21.7 Heliacal rising and setting of outer planets :

Outer planets are Mars, Jupiter and Saturn. Their angular velocities are lesser-th~ that of the Sun. When their longitudes are more t)lan that of the Sun, they can be seen in the western sky after sunset. When the difference of their longitudes and the Sun becomes lesser than the setting limit, they are not visible to the naked eye due to twilight and said to have been set in the west. The difference in longitudes go on decreasing and when their longitiudes equal to that of the Sun, they become combust (Pumasta). Now they appear above and go below the horizon with the Sun. After certain period, the Sun goes ahead and out


of the setting limit, they are seen in the eastern sky before sunrise as their longitudes become-lesser than that of the Sun. They are said to have risen in the east.

Outer planets do not set when they are retrograde as the difference between their longitudes and that of the Sun is more than 90°.

Outer planets set in the west and rise in the east.

21.8 Setting limit (Param Kalansa or Astansa) of Planets:

According to Udyastadhikara of Surya Sidhanta. Heliacal setting limit.

lfl~<nr~~~

llif~ "tRlt~-

l(cni~ll'll4~~~ ~~ ~· &>1!!1ill'll \{foi'l;j~ ~ ~II 11, II

Qll'ili~~q4l~: ~: !U(-01~'1141 I

lll'l~'iG4: Q~ill~~iiii(~lfq: 'Pif: II 19 II

~ ~ ~: ~:1 q9>'\" !l'ft'ii•lfft!l'illl&>fi&i~I(Q~q4)~~ II t. II

~sfttcl;: ~ ~{cyf"'i: I ~ ~ 'lSlim '41"lqi!fGt'{if4: II 't II

thv Longitudal distance of heliacal setting of pli .... Jets from the sun.

Moon

Mars

Mercury

Jupiter

Venus

Saturn

Direct Retrograde lZO

lZO

When the planets are within the heliacal setting limt, they are not visible by the unaided eye and set. This setting limit depends on the diameter of the disc. The Kalan5a (setting limit) of planets having bigger diameter will be lesser than the planet having smaller diameter. Mercury and Venus set while direct and retrograde also.

When they are in superior conjunction (direct motion), the diameter of their disc appears shorter as seen from the earth, than at inferior conjunction (retrograde motion). At inferior conjunction they are nearer to the earth than the superior conjunction. Therefore, their Kalansa


(Heliacal setting limit) becomes shorter in heliacal setting when they are retrograde.

21.9 The orbits of the planets are inclined at small angles to the ecliptic. Therefore, the longitudenal point of a planet and the planet do not appear on the horizon at the same time but the planet is seen on the horizon either some time earlier or some time after the longitudinal point of the ecliptic appears on the horizon due to latitude of the planet.

We had considered the longitudes for tN heliacal rising and setting of the planets. Declination of the Sun, terrestrial latitude of the observer etc. also affect the rising and setting of the planets. When the planets are not seen by the naked eye due to their nearness with the Sun, they are called heliacally set. Actually they are not visible due to twilight. Twilight is the light of the Sun reflected by the atmosphere of the earth (which is sufficiently high), when the Sun is below the horizon at the time of either rising or setting. In the evening twilight remains when the Sun goes down of the horizon upto 18° and in the morning it starts when the Sun comes up within 18° below the horizon. The time period of 18° going below and above is based on the declination of the Sun and the latitude of the observer. As such the time of heliacal rising and setting should not be decided only by the longitudes of the planets.

21.10 Heliacal setting of Jupiter is called Guru Aditya or Guru Badika and it remains for nearly one month. The auspicious ceremonies should not be performed during this period. The same way auspicious ceremonies are not performed when the Venus is also heliacally set.

lXXIII Stars

22.1 StaiS are luminous heavenly bodies in the cosmos and are formed by the gases. Sight of the sky studded with staiS is one of the nature's fascinating scene. These small twinkling points are exbemely delightful in a darl< night. Ancients tried to recognise these staiS with the known objects since long. The names of animals or objects, which were known then were given to the groups of staiS, like Saptrishi (seven saints), Mesh (Bull), Singha (Lion), Tula (Balance or scale) etc. The groups of staiS were started to be recognised by the names of rasis (signs) and nakshatras (constellations).

22.2 Two types of motions of the earth are commonly known (i) diurnal motion (ii) annual motion. Groups of staiS appear at different places in the sky at different times and periods of the year. Earth completes one revolution from west to east in one day which is its diurnal motion. Due to this motion staiS (which we consider as stationary) rise in the east in the early night and set in the west in the early morning. The staiS that are near to pole, revolve in a small circle around the pole. Due to revolution of the earth around the Sun some nakshatras (group of staiS) and other staiS are visible at different places at different time of the year. After one year they are again seen at the place where they wera one year ago. On seeing these staiS, ancients used to cultivate their lands and do other worldly affaiiS. The staiS used to guide the sailoiS. A peiSon having a very good eye-sight can see only 2,500 staiS (out of innumerable staiS) in the night of a clear sky as most of the staiS are far away from the earth and could not be seen by unaided eyes.

22.3 Names of the stars:

In historj,l, several different systems of naming the staiS have been devised. It includes names such as Sirius (Lubdhak), Conopus (Agastya), a Touri (Rohini) etc. StaiS are recognised by names and the following are the three main systems of keeping the names of the staiS.

(a) Many times the name of a most bright star is kept after the name of nakshatra or group of staiS in which it is found. Its example is Spica (Chitra) etc,.


(b) The most bright stars are represented by the Greek alphabet (a) and afteiWOrds the name of the nakshatra or group of stars is written. The most bright star of Leonis (Singhal nakshatra is Regulus, which is also called (ex) Leonis. The second category bright stars are called (!3) category stars.

(c) The English astronomer John Aamsteed gave the numbers to the stars of a group or constellation. These numbers are increasing from west to east. In case we want to a see 40 Signi named star, count upto 40 from the west in the Signus group of stars.

22.4 Magnitude of stars :

In olden times the brightness of the stars could be judged by the naked eye. Now we have clear and good scales to measure the brightness of stars. The brightness of stars in this scale, form a geometric progression, that is, the brightness of stars in two successive magnitude classes are in a constant ratio to one another. First magnitude stars are 2.512 times brighter than second magnitude stars, second magnitude stars are 2.512 times brighter than third magnitude stars and so on. A star of 1.3 magnitude is 2.512 times brighter than 2.3 magnitude star. The brightness goes on geometrically increasing as the magnitude goes on decreasing. The stars having negative (-) magnitude are more bright. The magnitude of Sirius is (-) 1.46, and of Conopus is(-) 0. 7. Sirius is brighter than Conopus. The maximum brightness of Moon is (-) 12.7, Venus (-) 4. 4, Mars (-) 2.8 and of other planets is lesser. The least among the planets is of Pluto equal to 14.

22.5 Colours of stars :

Stars have different colours because of their different tempratures. Most of them are of yellow-white colour. Sirius (Lubdhak) and Conopus (Agastya) are of Blue-white colour, while the colour of Orionis (Ardra) and Scorpii (Jyestha) is red.

Hot class 0 and B stars are blue, class A and Fare white, class G are yellow, class Kare orange and class Mare red. Astronomers developed a system in which the colours of the stars are represented by numbers. It is called Colour Index in which colour index of white star is zero. Blue star has a negative colour index and a red star a positive one. Colour Index of our Sun is 0.81 and its colour is yellow. Orionis and Scorpii are red and their colour index is more than one. Surface of blue and white stars is very hot and the other stars are comparatively cool. Units for measuring the distances of stars has already been given in chapter IV,

Nova :A star that suddenly brightens up to 10 magnitude, then subsides to previous brightness in the course of roughly a year.

166 Bements of Astronomy and Astrological Calculations

Red giant :A large red star that has completed its main sequence lifetime and has expanded to hundreds of times its initial size and whose surface has cooled. ,. ·

White dwarf: A star which is small and dense. The energy it radiates comes from the cooling of the interior.

Supemova : A rare stellar explosion in which the entire outer envelope of the star is blown away in a violent outburst, leaving a dense core behind.

Neutron star : The white dwarfs whose mass remain the same but the dimensions become very small. Their interior is an unbelievable dense of neutron gas. Their diameter reduces to nearly 15 kilometers.

Pulsars : A star that emits radiation in highly regular pulses and its magnetic field enlarges 100 billion times. It is thought to be a rotating neutron star. '

22.6 Spectrum of stars:

The seven coloured band formed by passing a light through a glass prisrr. is called spectrum. After recording stellar spectra of more than 5lac stars and analysing them, the stars were classified in various spectral classes. Their sequence was recorded 0, B, A, F. G, K and M. The categories are related to the temperatures of the stars. 0 category (type) stars are hottest and the temperature of their surface is 30,000°K or more. The stars that are young and in first plase fall in the category of 0 and B. The following table shows the type relating to their temperature.

Type

05 Bo Bs Ao As Fo Fs

Temperature

(K'}

35,000

21,000

13,500

9,700

8,100

7,200

6,500

Type

Go Gs '<o J<s Mo Ms

Temperature

(K'}

6,000

5,400

4,700

4,000

3,300

2,600

Our Sun whose surface temperature is 6000°, falls in G type. Stars having the lowest temperature are classified in M catageory.

22.7 Birth of stars:

Theory of the birth of stars has been developed by astronomers: according to this theory stars are born as protostars in dark clouds of


gas and dust in interstellar space. Nothing can be seen beyond these dense clouds but heat and infra-red radiation can pass through them. A star begins as cloud of cool gas (10° to 20°K), which contracts under its own gravitation. The interior heal£ up from vety low temperatures. After thousands of years the internal pressure reaches so high that the molecules cannot go away and it becomes a protostar. The protostar also rotates and tum faster as it contracts. When the temperature of protostar reaches 10 million° K, nuclear reactions begin and the time of converting hydrogen into helium arrives. Its nuclear furnace starts functioning and the birth of a star takes place. ·

Some stars are born in pair$ or in groups. Sun was born alongwit}l its solar system including the planets etc.

22.8 Mass and life time of stars :

The more is the mass of a star at birth the lesser will be its life time. The reason is that the stars have to balance the gravitational force which could be balanced by high temperature and it requires lot of energy. Thus more hydrogen is consumed in massive stars than the· smaller ones. Hence the stock of hydrogen of a massive star is exhausted early. When the star has consumed 12% of its hydrogen, the remaining hydrogen in the core is insufficient to continue the nuclear reaction. After that the outer layer swell up and cool. As ,the core of the star becomes increasingly smaller, hotter and denser, the remainder of the star becomes larger, cooler and more tenuous and the star becomes a red giant. Its temperature goes down by 3000°. Orionis, Tourl, Arcturus etc. are red giant stars. When the crust is unable to bear the great . pressure of the core, the crust runs away from the star and the size of the remaining star becomes small. This is called white dwarf. Temperature of the surface of the white .dwarf Is very high but the brightness is very low. These cannot be seen by the unaided eye. They take tens of millions of years to cool down. There are some stars whose brightness is irregular and changes in short times like in some hours, days or weeks. They are called variable stors.

22.9 Re.d giants takes 10 billion to 15 billion years to reach their old age and they get cooler and cooler, fainter and fainter, and approaches death as black .dwarfs. However, such case has not been observed, persumably because they are too faint. Many stars become super-nova an<;! their 9uter envelope is blown away in a violent outburst. It emits light" equal to millions of Sun at a time and the star gets disintegrated into small parts.ln the end it remains a revolving Neutron Star. Its diameter be.comes 10 ·to 20 kilometers. The core of stars, which are 30 to 50 times massive than the Sun, shrinks so much and the density'becoines so· high that even the light cannot pass through

.. ",• ,•\;'•'


them and they become black holes.

22.10 Larger groupings of stars are known as star clusters. Two types of stable star clusters have been recognized: open or galatic star clusters and globular star clusturs.

Galaxy : Galaxy is an "island universe" was established by the pioneering work of astronomers in the early decades of 20th century.

Types of Galaxies:

There are three basic types of galaxies namely spiral galaxies, elliptical galaxies and irregular galaxies.

1 (a) Spiral Galaxies: These are divided into two groups namely normal spiral galaxies and barred spiral galaxies. Most of these galaxies are normal spiral ones and only one-fourth are barred spirals. Spiral galaxies are similar to the Milky way. Barred spirals are so named because of the long bar of stars that passes through the central region of such a galaxy. Spiral arms extend from the ends of the bar.

1 (b) Elliptical galaxies, so called because of their smooth appearence, with an outline in the shape of an ellipse.

1 (c) Irregular galaxies have no special shape, and they are typified by the large and small magellanic clouds.

Milky Way Galaxy : lt is now known that our Sun is located in a large relatively flflt, spiral-shaped system that contains perhaps 100 billion stars, the open and globular clusters and large amount of gas and dust etc. are in between the stars. This system is known as Milky WayGlaxy.

Our galaxy is perhaps lens shaped rather than grind-stone shaped. Its diameter is about 1,00,000 parsecs and 10,000 parsecs thick. Our Sun is about 10,000 parsecs away from the centre of the system. The stars nearer to the centre of the galaxy complete a revolution in shorter period thc>.n .the distant stars. Sun's velocity is 200 kilometers per second and it completes one revolution in 200,000,000 (two hundred million) years .

. 2 (a) Open star clusters are irregularly shaped, loose groups of stars containing from a dozen to several hundreds stars. Pleiades, in the constellation Taurus is one of them. Roughly 900 open star clusters are known. The diameters of these star dusters are between 2 and 10 parsecs. The star densities in open star clusters is almost a hundred times the density near the Sun.

2 (b) Globular Clusters are spherical aggregates of stars that contain anywhere between a few thousands of stars and a million stars. Mar:! than hundred such clusters are known. In the centers of these clusters, densities may reach as high a; 1000 stars per cubic parsec. In


case we live on a star which is near the center of a large globular cluster, the sky would be spectacular. More than 1,00,000 stars of that cl~ster could be seen by the unaided eye and hundreds of stars appear brighter than Sirius. The sky would be so filled by the stars that it would never be dark.

2 (c) Associations contain low star-density or the number of stars is less in bigger spaces, Most of the stars in associations are hot, blue 0 and B group of stars. The interstellar dust obscures the blue light from stars more than it does the red light. Thus the dust dims the blue light from the stars. The blue light scattered from the stars illuminates the dust and perhaps it is the reason that the sky appears blue.

22.11 Nebulae is a cloud of interstellar matter, gas and dust etc. The word nebula (plural, nebulae) comes from Latin and means cloud. The dark patches of absorbing material are called dark nebulae. The temperature in a bright gaseous nebula is around 10,000°K, and thP. densities are low, arounJ 100 atoms per cubic centimeter.

IXXIIII Longevity

23.1 Longevity of a native can be determined by different methods. Here we shall consider only mathematical ones and out of these (1) Pindayu (2) Arnsayu and (3) Naisargikayu.

There are different views of the prominent astrologers but the most popular methods are given here.

The Moon, Mercury, Jupiter and Venus are considered benefics while Sun, Mars and Saturn are taken as malefics.

Arnsayu is calculated when the Lagna is stronger than the Sun and the Moon. Pindayu is taken in case the Sun is stronger than the other two. Naiksargikayu is applied when the Moon predominates the Sun and the Lagna.

23.2 Pindayu:

Pindayu is considered when the Sun is stronger than the Moon and the Lagna. The aggregate number of (Pindaurdaya) years assigned to the Sun, Moon, Mars,Mercury, Jupitar, Venus and Saturn in their deep exaltation states are respectively 19, 25, 15, 12, 15, 21 and 20 years. There is no physical existence of Rahu and Ketu and they are simply mathematical points, so they are not considered for Ayurdayas. At deblitation point the planets bestow half of the life span which is 9.5, 12.5, 7.5, 6, 7.5, 10.5 and 10 years respectively. in between these positions the number of years contributed by them is taken proportionately.

After finding out the Ayu given by the planets, following reductions are done.

23.21 Chakrapotha Haran or Chakrardhahanl:

The method given in Sripatipaddhati requires more mathematical calculatior., as the reduction is related to their (longidudal difference from the Lagna upto six signs) in backwards direction of the Lagna. A simple method is given in Brihatjataka and Jatakparijata which is

followed these days and the same is :

The Ayu bestowed by a planet is reduced in proportion as per


their position in different Bhavas from XII to VII in descending order. The following table shows the reduction in the Ayu.

XII XI X IX Vlll VII

Planet Bhava Bhava Bhava Bhava Bhava Bhava

Malefic 1 1J2 1/3 1/4 1/5 1/6 Benefic 1J2 1/4 1/6 118 1/10 1/12

In case there is more than one planet in any of these six houses, the reduction is applied to the strongest planet in that house only.

23.22 Shatrukshetriyo Heron or Sltatrulcsltetriya '-tl:

If a planet is posited in the house of a natural enemy, it loses 1/3 of the term obtained after chakrapatha haran but this reduction is not made, if the planet is in retrograde motion. Some writers exempt Mars also from this reduction but this idea is not accepted by the majority.

23.23 Astcmgata Haran or Astangtrtehanl :

When a planet is eclipsed (combust) by the sun, it loses 1/2 of the Ayu given by it. Venus and Saturn are exempt from this Haran. A planet is said to be eclipsed when it disappears within a certain limit from the sun as its light being overpowered by that of the sun. They are eclipsed when they are within the limit given below. either forwards or backwards from the sun.

Moon Mars Mercury Jupiter Venus Saturn

Direct 12" 17° w no 100 15o·

Retrograde - - 1ZO - 8" ·-

When a planet is combust in the house of its natural enemy, is liable to lose 1/2 as well as 1/3 of its Ayurdaya but as per Sripatipaddhati it suffers the loss of 1/2 Ayu only. The shatrukhtsiya haran will not be applicable in such cases or they will lose only 1/2 of the Ayu only. If Venus and Saturn are liable for both the reductions, they will lose 1/3 of the Ayu as they are exempt from Astangata haran.

23.24 Krurodaya Haran or Krurodaya hanl:

When one or more malefics are in Lagna, Krurodaya Haran is applicable.

Krurodaya haran

(Reduction in years)

= Number of Navamsas passed by the

Lagna in that sign X total Ayu given by


the malific planet after _other harans + 108.

This haran is subject to the following conditions:

{i) In case the ascendant is aspected by a benefic, the haran so obtained is reduced to half.

{ii) When there are more than one malefics in the Lagna, the planet nearer to the Lagna only is liable to this reduction.

{iii) If the Lagna is occupied by a malefic which is Lagna lord also, no reduction due to this haran is done.

{iv) In case a benefic as well as a malefic are in the Lagna. this reduction is to be done as stated by Mukul Daivagya 'Parvatiya' in his book i'\yurnirnaya .

23.25 Method:

{i) Convert the nirayana longitudes of the planets into degrees.

{ii) Write down the exaltation points of the planets.

{iii) Find out {i) minus {ii) or {ii) minus {i) but N-le difference should be more than 180°. In case it is less than 180° deduct the difference from 360° and it will be called the arc of longevity.

{iv) Multiply the arc of longevity by the full term of the planet and divide it by 360. the gross number of years contributed by the planet are arrived at.

{v) On applying harans or reduction to {iv), the net number of years given by the planet are obtained.

{vi) Lagna contributes the number of years of Ayu equal to the Navamsas passed by the Lagna in the rashi of Lagna. Number of sign is ignored for calculating Navamsas passed. In the example longitude of Lagna is 1 sign. 23 degrees and 18 minutes. Now ignoring the sign we see that the lagna has passed 6 Navmansas and 3° 18' in that sign .. Now one Navmansa = 3a 20' = 200', so the Ayu contributed by 3° 18' = 198' is equal to 198/200 years or 0.99 years.

(The Ayu contrubuted by the Lagna in this case will become 6.99 years.)

23.26 Now we take an example to illustrate the method of Pindayu. A native born at Delhi on 23.5.1951 at 6:30AM {I.S.T)


Planet Longitudes -- longitudes in

s 0 ' Degrees upto 2 places of decimals

Sun 1 7 56 37.93 Moon 8 3 35 243.58 Mars 1 7 49 37.82

Mercury 0 12 45 12.75

Jupiter 11 13 21 343.35

Venus 2 20 19 80.32

Saturn (R) 5 2 26 152.43

Rahu 10 22 45 322.75

Ketu 4 22 45 142.75

Lagna 1 23 18 53.30

!V Asc Jup Mer Sun Ven

Mar .1.

Rahu

Ketu

Moon Sat (R)

Longitude Exaltation Difference Gross Ayu contributed point

Sun 37.93 10 332.07 332.07 X 19 + 360; 17.526

Moon 243.58 33 210.58 210.58 X 25 -i- 360; 14.624

Mars 37.82 298 260.18 260.18 X 15 -i- 360; 10.841

Mer 12.75 165 207.75 207.75 X 12 + 360 = 6.925

Jup 343.35 95 248.35 248.35 X 15 + 360 = 10.348

Ven 80.32 357 276.68 276.68 X 21 + 360 = 16.140

Sat 152.43 200 312.43 312.43 X 20 + 360 = 17.357


Gross Ayu Chakrapath Shatrukihetriya Astangada Krurodaya NetAyu

Haran Harar Hararon Haran in years

Sun 17.526 - 1/3 - 0.756 10.928

Moon 14.624 1/10 - - - 13.162

Mars 10.841 - - 1/2 - 5.420

Mer. 6.925 1/2 - - - 3.463

Jup. 10.348 1/4 - - - 7.761

Ven 16.140 - ,. - - 16.140

Sat 17.357 - - - - 17.357

Lagna 6.990 as calculated earlier in para 26.25 (vi) 6.990

Total 81.221 yrs

Krurodaya haran-This reduction is applied to the Sun as it is nearer to the Lagna, than Mars.

Ayu given by the Sun after the first three Harans

= 17.526-(17.526 + 3)

= 17.526- 5.842 = 11.684

Krurodaya haran = (6.99 X 11.684) + 108 = 0.756 years.

Net Ayu given by the sun= 11.684-0.756 = 10.928

·Net Ayu given by Moon= 14.624- (14.624 + 10)

= 14.624- 1.462 = 13.162

Similarly deducting 1/2 from Mercury and 1/4 from Jupiter we have obtained the above Net Ayus.

0.221 years = 0.221 x 12 = 2.652 months = 0.652 x 30 = 19.560 days. Or 81 years 2 months 19.56 days.

23.3 Amsayu :

Amsayu is calculated when the lagna is more powerful than the Sun and the Moon.

Number of years of life in Amsayu is equal to the number of Navamansas passed from Aries by the planets subject to certain Bharans (additions) and Harans (reductions). One Navmansa is equal to 3° 20· = 200'. Orie method adopted by most of writers to find the gross period given by the planets is to convert the longitudes of the planets into minutes and divide it by 200. Quotient is again divided by 12, the remainder after this second division gives the number of years


contributed by the planets. Remainder of the first division denotes the part of the year, which is calculated on dividing the remainder by 200 and obtained in decimals.

The second and easy method is to prepare the Navmansa chart. The number of sign occupied by the planet in this chart minus one gives the complete number of years. The number of degrees and minutes passed from the previous Navmansa divided by 200 shows the part of the year in decimals. Ayu given by the Lagna is also calculated likewise. It shall be explained by the example horoscope.

The Ayu granted by a planet is subject to both Bharans and Harans also.

23.31 Bharans:

(a) In case a planet is retrograde or in the sign of exaltation, the Ayu granted by the planet is multiplied by 3.

(b) When a planet is Vargottam or in its own sign or own navmansa or own dreshkona, the term given by it is multiplied by 2.

(c) The multiplication will be done once only. In case the Ayu is liable to be multiplied by 3 and 3 or 3 and 2 or 2 and 2 according to (a) and (b), the multiplication is to be done once and that too by the highest factor.

23.32 Harans:

Harans are calculated as in Pindayu on the Ayu obtained after Bharans. Krurodaya Haran is not applicable in this system of finding the Ayurdaya. ·

21.33 Now we take the horoscope taken in Pindayu:

Planet Longitudes

s 0

Sun 1 7 56 Moon 8 3 35

Mars 1 ·7 49

Mer. 0 12 45

Jup 11 13 21

Ven 2 20 19

Sat (R) 5 2 26

Lag. 1 23 18


Rashi Chart RashiChart

VAse Jup Mer Sun Ven

Mars~

Rahu

Ketu

Moon Sat (R)

Navamsa Chart Navamsa Chart

Sun Ven Moon Mars Rahu

Asc, Mer

/,

Sat

Jup Ketu

Dreshkona Chart Dreshkona Chart

Ketu Sun Mars

Ven Jup

r Asc, Mer

~

Moon Rahu Sat


Sun is in the 12th sign in the Navmansa chart showing that it has passed eleven navmansas from Aries and in the 12th Navamsa it has covered 7o 56'- 6° 40' = 1° 16' = 76' out of 200' (duration of one navmansa). Ufe given by sun = 11 + 76 + 200

= 11 + 0.380 = 11.380 years.

For part of a year the longitudes in a sign in the Rashi chart are seen and navmansas are complete at 3° 20', 6° 40', 10°, 13° 20', 16° 40', 20°, 23°20', 26° 40' and30°. The part of navmansa is equal to the longitude of a planet neglecting sign minus the complete navmansa immediately preceeding. The part of a year life awarded is in proportion of this difference divided by 200

Now consider the Moon, it is in 2nd navmansa in navmansa chart. So one navmansa has completed showing 1 year of life. Part of the year is (3° 35'- 3° 20') + 200' or 15 + 200 = 0.075 years. Ayu awarded by the Moon = 1.075 years. This way the Ayurdaya of all the

. planets including the Lagna are calculated and Bharans as well as Harans are applied as discussed earlier.

Pross years Bharan Ayu after Chakrapath Shatru Astangata

Bharan Kshtriya

Sun 11.380 - 11.380 - 1/3 -Moon 1.075 - 1.075 1/10 - -Mars 11.345 - 11.345 - - 1/2

Mer. 3.825 - 3.825 1/2 - -Jup. 7.005 x2 14.010 1/4 - -Ven 0.095 - 0.095 - - -Sat 9.730 x3 29.190 - - -Lagna 3.990 - - - - -

59 years+ 0.925 x 12 =59 yrs. + 11.1 months = 59 yrs 11 months + 0.1 x 30 days.

= 59 yrs 11 months 3 days.

NetAyu

7.587

0.968

5.672

1.913

10.510

0.095

29.190

3.990

59.925!,'S.

Saturn is retrograde, so Ayu given by it is multiplied by 3, Jupiter is in its own sign, so its Ayu is multiplied by 2. Harans are as in Pindayu except Krurodaya Haran.

23.4 Naisargikayu is calculated when the Moon is stronger than the Sun and the Lagna. It is calculated like Pindayu. Number of years of life given by the planets Sun, Moon, Mars, Mercury, Jupiter, Venus


and Saturn at their deep exaltation points are 20, 1, 2, 9, 18, 20 and 50 years respectively.

Method of calculation including Harans is the same as that of Pindayu.

23.5 Nakshatrayu:

It is also calculated like Pindayu. The difference is that the m9ximum span of life in years contributed by the planets Sun, Moon, M~rs, Rahu, Jupiter, Saturn, Mercury, Ketu and Venus is 6, 10, 7, 18, 16, 19, 17,7 and20 years respectively which is the number of years of their contribution in vimshotri dash a system. This Ayu is contributed at their deep exaltation points. The Harans are the same and no Bharans as in Pindayu. This method is different from that of Kalidi!is.

lXXIV I Shadbala

24.1 Shadbala consists of six different type of strengths. The same are:

(i) Positional strength (Sthana bala) (ii) Directional strength (Dig bala) (iii) Temporal strength (Kal bala) (iv) Motional strength (Chesta bala) (v) Natural strength (Naisargik bala) (vi) Aspectual strength (Drik bala)

Rahu and Ketu have no physical existence and they are simply mathematical planets. So their strength is not calculated. The strength of the seven planets (Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn) are found out for the following purposes :

(i) To ascertain whether the Lagna or the Moon or the Sun is stronger for the calculation of Amshayu, Naisargikayu and Pindayu.

(ii) Stronger planets are expected to give good results while the weaker planets bestow bad results.

(iii) Results of Dasa and Antar-Dasa depends on the strength of the Dashanath and Antardasanath. Normally the results of Antardasanath are felt during the period of Antardasha but if the Dashanath is much more powerful than the Antardashanath the result will be according to Dashanath.

(iv) Bhava results are also influenced by the strength of the planet which is lord or positing or aspecting or the Karka of the Bhava. The stro~ger the planet, the better will be the results of that Bhava.

(v) lshtaphala or Kashtaphala depends on the Uchchabala and Chestabala of the planets. As the name suggests when Ishtaphala is more than the Kashtaphala, the native is mentally happy but in the reverse situation he is mentally unhappy.

242 A standard horoscope is taken before proceeding to actual calculation of the shadbala. The method will be illustrated by this

180 Elements of Astronomy and Astro!9gical Calculations .

example.

Date of birth= 23-5-1951

Time of birth = 6:30AM

Terrestrial latitude 28° 39' (N)

Terrestrial longitude 77° 13' (S)

Aynamsa: 23° 10':45" = 23° 18

Planet Longitude sign Degree

Sun 1 7

Moon 8 3

Mars 1 7

Mercury 0 12

Jupiter 11 13

Venus 2 20

Saturn (R) 5 2

Rahu 10 22

Ketu 4 22

Ascendant 1 23

X cusp. 10 6

Zodiac = 12 signs.

1 sign = 30° (Degree)

1° = 60' (Minute)

Minute

56

35

49

45

21

19

26

45

45

18

47

Day : Wednesday

L.M.T. = 6h:8"':52'

Sunrise = 5:30

Sunset= 19:6

Longitude in degrees upto 2 Places of decimals

37.93

243.58

37.82

12.75

343.35

80.32

152.43

322.75

142.75

53.30

306.78

The minutes are converted into decimals of a degree on multiplying it by 100 and dividing by 60

as 25' = 25 x 100 + 60 = 25 x 10 +-6 ~ 250 + 6 = 0.42°

in short multiply the minutes by 10 and divide by 6.

Numbers after the decimal are obtained

As 38' = 380 + 6 = 0.63°

or 57'= 570 + 6 = 0.95°

24.3 Standard horoscope and Us seven Vargas are :

Elements of Astronomy ar.d Astrological Calculations 181

Rashi Chart RashiChart

V Asc, Jup Mer Mars Ven

Sun ~

Rahu

Ketu

Moon Sat (R)

Oreshkona Chart (0/3) Oreshkona Chart (0/3)

Ketu Sun Mars

Ven Jup

v Asc, Mer

/, '

Moon Rahu Sat

.

Saptmansa Chart (0/7) Saptmansa Chart (0/7)

v Sat Asc. Mer

/,

Rahu

Ketu

Sun Moon

Venus Mars Jup


Navmansa Chart (0/9) Navmansa Chart (0/9)

Sun Rahu Moon Mars Ven

I:V Asc. Mer

,/,

Sat

Jup Ketu

Owadshamsa Chart (0/12) Dwadshamsa Chart (0/12)

Ketu

f/ Asc. Ven

/.

Sun Moon Mars

Jup

Rahu Sat Mer

Trimshamsa Chart (0/30) Trimshamsa Chart (0/30)

Jup Moon Sat Ven

~ As c.

~

Mer Sun Mars


Hora Chart (D/2)

4 Sun Mars Jup Ven Sat Moon

Mer

The strength of plands is measured in Rupa. One Rupa is equal to ov Shashtiamsas. Shashtiamsas will be abbreviated by 'sh'.

24.4 Positional strength or sthana bala:

The strength is gained by a planet due to its position in its Rashi, uchcharashi, enemy sign etc. This strength or weakness is shown as positional strength. It consists of the following five balas :

(i) Uchchabala

(ii) Saptvargiyabala

(iii) Yugmc.-yugm bala or Ojayugmarasyamsa bala

(iv) Kendrabala

(v) Dreshkon bala or Drekkana bale.

24-41 (i) Uchchabala:

A planet gets one Rupa bala when it is at its deep exaltation point and o (zero) at its deblitation point. There is gradual increase from deblitation point to the exaltation point and decrease from exaltation point to deblitation point. There is a difference of 180° between these points from either side. The difference in strength is 1 Rupa or 60 sh. So in X

0 the increase from deblitdtion point will be X0 x 60 + 180 = x/3 sh. So formula for uchchabala becomes : the difference between the longitude of the pla~et and its deblitation point or vice-versa but less than 180°, divided by three will give the Uchchabala.

Let the longitudes of the planet be X 0 and oo of deblitation point. x- D or D- x should be less than 180°. In case it comes more than 180° eitherrevese x and D or deduct the difference from 360°. Uchchbala

x-D 0-x =--or--, where D- x or x- Dis less than 180°.

3 3


Longitudes deblitation Difference not Uchchabala in decimals point exceeding 180° is sh

Suri 37.93 190 152.07 50.69

Moon 243.58 213 30,58 10.19

Mars 37.82 118 80.18 26.73

Mer 12.75 345 27.75 9.25

Jup 343.35 275 68.35 22.78

Ven 80.32 177 96.68 32.23

Sat 152.43 20 132.43 44.14

24.42 (ii) Saptvargiysbala :

Prepare the Panchdha Maitri chakra.

Natural Permanent friendship etc are :

Planet Friend Neutral Enemy

Sun Moon, Mars, Jupiter Mercury Venus, Saturn

Moon Sun, Mercury Mars, Jupiter, -

Venus, Sat

Mars Sun, Moon, Jup Venus, Sat Mer

Mercury Venus, Sun Mars, Jup, Sat Moon

Jupiter Sun, Moon, Mars Sat Mercury, Ven.

Venus Mer, Sat Mars, Jup Sun, Moon

Saturn Mer, Ven Jup Sun, Moon, Mars

Tatkalik or temporary friendship chart :

Planets in II, Ill, IV, X, XI and XII houses from a planet are its temporary friends and those in I, V, Vl, VII, VIII and IX houses are its temporary enemies.

Planet Friend Enemy

Sun Ver, Mer, Jup Moon, Mars, Sat Moon Jup, Sat Sun, Mars, Mer, Venus Mars Mer, Jup, Ven Sun, Moon, Sat

Mer Sun, Mars, Jup, Ven Moon, Sat Jup Sun, Moon Mars, Mer, Ven Sat Ven Sun, Mars, M2r, Jup, Sat Moon Sat Moon, Venus Sun, Mars, Mer, Jup

I


The combination of the above two typ.es of friendship gives the following relationship :

Tempoi"GG'JJ Natural Resultant

Friend Friend Fast Friend (F.F.)

Friend Neutral Friend(F.)

Friend Enemy Neutral(N)

Enemy Neutral Enemy(E)

Enemy Enemy Bitter Enemy (B.E.)

Enemy Friend· Neutral(N)

Panchdha Maitri Chakra is

Planet F. F. F. N. E. B.E.

Sun Jup Mer Ven, Moon, - Sat Mars

Moon - Jup, Sat Sun, Mer Mars, Ven -Mars Jup Ven Sun, Moon, Sat -

Mer

Mer Sun, Ven Mars, Jup - Sat Moon

Jup Sun, Moon, - Mer, Ven Sat -Mars

Ven Mer, Sat Mars, Jup Sun - Moon

Sat Ven - Mer, Moon Jup Sun, Mars

The planets get the following strength due to their position in Mooltrikona Rashi chart (D/1) only and for all the charts in own rashi, or the houses of FF, F, N, E and BE as given below:

(i) Mooltrikona Rashi = 45 sh (ii) Own rashi = 30 sh (iii) Fast Friends (F. F.) sign = 22.5 sh (iv) Friends (F) sign = 15 sh (v) Neutrals (N) sign = 7.5 sh (vi) Enemy's (E) sign ·= 3.75 sh (vii) Bitter enemy's (BE) sign = 1.875 sh. From Panchdha Maitri chart we observe : No planet is in its Mooltrikona sign in rashi chart (D/1). Jupiter is

in own sign in Rashi Chart as vyell in saptrnansa chart, it will get 30 sh for both charts.

Moon is in Friend's sign in Dreshkon chart so it will get there 15sh. Mercury is in Moon's sign in Navmansa chart which is BEs house, it will


get only 1.875 sh. there. This way the strength for various planets and various Vargas for the example horoscope is given below :

Chart Sun Moon Mars Mer Jup Ven Sat Rashi 7.5 15.0 15.0 15.0 30.0 22.5 7.5 Hora 7.5 7.5 7.5 22.5 22.5 1.875 7.5 Dreshkon 7.5 15.0 15.0 22.5 22.5 22.5 7.5 Saptmansa 22.5 15.0 22.5 30.0 30.0 30.0 3.75 Navmansa 22.5 3.75 22.5 1.875 22.5 15.0 30.0 Dwadshamsa 30.0 15.0 7.5 30.0 22.5 22.5 7.5 Trimsamsa 15.0 3.75 7.5 15 30.0 22.5 22.5

Total Saptvargiya bala 112.50 75.00 97.50 136.875 180.00 136.875 86.25

24.43 (iii) Yugmayugmbala or Ojayugmarasyma bala:

It is a strength gained by a planet on account of occupying an odd or even Rashis in the Rashi and Navmansa charts.

Sun, Mars, Mercury, Jupiter and Saturn are powerful in odd Rashis in the Rashi and Navmansa charts and they get 15 sh for each. In case any of these in odd Rasi in D/1 it will get 15 sh and if in odd Navmansa also it will again obtain 15 sh. While for occupation of even Rashi or even Navmansa it will get 0 (zero).lt is in odd Rashi and even Navmansa its strength = 15 + 0 = 15 sh. If in even Rashi and odd Navmansa, strength = 0 + 15 = 15 sh. If in even Rashi and even Navmansa, it gets 0 + 0 = 0 sh, In case it is in odd Rashi and odd Navmans. its strength = 15 + 15 = 30 sh.

Moon and Venus get the strength in even Rashi and even Navmansa.

The Yugmayugm bala is :

Planet Rashi Navmansa Total andBala andBala Yugmayugm bala

Sun 2 even= 0 12 even= 0 0

Moon 9 odd= 0 .2 even = 15 15

Mars 2 even= 0 12 even= 0 0

Mer 1 odd= 15 4 even= 0 15

Jup 12 even= 0 8 even= 0 0

Ven 3odd=O 1 odd= 0 0

Sat 6 even= 0 10even = 0 0


24.44 (iv) Kendra bala:

Planets in Kendra (1, IV, VII and X houses) in Rashi chart get 60 sh bala . in Panpharas (II, V, VIII and XI houses) obtain 30 sh and planets in Apoklima (Ill, VI, IX and XII houses) obtain 15 sh bala. as Kendra bala.

There is diversity of opinion as to what Kendras are. We follow the system in which the Bravas are decided as per Rashi chart and not by Chalit chart which is Parashar's view.

24.45 (v) Dreshkon bala:

Masculine planets (Sun, Mars and Jupiter) obtain the strength of 15 sh. in case they are posited in the Ist Dreshkon (0° to 10°) of any sign. Hermaphrodites planets (Mercury and Sa tum) get 15 sh. Bala. if they are in the 2nd Dreshkon (10° to 20°) of any sign. Female planets (Moon and Venus) get 15 sh. Bala, when they are in the 3rd Dreshkon (20° to 30°) of any sign as Dreshkon Bala, otherwise zero. Here. Sun a male planet is in Ist Dreshkon will15 sh. while Sat is also in Ist Dreshkon will get 0 sh. bala. Kendra bala and Dreshkon bala of the example horoscope are given below :

Planet Kendra Bala Dreshkon Bala Kind of house No. ofDreshkon

Sun Kendra 60 sh. I 15sh.

Moon Panphora 30sh. I 0

Mars Kendra 60sh. I 15 sh.

Mer Apoklima 15 sh. II 15sh.

Jup Panphara 30sh. I! 0

Ven Panphara 30 sh. III 15 sh.

Sat. Panphara 30sh. I 0

Total Position strength (sthan bala)

Planet Uchchbala Saptvargiya Yugma Kendra Dreshkon Total Bala Yugm bala Ba!a Ba!a Sthan ba!a

Sun 50.69 112.50 0 60.00 15.00 238.19

Moon 10.19 75.00 15.00 30.00 0 130.19

Mars 26.73 97.50 0 60.00 15.00 199.23

Mer 9.25 136.87 15.00 15.00 15.00 191.12

Jup 22.78 180.00 0 30.00 0 232.78

Ven 32.23 136.87 0 30.00 15.00 214.10

Sat 44.14 86.25 0 30.00 0 160.39


24.5 Digbala (Directional strength) :

Digbala is the strength of the planet gained due to the direction in which it is posited in the horoscope.

Ascendant represents the East, Descendant (VII house) represents the West, Tenth cusp (Meridian cusp) represents the South and the IV cusp represents the North in a horoscope.

The powerful and powerless directions of the planets is tabulated below:

Planet Powerful point Powerless point

Jupiter & Mercury I house cusp VII house cusp

Moon&Venus IV house cusp X house cusp

Saturn VII house cusp I house cusp

Sun and Mars X house cusp IV house cusp

Representation of powerful house by an horoscope is :

It is quite interesting to draw inference from natural phenomena, with regard to the directional strength of the planets, by placing the Sun at the 4 Kendras. When the Sun is at the 1st Kendra i.e., Lagna will indicate the dawn or early morning which time is favourable for religions Pujas or studies and learning. Hence it preside over learning and religion (Jupiter and Mercury) are strong in the morning or say Lagna. When the Sun is in the IV house, it is the time around mid-night. At this portion of time women 1\l'e strong, so the female planets (Moon and Venus) are strong in IV house. Sun in the 7th house indicates the time of evening which is called Asura-Sandhya:the tamsic planet (Saturn) is


strong in VII house. When Sun is in the lOth house, it is mid-day. It is the time for action, therefore the two male planets (Sun and Mars) are· strong in 1Oth house. Digbala is calculated by subtracting the powerless point from the longitude of the planet subject to less than 180°. if it is more than 180° deduct it from 360°. Divide the difference which is less than 180° by 3 and Digbala is obtained.

Calculation ofDigbala of the example horoscope:

I cusp 53.30 lV cusp 126.78

VII cusp 233.30 X cusp 306.78

Planet Longitude Powerless Difference Digbala

of planet point less than 180°

Sun 37.93 126.78 88.85 88.85 + 3 = 29.62

Moon 243.58 306.78 63.20 63.20 + 3 = 21.07

Mars 37.82 126.78 88.96 88.96 + 3 = 29.65

Mer 12.75 233.30 139.45 139.45 + 3 = 46.48

Jup 343.35 233.30 110.05 110.05 + 3 = 36.68

Ven R0.32 306.78 133.54 133.54 + 3 = 44.51

Sat 152.43 53.30 99.13 99.13 + 3 = 33.04

24.6 Kal Bala (Temporal strength)

As the name suggests Kal bala is the strength gained by a planet · due to time of the birth which includes, day or night, year of birth, day of birth etc. It consists of nine balas given below :

(i) Nathonnath bala

(ii) Paksha bala

(iii) Tribhag bala

(iv) Abda bala

(v) Masa bala

(vi) Vara Bala

(vii) Hora bala

(viii) Ayan bala

(ix) Yuddha bala

Thes~ strengths are explained and calculated for the-ex~mple horoscope.

24.61 (i) Nathoimath bala or Diva-Ratri bola:

Time interval from mid-night to mid-day is called Purva-Nath and from mid-day to mid-night is Paschim-Nath or Unnath. So this strimgh is known as Notho-Natha Bala.

Sun, Jupiter and Venus are most powerful at mid-day and

· 190 Elements of Astronomy and Astrological Calculations

powerless at Mid-night. Mars, Moon and Saturn are powerful at midnight and powerless at mid-day. Mercury is always powerful.

Sun, Jupiter, Venus get 60 sh. bala at mid-day and zero at midnight. While Moon, Mars and Saturn get 60 sh. bala at mid-night and 0 at mid-day. Mercury always get 60 sh. The method of finding the time of mid-day. in 'I.S.T. has already been given in para 4-7. By subtracting 12 hours from it we get the time of mid-night in J.S.T.

In 12 hours = 720 minutes the strength increases from 0 to 60 sh. so in one minute it will increase by 60 + 720 and in x minutes from powerless point it will be 60 X x + 720 = x + 12. Now the formula becomes : if the birth time is before noon, find the duration of time after mid-night which is called x in minutes and divide by 12 for the strength of the planets that are strong at mid-day. In case the time of birth is after mid-day and before mid-night, subtract the time converted into railway time (3 P.M. = 12 + 3 = 15 hours) from 24 and dividing it by 12, strengths of planets that are strong at mid-day is knwon.

Subtracting the strength of Sun etc from 60. The strength of the planets which are powerful at mid-night is known.

Time of sun set = 19 : 06 I.S.T.

Time of Sun rise = 5 : 30 l.S.T.

Oinman

Mid-day

= 13 : 36 hours and 1/2 Oinman = 6 : 48

= 5 : 30 + 6 : 48 = 12 : 18

The other method for finding mid-day

At Delhi the mean mid-day time = 12 + 0: 21 : 8 = 12 : 21 : 8

Equation of time on 23rd May = (-) 0 : 3

Mid-day to nearest minute = 12: 18

Mid-night = 12 : 18- 12 = 0 : 18 I.S.T.

Time of birth = 6 : 30 l.S.T.

As it is after mid-night and before mid-day. The strength of sun, Jupiter and Venus = (6 : 30- 0 : 18) + 12 sh.

= 6h: 12m+ 12 = 372m+ 12 = 31 sh. each

Strength of Mars, Moon and Saturn = 60-31 = 29 sh. each Nathonathbala of Mercury = 60 sh.

24.62 (ii) Paksha bala is the strength of the planets obtained by the fortnight/Paksha in which the native was born. Actually it is related with the angular distanc;,e of the Moo~ from the Sun. When the Moon is

. weak, from Krishan Paksha Ashtami to Sukla Paksha Ash !ami (less than half). the Malefic planets are more powerful and the time when


the Moon is more than half Benefics are more powerful.

The Moon, Mercury, Jupiter and Venus are Benefics. The sun, Mars and Saturn are Malafics.

Paksha Bala of Moon = 2 x Paksha Bala of Benefics.

Method of Calculation:

(i) Find out the differer.ce of longitudes of Moon and the Sun i.e. Longitude of Moon-·1·-.; ''Jitudz of Sun.

(ii) If the difference i5 n 1•:.re than l.SL)o either deduct it from 360° or find out longitude of Sun--longitude of Moon.

(iii) As the Paksha Bala of Bendics is zero at the end of Amavasya (When sun and Moon have equal longitudes) and it is 60 sh. at the end of Pumima when the difference between the longitudes of the Moon and the Sun is 180°. The formula becomes, Pakshabala of Benefics = (Longitude of Moon -Longitude of Sun) x 60 + 180

or (Longitude of Sun- Longitude of Moon) X 60 + 180

The difference of longitudes should be less than 180°.

Paksha Bala for the example horoscope is :

Longitude of the Moon = 243.58

Longitude of the sun = 37.93

Deducting we get = 205.65 which is more than 180° so deducting it from 360° we get = 360-205.65 = 154.35 (A)

or37.93 -243.58 = 37.93 + 360-243.58 = 397.93-243.58 = 154.35 equals to (A)

Pakshabala ofBenefics = 154.35+3 = 51.45 sh. (as60+180=3)

Pakshabla of Malefics = 60- 51.45 = 8.55 sh.

Pakshabala of Moon = 51.45 X 2 = 102.90 sh.

Pakshabla of the planets is-

Sun

8.55

Moon Mars Mer

102.90 8.55 51.45

24.63 (ill) Trlbhagbala :

Jup

51.45

Ven Sat

51.45 8.55

Dinman or duration of day is the time elapsed between sun rise to Sun set and Ratriman or the duration of night is the time from sun set to sun rise. As both of these are divided into three equal parts, so it is called Tribhag (one-third part) bala. The lord of the part gets 60 sh. bala. Jupiter always get 60 sh. bala. The first part of the day from Sun rise to the time got after adding one third of the day. The second part is


from the time of ending of first part to the time after adding one third of the day in it. The third part from the end of second part to sunset. Similarly the three part> are in the night from sunset to next sunrise.

For example horoscope:

Sun rise = 5 : 30, Sun Set = 19 : 06

Dinman = 19 : 06 - 5 : 30 = 13 : 36,

Ratriman = 24- 13 : 36 = 10 : 24

one third of Dinman = 13 : 36 + 3 = 4 : 32

I part of day ends at 5: 30 + 4: 32 = 10: 02

II part of day ends at 10: 02 + 4: 32 = 14: 34

III part of day ends at 14: 34 + 4: 32 = 19: 06

One third of Ratriman = 10: 24 + 3 = 3: 28

I part of Ratri rmds at = 19: 06 + 3 : 28 = 22 : 34

II part of Ratri ends at = 22 : 34 + 3 : 28 = 26 : 02 or 2 : 02 A.M. of next date

III part of Ratri ends at = 2 : 02 + 3 : 28 = 5 : 30

Lords of the various parts of Day and Night are as under :

Part

II

Ill

Day

Mercury

Sun

Saturn

Night

Moon

Venus

Mars

The native of the example horoscope was born at 6 : 30 AM. Which falls in the I part of the day whose lord is Mercury, so Mercury gets = 60 sh. bala and Jupiter gets = 60 sh. bala.

24.64 (iv) Abda-bala:

Abda means year. In Indian astronomy a year is considered of 360 days and a month of 30 days. These are not related to the motion of the Sun or the Moon.

Abdhadipati is the Lord of the first day of such a year and gets 15 Shashtiamsas as Ahda bala and rest of the planets get zero.

Ahargana is the number of days elapsed since beginning of the creation to particular epoch. These Ahargana are known as Srishtyadi Ahargana.

Srishtyadi Ahargana upto 31/12/1940 = 714,404, 138, 157

Dividing these by 360 X 7 = 2520 we get Q = 283, 493, 705 and

Elements of Astronomy and Astrological Cakulalions 193

1557 as Remainder. These have been divided by 2520, as the same day arrives after 7 such years. To avoid tedious calculations a table of Ahargana.has been prepared by taking 1557 days completed upto 31/ 12/1940 which is given before Ayanbala. The results arrived at according Ia this table will tally with those calculated from the Srishtyadi Ahargana.

24.65 Abda bala :

Ahargana on 31/12/1950 = 5209

Noofdayspassedfrom 1-1-51to30-4-1951 = 120

22

1

No. of days passed in May

Current day

Total

= = = 5352

Now on dividing 5352 by 360 we get Q = 14 and Remainder = 312.

In one year there are 360 days and dividing it by 7 we gel Q = 51 and R = 3. So 51 are the completed weeks and 3 days are left.

14 years have been completed in example horoscope and the number of days more than completed weeks = 14 x 3 = 42

Upto the first day of the next year the number of days is 42 + 1 = 43, dividing 43 by 7, the remainder is 1. So one day is more than the completed weeks.

1 represents Sunday, 2 for Monday, 3 for Tuesday, 4 for Wednesday, 5 for Thursday, 6 for Friday, 0 or 1 for Saturday.

As the remainder is 1 so it was Sunday and its Lord the Sun gels Abda bala = 15 sh and others nil.

24.66 Masa bala :

Lord of the fin.t day of the month gets 30 sh and others zero. In a month there are 30 days, when divided by 7, the Q = 4 and remainder is 2. So in a month 2 days are more than the completed weeks.

Ahargana is 5352, dividing it by 30, the Q comes 178 and R is 12 showing that 178 months had been completed.

Now multiply the Q by 2 and add 1, for finding the 1st day of month ln which the native was born. ·

178 x 2 + 1 = 356 + 1 = 357 days more than the completed weeks.

Now 357 + 7 and remainder is zero.

The remainder o means the first day of the month was Saturday and Saturn became Masadhipati. It obtained 30 sh. as Masabala and the remaining planets got zero.


24.67 Vara bala:

Lord of the day gets 45 sh. and others zero. Ahargana is 5352, dividing it by 7. the Q = 764 and R = 4. The remainder 4 indicated that the day was Wednesday. Its lord Mercury gets 45 sh. as Vara bala and the rest zero.

24.68 Hora bala:

One hora = one hour and 1st hora starts from the Sunrise and last for one hour. There are 24 horas in a day. The lord of 1st hora is the lord of the day. For calculating the Horadhipati keep the planets in a circle in their descending order of sidereal time in anti-clock wise direction. Start counting from the lord of first hora in the same direction (anticlock wise) the lord of the required hora can be known.

7, 14,21 Ven

23, 16, 9, 2 Moon

Fig. 32

Mars 5, 12, 19

Jup 4. 11, 18

Saturn 3, 10, 17,24

Here lord of 1st hora is Mercury (as it was Wednesday) Lord of 2"" hora is Moon and so on as indicated against each. In the example horoscope:

Birth time

Sun rise

Difference

= 6:30:0

= 5:30:0

= 1:0:0

As it comes to exact one hour and the 2nd hora starts at that time. So the Lord of 2nd hora, the Moon get 60 sh. as hora bala and rest plal")ets zero.

Sripatipaddhati has giben other method of knwoing the number of hora and it is.

Longitude of Lagna = 1' 23° 18'

deduct longitude of the sun = 1 7 56

0 15 22

Multiplying it by 2 we get =0 15 22 X 2 = 1 : 0 : 44


As it was more than 1. So it was second hora. Table I of Ahargana

Ending Ahargana Ending Ahargana Ending Ahargana 31st Dec. 31s: Dec. 31st Dec.

1940 1557 1970 12514 2000 23472 1941 1922 1971 12879 2001 23837 1942 2287 1972 13245 2002 24202 1943 2652 1973 13610 2003 24567 1944 3018 1974 13975 2004 24933 1945 3383 1975 14340 2005 25298 1946 3748 1976 14706 2006 25663 1947 4113 1977 15071 2007 26028 1948 4479 1978 15436 2008 26394 1949 4844 1979 15801 2009 26759 1950 5209 1980 16167 2010 27124 1951 5574 1981 16532 2011 27489 1952 5940 1982 16897 2012 27855 1953 6305 1983 17262 2013 28220 1954 6670 1984 17628 2014 28585 1955 7035 1985 17993 2015 28950 1956 7401 1986 18358 2016 2931(~

1957 7766 1987 18723 2017 29681 1958 8131 1988 19089 2018 30046 1959 8496 1989 19454 2019 30411 1960 8862 1990 19819 2020 30777 1961 9227 1991 20184 2021 31142 1962 9592 1992 20550 2042 31507 1963 9957 1993 20915 2023 31872 1964 10323 1994 21280 2024 32238 1965 10688 1995 21645 2025 32603 1966 11053 1996 22011 2026 32968 1967 11418 1997 22376 2(127 33333 1968 11784 1998 22741 2028 33699 1969 12149 1999 23106 2029 34064


24.69 Ayan Bala:

The strength gained by a planet due to its position in the North or South of the celestial equator is called the Ayan Bala. Ayan bala is based on the declination of a planet. There are two types of Kranti (declination) in Indian Astronomy. (i) Actual declination known as 'Spastha' Kranti is the angular distance of a planet from it to the foot of the perpendicular on the celestial equator. (ii) The other type of declination known as 'Madhyama' Kranti. When a perpendicular is drawn from a point on the ecliptic which coincides with the longitude of the planet to the celestial equator, the angle subtended by this arc is 'Madhyama' Kranti. In other words the planet is assumed to be at the ecliptic and its perpendicular angular distance from the celestial equator is 'Madhyama' Kranti.

for calculation of Ayan bala, this Madhyama Kranti is used. When a planet is towards North of the celestial equator, its declination is suffixed by Nor +, if it is towards South, the declination is suffixed by S or-. Sun crosses the celestial equator twice in a year, one about 21/3 going from south of the equator to North and this point is known as vernal equinox (spring equinox). The other time about 23/9 moving from North to South, this point is called autumnal equinox. Declination of the Sun is zero on both these occasions and the sun is on sayana Aries and sayana Libra.

This Madhyama Kranti is found out from the Sayana longitudes of the planets.

Three methods of finding the declination used for Ayan bala, are given here :

(a) The olden method for obtaining the value of declination as narrated by Bhaskaracharya in his wmks Brahmtulya which is also called Karankutuhal, is as under : ·

(i) Convert the Nirayana longitude into sayana longitudes.

(ii) Find the nearest distance of this longitudes from the equinotical points (called Bhuja) by the following method :

When sayana longitudes are oo to 90°, Bhuja = longitude- oo

When sayana longitudes are 90° to 180°, Bhuja = 180o -longitude

When sayana longitudes are 180° to 270°, Bhuja = longitude- 180°

When sayana longitudes are 270° to 360°, Bhuja = 360° -longitude

The declination is north, when the sayana longitudes is between oo and 180°, it is south if the sayana longitude is 180° to 360°.

Elerr.znts of Astronomy and AStrological Calculations 197

(iii) When Bhuja is Declination is ()" = 0' 15° = 362' + 0 =362' 30° = 362' + 341' == 703' 450 = 703' + 299' == 1002' 600 == 1002' + 236' == 1238' 75° = 1238 + 150' == 1388' 90" = 1388' +52 = 1440' = 24°

In Indian Astronomy maximum declination c.i the sun is taken as 24° North or South, while it is about 23° 27' as per modem astronomy. Here 24° shall be taken, in the third method 23° 27' will be considered.

For the intermediate positions, it is calculated by the rule of three.

The declination and Ayan Bala of the example horoscope is calculated :

Aynamsa = 23°.18

Planet ~irayana longitudes !Sayan a Bhuja= Difference from

' 0 ' Degrees in longitudes nearest equinotical point Decimals

Sun 1 7 56 37.93 61.11 61.11-0 = 61.11 Moon 8 3 35 243.58 266.76 266.76- 180 = 86.76 Mars 1 7 49 37.82 61.00 61.00-0 = 61.00 Mercury 0 12 45 12.75 35,93 35.93-0 = 35.93 Jupiter 11 13 21 343.35 6.53 (.53- 0 = 6.53

Venus 2 20 19 80.32 103.50 180 - 103.50 = 76.50

Saturn 5 2 26 152.43 175.61 180- 175.61 = 4.39

Sayan longitudes of all the planets except Moon are less than 180° so their declination is North and of Moon South.

Declination

Planets in Minutes Degree M Degrees in decimals

Sun 1238 + (1.11 X 150) + 15,.,12~9.10 20 49 20.82 (N)

Moon 1388 + (11.76 X 52)+ 15=1428.77 23 49 23.81 (S) Mars 1238 + (1 X 150) + 15=1248.00 20 48 20.80 (N)

Mer 703 + (5.93 X 299) + 15=821.20 13 41 13.69 (N)

Jup 0 + (6.53 X 362) + 15=157.59 2 37 2.62 (N)

Ven 1388 + (1.50 X 52\+ 15=1393.2 23 13 23.2L (N)

Sat. 0 + (439 X 362) + 15=105.94 1 46 1.77 (N)

198 Elements of Astronomy and A~trological Calculations

Every planet gets 0.5 Rupa = 30 sh. bala at the equator. The strength of Sun, Mars, Jupiter and Venus increases as they move towards north and becomes 60 sh. when their declination reaches 24° (N) and their strength decreases as they go Southwards. and becomes zero sh. at 24 (S) declination. Just opposite to them strength of Moon Saturn decreases when they move towards North and increases in the Southern declination i.e. their strength at 24° (N) declination is zero and at 24° (S) is 60 sh. Mercury's strength increases in both the directions and becomes 60 sh. at 24° (N) or 24° (S) declinations. Sun' sAyan Bala is always doubled. The formula becomes that for Sun, Mars, Jupiter and Venus Northern declination is additive in 24 and Southern declination is deductive from 24. For Moon and Saturn the Southern declination is additive and Northern one deductive from 24. While for Mercury both the declinations are additive in 24.

Maximum difference in declination is from 24° South to 24° North or vice-versa = 24 + 24 = 48° and the maximum difference in strength is 0 to 60 sh. = 60 sh.

So in 48° strength gained = 60 sh. as Ayan bala

in X0 strength gained = 60 X x + 48

=X X 5 + 4 sh.

As the declinations of Sun, Mars, Jup and Venus are Northern, so they are additive, Moon's is sourthern one so additive, Saturn's is Northern, so deductive while Mercury's is always additive

Planet Ayanbala in shashtyamsas

Sun 2 X (24 + 20.82) X 5 + 4 = 112.05

Moon (24 + 23.81) X 5+4 = 59.76

Mars (24 + 20.80) X 5 + 4 = 56.00

Mer (24 + 13.69) X 5+4 = 47.11

Jup (24 + 2.62) X 5+4 = 33.28

Ven (24 + 23.22) X 5+4 = 59.03

Sat (24 - 1. 77) X 5 + 4 = 27.79

24.70 (b) Modern method of calculating declination :

Here also we are presuming that the planets are moving at the ecliptic and the maximum declination on each side is 24°. It is illustrated with the help of a diagram.

In the above figure of a celestial sphere, ACBD is the celestial equator,ECFD is ecliptic the angle between them formed ~t C (Vernal

Elements of Astronomy and Astrological Calculations 19g

Fig.33

equinox) is 24°. 0 is the centre of the earth and centre of the celestial sphere. Let L be a planet and LM is perpedicular arc at the equator so angle CML = goo. CL = mo = sayan longitude of the planet and d is the declination.

Sin formula of the spherical trignometry is

sin a sin b sin c --= --=--sin A sin B sin C

Where A, B and C are angles of a spherical triangle and a, b and c are the sides opposite to them:

Applying it in sperical triangle CML for angles C and M alongwith their corresponding sides we get

sind sin m ---=---sin 24° sin goo

sin 24 x sin m as sin goo= 1 sin d = -----,

1:-----

= sin 24 X sin m.

Let us find out declination for longitudes 15°,30°, 45°, 60°, 75°, and goo

sind = sin 24° x sin 15° = 0.4067 x 0.2588 = 0.1053 or d = 6° 1' = 361'

Counsulting table of sin9 for 24° and 15° and sin inverse as done


for Antilogrithms for calculation of longitudes of planets for 0.1053 we have obtained the declination. sin d ~ sin 24• x sin 30• ~ 0.4067 x 0.5 ~ 0.2034 or d ~ 11•44• ~ 704'

sind ~ sin 24• X sin 45• = 0.4067 x 0.7071 ~ 0.2878 or d ~ 16.43' ~ 1003'

sin d = sin 24• x sin 60° ~ 0.4067 x 0.8660 = 0.3522 or d ~ 20•37' ~ 1237'

sin d ~ sin 24• X sin 75• ~ 0.4067 x 0.9659 ~ 0.3928 or d = 23•3• = 1388'

sind = sin 24• x sin 90• = sin 24• x 1 or d = 24• = 1440'

On comparing these with those of Bhaskaracharya's values, there is negligible difference of 1' in the value of 15°, 30°, 45° and 60° Bhuja.

Noe we f!:1d out for the example horoscope.

Bhuja

Sun 61.11 sind = sin 24 x sin 61.11 = 0.4067 x 0.8756 = 0.3561 or d = zoo 52' = 20.87 (N)

Moon 86.76 sind= sin 24 x sin 86.70 = 0.4067 x 0.9984 = 0.4060 or d = 23° 57' = 23.95 (S)

Mars 61.00 sind= sin 24 x sin 61.00 = 0.4067 X 0.8746 = 0.3557 or d = zoo 50' = 20.82 (N)

Mer 35.93 sind =sin 24 x sin 35.93 = 0.4067 x 0.5868 = 0.2387 or d = 13° 49' = 13.82 (N)

Jup6.53 sind= sin 24 x sin 6.53 = 0.4067 X 0.1137 = 0.0462 or d = zo 39' = 2.65 (N)

Ven 76.50 sind =sin 24 X sin 76.50 = 0.4067 X 0.9724 = 0.3955 or d = 23° 18' = 23.30 (N)

Sat 4.39 sin d = sin 24 x sin 4.39 = 0.4067 x 0.0765 = 0.0311 or d = 1 o 47' = 1.78 (N

Comparing these with those arrived at by olden method, we find a negligible difference in declination and the maximum difference in Ayanbala in this horoscope is in the case of Moon :

Its Ayan Bala = (24 + 23.95) x 5 +4 = 47.95 x 5 +4 = 59.94 while earlier it was 59.76 showing a difference of 0.18 sh. only. This difference is que to the values calculated by Bhaskaracharya's method is the average froin 75° to 90° while the same are nearer to correct value by the modem method.

24.71 (i) The easiest way to find the declination is either to prepare a tab!e of declination for sayana longitudes which is given after this para or to convert the Nirayana longitudes of the horoscope to the year for which the ephemeries is being consulted and find out the declination of the sun for those longitudes. This declination will be a


part of maximum declination = 23° 27' and not 24°. However, the difference in Ayanbala calculated by this method and the traditional method will not differ by more than 0.7 shashtiamsa.

(ii) This method is explained with the help of example horoscope : Ephemeries for the year 2003 shall be used for finding out the declination of the planets. In 2003 the Aynamsa is 23° 54' while at the time of birth of the native it was 23° 11' rounded to nearest minute.

Difference in aynamsa = 23° 54' - 23° 11' = oo 43'

This difference is to be subtracted from the nirayana longitudes of the horoscope for making them Nirayana longitudes of 2003.

Planet Nirayana longitudes Declination of the sun as perepheme-

as per horoscope after ries 2003 =· Dedi-

subtraction nation of planet

' 0 ' ' 0 ' ' 0 '

Sun 1 7 56 1 7 13 20 23 N

Moon 8 2 35 8 1 52 23 24 s Mars 1 7 49 1 7 06 20 21 N

Mercury 0 12 45 0 12 02 13 30 N

Jupiter 11 13 21 11 12 38 2 37 N

Venus 2 20 19 2 19 36 22 45 N

Saturn 5 2 26 5 1 43 1 44 N

As stated above this declination is a part of maximum declination· of 23° 27'. The difference between 24° and 23° 27' = 33'. Maximum difference inAyanbala = 33' x 5+4 = 0.55 x 5+4 = 0.7shashtiamsa, which is negligible or the formula for Ayanbala be amended as ·

(23° 30' + d) X 60 _ (23.5 ± d) X 60. 47 - 47

Table of declination from Bhuja when maximum declination is 24°

Bhuja Declination Bhuja Declination in Degrees ih in Degrees in

Degrees Deg. Min. Decimals Degrees Deg. Min Decimals

1 0 24 0.40 6 2 26 2.43 2 0 49 0.81 7 2 so 2.83 3 1 13 1.22 8 3 15 3.24 4 1 38 1.63 9 3 39 3.65 5 2 02 2.03 10 4 03 4.05


11 4 27 4.45 51 18 25 18.43 12 4 51 4.85 52 18 41 18.69 13 5 15 5.25 53 18 57 18.95 14 5 39 5.65 54 19 12 19.21 15 6 02 6.04 55 19 27 19.45 16 6 26 6.43 56 19 42 19.70 17 6 50 6.83 57 19 57 19.94 18 7 13 7.22 58 20 10 20.17 19 7 36 7.61 59 20 24 20.40 20 8 00 8.00 60 20 37 20.62 21 8 23 8.38 61 20 50 20.84 22 8 45 8.76 62 21 03 21.04 23 9 08 9.14 63 21 15 21.24 24 9 31 9.52 64 21 26 21.44 25 9 54 9.90 65 21 38 21.63 26 10 16 10.27 66 21 48 21.81 27 10 38 10.64 67 21 59 21.99 28 11 00 11.01 68 22 09 22.16 29 11 22 11.37 69 22 19 22.31 30 11 44 11.73 70 22 28 22.46 31 12 06 12.10 71· 22 37 22.61 32 12 27 12.45 72 22 45 22.76 33 12 48 12.80 73 22 53 22.89 34 13 08 13.14 74 23 01 23.02 35 13 29 13.49 75 23 08 23.13 36 13 50 13.83 76 23 15 23.24 37 14 10 14.17 77 23 21 23.35 38 14 30 14.50 78 23 27 23.44 39 14 50 14.83 79 23 32 23.53 40 15 09 15.15 80 23 37 23.61 I·

41 15 28 15.47 81 23 41 23.69 42 15 47 15.79 82 23 45 23.75 43 16 06 16.10 83 23 49 23.81 44 .16 25 16.41 84 23 51 23.86 45 16 43 16.71 85 23 54 ·23.90 46 17 00 17.01 86 23 56 23.94 47 17 18 17.30 87 23 58 23.96 48 17 35 17.59 88 23 59 23.98 49 17 52 17.87 89 24 00 23.99 50 18 09 18.15 90 24 00 24.00

< ...


24.8 Yuddhabala :

Two planets are said to be at war when the distance between

them is less than one degree. As per Parasar the planet is overcome

which is rough, discoloured or South of the other, that is the conguerer

whose disc is the brighter and larger whether it be north or south of the

other. But the method given uy shri B.V. Raman is followed largely. It

states that planet having lesser longitude wins and gains some

strength while the same amount of strength is deducted from the loser.

The Sun and the Moon are two luminaries and as such no planet

goes at war with them. A planet which is nearer to Sun is called combust

and nearer to Moon is called in Samagama. So the planets Mars,

Mercury, Jupiter, Venus and Saturn can be at war with any of them.

24.81 Calculation ofYuddhabala :

Calculate the sum of Sthan bala, Digbala and Kala bala upto

Hora bala of both the planets separately and find out the difference in

shashtiamsa. This difference is to.be divided by the difference of their

discs measured in seconds. This result is added to the winner planet

and subtracted from the loser.

Diameter of the discs of planets.

Mars Mercury Jupiter Venus Saturn

9".4 6".6 190".4 16".6 158".0

No planet is at war in the example horoscope, however, we may

take another one for this. The longitudes of Mercury and Jupiter are

170" .53 and 170°.45 and their strength up to Hora bala (Positional strength

+ Directional strength + Kala bala upto Hora bala) are 444.51 and

305.45 respectively.

Difference in strength = 444".51- 305.45 = 139.06 sh.

Difference in this discs = 190" .4- 6".6 = 183" .8

Yuddhabala = 139.06 + 183.8 = 0.8 sh.

Mercury is loser so its Yuddhabala is- 0.8 sh.

Jupiter is winner hence its Yuddhabala is +0.8 sh.


Total Kalabalafor the example horoscope.

Name of Name of planets

bala Sun Moon Mars Mercury Jupiter Venus Saturn

Nathonatha 31.00 29.00 29.00 60.00 31.00 31.00 29.::JO

Paksha 8.55 102.90 8.55 51.45 51.45 51.45 8.55

Tribhag 0.00 0.00 0.00 60.00 60.00 0.00 0.00

Abda 15.00 0.00 0.00 0.00 0.00 0.00 0.00

Masa 0.00 0.00 0.00 0.00 0.00 0.00 30.00

Vara 0.00 0.00 0.00 45.00 0.00 0.00 0.00

Hora 0.00 60.00 0.00 0.00 0.00 0.00 0.00

Ayan 112 .0~ 59.76 56.00 47.11 33.28 59.03 27.79

Yuddha - - - - - - -Total 166.6( 251.66 93.55 263.56 175.73 141.48 95.34

lXXVI Chestabala or Motional strength

25.1 Chestabala is the strength of a planet gained by it due to retrogression. When the planets are retrograde, they are nearer to the earth. Their gravitational force on the earth becomes more.

The Sun appears to move round the earth, so it never retrogrades. The Moon moves around the earth and hence its motion is also never retrograde, as their longitudes are Jeo-centric longitudes, used in Indian Astronomy, are ever increasing and never decreasing.

Formulae for calculating Chestabala is Chesta Kendra = Sheeghrocha - (Mean longitude + True longitude) + 2 in case Chesta Kendra is more than 180°, deduct it from 360° or reverse the position i.e.

Chesta Kendra = (Mean longitude + Ture longitude) + 2 -sheeghrocha

Chestabala = Chesta Kendra + 3

For Chesta Kendra, sheeghrocha and Mean longitudes are to be found out as true longitudes are given in the horoscope.

Sun's mean longitudes= Mean longitudes of Mercury

= Mean longitude of Venus = Sheeghrocha of Mars = Sheeghrocha ofJuplter = SheeghrochaofSatuml.e.itequals to mean longitudes of inner planets and sheeghrocha of outer planets.

Hence Mean longitudes of Sun, Mars, Jupiter, Saturn and Sheeghrocha of Mercury and Venus are to be calculated first.

25.2 Procudurefor calculation:

Tables for mean longitudes of Sun, Mars, Jupiter, Saturn and Sheeghrocha of Mercury & Venus are given after the calculation of Chestabals. The positions at 0 hour on 1st January 1900 A.D. at 76°E are given in which the longitudinal motion upto the date and time of birth of the native are to be added.

Number of days from the start of the year 1900 upto 0 hour of 23rd May, 1951 are as under.

Years passed = 51 (As the starting year is 1900 not 1901)


Number of days = 51 x 365

leap days= 51+ 4 = 18615

= 12 (complete leap days)

Days from 1/1 to 22/5 = 142 Number of day from Ohr to 6:30AM l.S.T. = 0.25

(As Ujjain time is 6:30-26 = 6:04)

Total number of days = 18769.25

Mean longitudes Sheeghrocha

Sun Mars Jupiter Saturn Mercury Venus

10,000 days 136.0265 200.19 110.96 334.39 243.18 181.46

8,000 days 324.8212 232 .15 304.77 267.51 338.54 217.17

700 days 329.9218 6.81 58.17 23.41 344.62 41.50

60 days 59.1360 31.44 4.99 2.01 245.54 96.13

9 days 8.8705 4.72 0.75 0.30 36.83 14.42

0.25 days 0.2464 0.13 0.02 0.01 1.02 0.40

for 18,769.25

days 859.0224 475.44 479.66 627.63 1209.73 551.08

Value at epa<±

or beginning 257.4568 270.22 220.04 236.74 164.00 328.51

correction - - (-) 3.67 + 5.05 + 6.60 -5.01 I

A B c D

Total 1116.4792 745.66 696.03 869.42 1380.33 874.58

Deduct

Multiple

of360 -1080.0000 (-)720.00 -36.0.0 -720.00 -1080.00 -720.00

rounded to

2 places of

decimals 36.48 25.66 336.03 149.42 300.33 154.58

(A) = 3.33 +51 X 0.0067 = 3.67, (8) = 5 + 0.001 X 51 = 5.05, (C) = 6.ff7- 0.00133 x 51 = 6.67- 0.07 = 6.60, (D) = 5 + 0.0001 x 51 = 5.01


Chestabala

Planet ~ True Mean 1/2 of Col.2-5 or 5-2 Chestabala longitude longitude col3+4 subject to less 6+3

than 180" Chesta Kendra

1 2 3 4 5 6 7

Mars 36.48 37.82 25.66 31.74 4.74 1.58 Mercury 300.33 12.75 36.48 24.62 84.29 28.10 Jupiter 36.48 343.35 336.03 339.69 56.79 18.93 Venus 154.58 80.32 36.48 58.40 96.18 32.06 Saturn 36.48 152.43 149.42 150.93 114.45 38.15

Table-I

Mean Solar Daily Motion (in degrees) Mean position of the Sun

At 0 hr on 1st January 1900 A.D. 76° E (called epoch) = 25T 4568

Units

1. 0.9856 2. 1.9712 3. 2.9568 4. 3.9424 5. 4.9280 6. 5.9136 7. 6.8992 8. 7.8848 9. 8.8704

Units

1. 0.524 2. 1.048 3. 1:572 4. 2.096 5. 2.620 6. 3.144 7. 3.668 8. 4.192 9. 4.716

Hundreds Thousands Ten thousands

98.5602 265.6026 136.0265 197.1205 171.2053 272.0531 295.6808 76.8080 48.0796 34.2411 342.4106 184.1062 132.8013 248.0133 320.1327 231.3616 153.6159 96.1593 329.9218 59.2186 232.1868 68.4821 324.8212 8.2124 167.0424 230.4239 144.2389

Table-II

Mean Motion of Kuja (Mars) Mean Position at the Epoch = 270.22°

Hundreds Thousands Ten thousands

52.40 164.02 200.19 104.80 328.04 4Q.39 157.21 132.06 ~40.58

209.61 296.08 80.78 262.Dl 100.10 280.97 314.41 264.12 121.16

6.81 68.14 321.36 59.22 232.15 161.55 111.62 36.17 1.74


Units

1. .08

2. .17

3. .25

4. .33

5. .41

6. .50

7. .58

8. .66

9. .75

Table-Ill

Mean Motion of Jupiter Mean Position at the Epoch = 220°.04

Tens Hundreds Thousands Ten thousands

.083 8.31 83.1 110.96

1.66 16.62 166.19 221.93

2.49 24.93 249.29 332.89

3.32 33.24 332.39 83.85

4.15 41.55 55.48 194.82

4.99 49.86 138.58 305.78

5.82 58.17 221.67 56.74

6.65 66.48 304.77 167.71

7.48 74.79 27.87 278.67

Less correction (3.33 + 0.0067t)

Units

1. .03

2. .07

3. .10

4. .13

5. .17

6. .20

7. .23

8. .27

9. .30

Table-W

Mean Motion of Saturn Mean Position at the Epoach = 236°.74

Tens Hundreds Thousands Ten thousands

.33 3.34 33.44 334.39

.67 6.69 66.88 308.79

1.00 10.03 100.32 283.18

1.34 13.38 133.76 257.57

1.67 16.72 167.20 231.97

2.01 20.06 200.64 206.36

2.34 23.41 234.08 180.75

2.68 26.75 267.51 155.14

3.01 30.10 300.95 129.54

Add correction (5° + 0.001 t)


Table-V

Mercury's Apogee Product Table (Mercury's Seeghrochcha)

The adopted Apogee of the planet is 164° at the epoch. Its mean position is equal to that of the Sun.

Add correction : (6.67- 0.00133 t)

Units Tens Hundreds Thousands Ten thousands

1. 4.09 40.92 49.23 132.32 243.18

2. 8.18 81.84 98.46 264.64 126.36

3. 12.28 122.77 147.70 36.95 9.54

4. 16.37 163.69 196.93 169.27 252.72

5. 2C.46 204.62 246.16 301.59 135.90

6. 24.55 245.54 295.39 73.91 19.08

7. 28.65 286.46 344.62 206.23 262.26

8. 32.74 327.38 33.85 338.54 145.44

9. 36.83 8.31 83.09 110.86 28.63

Table-VI

Product Table of Apogee of Venus (Venus Seeghrochcha)

The Apogee at the epoch is 328 o .51

Less Correction : (5° + 0.0001 t)

Units Tens Hundreds Thousands Ten thousands

1. 1.60 16.02 160.21 162.15 181.46

2. 3.20 32.04 320.43 324.29 2.93

3. 4.81 48.06 120.64 126.44 184.39

4. 6.41 64.09 280.86 288.59 5.86

5. 8.01 80.11 81.07 90.73 187.32

6. 9.61 96.13 241.29 252.88 8.78

7. 11.21 112.15 41.50 55.02 190.25

8. 12.82 128.17 201.72 217.17 11.71

9. 14.42 144.19 1.93 19.32 193.18

210 Elements of A<tronomy and Astrological Calculations

25.3 Natural Strength or Naisargikabala:

The Natural strength of a planet depends upon the luminosity of the planets. It is the same for all the horoscopes.

As per Sripatipaddhati the values of this bala are shown in the following table :

Planet Natural Strength

in Rupa in Shashtiamsas

Sun 1 or 7/7 60 X 7/7 = 60.00

Moon 6/7 60 X 6/7 = 51.43

Mars 2/7 60 X 2/7 = 17.14

Mercury 3/7 60 X 3/7 = 25.71

Jupiter 4{7 60 X 4/7 = 34.29

Venus sn 60 X 5/7 = 42.86

Saturn 1/7 60xl/7= 8.57

Parashara has rounded off to the nearest sh. i.e. 60, 51, 17, 26, 34, 43 and 9 respectively.

25.4 Drikbala or Aspectual strength:

It is strength gained by a planet due to aspect of other planets on it. A planet which is looked upon is called the aspected planet and the one looking is known as aspecting planet. When we see anything, we are behind and the aspected is ahead. To find the distance between the two the behind is subtracted from the ahead. Similarly here, the aspect angle becomes the aspected planet minus the aspecting one. Aspect of benefic planets increase the strength while the aspect of malefics decrease it.

25.41 Planetary aspects:

Normally planets aspect the other planets most powerfully when they are at 180° distance. The aspectual strength of all the planets at such a distance is 1 Rupa or 60 sh. When the aspected planet is 300° to 360° and oo to 30° ahead of the aspecting planet, the aspectnal strength is nil. A planet starts aspecting the other when the aspected planet is 30° ahead. When the aspected planet is ahead by 60° or 270° the strength is 1/4 Rupa or 15 sh, at 90° and 210° it is 3/4 Rupa or 45 sh and at 120° and 240° it becomes 1/2 Rupa or 30 sh.

Elements of Astronomy and Astrological Calculations· 211

25.42 Special aspects:

Mars special aspect at 90° and 21 oo is full or 1 Rupa equal to 60 sh. At these points normal aspect is 45 sh, the addition is 60-45 = 15 sh.

Jupiter's special aspect at 120° and 240o is full or 60 sh. It is increased by 60 - 30 = 30 sh. to the normal aspect value. Saturn's special aspect at 60° and 270° is full or 60 sh. It increases by 60-15 = 45sh.

Though Mr. B.V Raman was of the view that these additions in the case of Mars, Jupiter and Saturn were to be done for the whole of IV & Vlll, V & IX and Ill & X houses respectively but Sripatipaddhati

states that the additions are on the degrees mentioned above. So the increase or decrease should be accounted for from 30o earlier to 30° after them as done by Shri S.K. Duggal. Here Sripatipaddhati shall be followed.

25.43 Aspect angle or Drishti Kendra is the longitudinal difference of Aspected planet and aspecting planet or Aspected planetAspecting planet.

Method:

(i) The aspect angle of all the planets shall be worked out.

(ii) Drishti Pinda of these aspect angles is to be calculated as per chart or the methods given below.

(iii) Drishti Pinda or value of Benefics is Subha or benefic while that of Ashubha or Malefics is ashubhla or malefic.

(iv) Add shubha and Ashubha Drishti values seperately and deduct Ashubha value from the shubha value. If shubha is more it is

+ otherwise-.

(v) The net Drishti value is to be divided by four and the aspect strength of a planet is arrived at.

Calculation ofDrishti Pinda:

(i) Table at 1 o interval from 30° to 300° of aspect value are given. For intermediate values the Drishti Pinda can be calculated by the rule of three.

25.44 (ii) Normal aspect value can be found out by any of the two methods.


(a) Method· I

Aspect angle

0 - 30 degrees

30 - 60 degrees

60 - 90 degrees

90- 120 degrees

120- 150 degrees

150- 180 degrees

180- 300 degrees

300-360 degrees

25.45 (b) Method -II

Drishti Pinda

=zero

= (DK-30)/2

= (DK- 60) + 15

= (120- DK)/2 + 30

= (150-DK)

= (DK-150) x 2

= (300- DK)/2

=zero.

180"

300"

At different intervals Drishti values have been given and for intermediary positions Drishti values are increased or decreased proportionally.

25.46 (iii) Special aspect strength of Mars, Jupiter and Saturn are taken full at 90° and 210° in case Mars, 120° and 240° for Jupiter and 60° and 270° for Saturn. 60 sh is the value at these points and not for the whole house. In case the difference between aspected and aspecting planets falls short of or is in excess upto 30°, this special aspect value is to be reduced proportionally and this reduced special aspect value is additive in the normal aspect value. It is explained through examples after the value chart.


Drishti Pind of Plants

Aspect Sun Mars Jup. Sat Aspect Sun Mars Jup. Sat Angle etc Angle etc

1 2 3 4 5 1 2 3 4 5

1 2 3 4 5 63 18.0 19.5 18.0 58.5

0 to} 64 19.0 21.0 19.0 58.0 30" 0.0 0.0 0.0 0.0 65 20.0 22.5 20.0 57.5 31 0.5 0.5 0.5 2.0 66 21.0 24.0 21.0 57.0 32 1.0 1.0 1.0 4.0 67 22.0 25.5 22.0 56.5 33 1.5 1.5 1.5 6.0 68 23.0 27.0 23.0 56.0 34 2.0 2.0 2.0 8.0 69 24.0 28.5 24.0 55.5 35 2.5 2.5 2.5 10.0 70 25.0 30.0 25.0 55.0 36 3.0 3.0 3.0 12.0 71 26.0 31.5 26.0 54.5 37 3.5 3.5 3.5 14.0 72 27.0 33.0 27.0 54.0 38 4.0 4.0 4.0 16.0 73 28.0 34.5 28.0 53.5 39 4.5 4.5 4.5 18.0 74 29.0 36.0 29.0 53.0 40 5.0 5.0 5.0 20.0 75 30.0 37.5 30.0 52.5 41 5.5 5.5 5.5 22.0 76 31.0 39.0 31.0 52.0 42 6.0 6.0 6.0 24.0 77 32.0 40.5 32.0 51.5 43 6.5 6.5 6.5 26.0 78 33.0 42.0 33.0 51.0 44 7.0 7.0 7.0 28.0 79 34.0 43.5 34.0 50.5 45 7.5 7.5 7.5 30.0 80 35.0 45.0 35.0 50.0 46 8.0 8.0 8.0 32.0 81 36.0 46.5 36.0 49.5 47 8.5 8.5 8.5 34.0 82 37.0 48.0 37.0 49.0 48 9.0 9.0 9.0 36.0 83 38.0 49.5 38.0 48.5 49 9.5 9.5 9.5 38.0 84 39.0 51.0 39.0 48.0 50 10.0 10.0 10.0 40.0 85 40.0 52.5 40.0 47.5 51 10.5 10.5 10.5 42.0 86 41.0 54.0 41.0 47.0 52 11.0 11.0 11.0 44.0 87 42.0 55.5 42.0 46.5 53 11.5 11.5 11.5 46.0 88 43.0 57.0 43.0 46.0 54 12.0 12.0 12.0 48.0 89 44.0 58.5 44.0 45.5 55 12.5 12.5 12.5 50.0 90 45.0 60.0 45.0 45.0 56 13.0 13.0 13.0 52.0 91 44.5 59.0 45.5 44.5 57 13.5 13.5 13.5 54.0 92 44.0 58.0 46.0 44.0 58 !4.0 14.0 14.0 56.0 93 43.5 57.0 46.5 43.5 59 14.5 14.5 14.5 58.0 94 43.0 56.0 47.0 43.0 60 15.0 15.0 15.0 60.0 95 42.5 55.0 47.5 42.5 61 16.0 16.5 16.0 59.5 96 42.0 54.0 48.0 42.0 62 17.0 18.0 17.0 59.0 97 41.5 53.0 48.5 41.5


98 41.0 52.0 49.0 41.0 138 12.0 12.0 24.0 12.0 99 40.5 51.0 49.5 40.5 139 11.0 11.0 22.0 11.0 100 40.0 50.0 50.0 40.0 140 10.0 10.0 20.0 10.0 101 39.5 49.0 50.5 39.5 141 9.0 9.0 18.0 9.0 102 39.0 48.0 51.0 39.0 142 8.0 8.0 16.0 8.0 103 38.5 47.0 51.5 38.5 143 7.0 7.0 14.0 7.0 104 38.0 46.0 52.0 38.0 144 6.0 6.0 12.0 6.0 105 37.5 45.0 52.5 37.5 145 5.0 5.0 10.0 5.0 106 37.0 44.0 53.0 37.0 146 4.0 4.0 8.0 4.0 107 36.5 43.0 53.5 36.5 147 3.0 3.0 6.0 3.0 108 36.0 42.0 54.0 36.0 148 2.0 2.0 4.0 2.0 109 35.5 41.0 54.5 35.5 149 1.0 1.0 2.0 1.0 110 35.0 40.0 55.0 35.0 150 0.0 0.0 0.0 00 111 34.5 39.0 55.5 34.5 151 2.0 2.0 2.0 2.0 112 34.0 38.0 56.0 34.0 152 4.0 4.0 4.0 4.0 113 33.5 37.0 56.5 33.5 153 6.0 6.0 6.0 6.0 114 33.0 36.0 57.0 33.0 154 8.0 8.0 8.0 8.0 115 32.5 35.0 57.5 32.5 155 10.0 10.0 10.0 10.0 116 32.0 34.0 58.0 32.0 156 12.0 12.0 12.0 12.0 117 31.5 33.0 58.5 31.5 157 14.0 14.0 14.0 14.0 118 31.0 32.0 59.0 31.0 158 16.0 16.0 16.0 16.0 119 30.5 31.0 59.5 30.5 159 18.0 18.0 18.0 18.0 120 30.0 30.0 60.0 30.0 160 20.0 20.0 20.0 20.0 121 29.0 29.0 58.0 29.0 161 22.0 22.0 22.0 22.0 122 28.0 28.0 56.0 28.0 162 24.0 24.0 24.0 24.0 123 27.0 27.0 54.0 27.0 163 26.0 26.0 26.0 26.0 124 26.0 26.0 52.0 26.0 164 28.0 28.0 28.0 28.0 125 25.0 25.0 50.0 25.0 165 30.0 30.0 30.0 30.0 126 24.0 24.0 48.0 24.0 166 32.0 32.0 32.0 32.0 127 23.0 23.0 46.0 23.0 167 34.0 34.0 34.0 34.0 128 22.0 22.0 44.0 22.0 168 36.0 36.0 36.0 36.0 129 21.0 21.0 42.0 21.0 169 38.0 38.0 38.0 38.0 130 20.0 20.0 40.0 20.0 170 40.0 40.0 40.0 40.0 131 a. 19.0 19.0 38.0 19.0 171 42.0 42.0 42.0 42.0 132 18.0 18.0 36.0 18.0 172 44.0 44.0 44.0 44.0 133 17.0 17.0 34.0 17.0 173 46.0 46.0 46.0 46.0 134 16.0 16.0 32.0 16.0 174 48.0 48.0 48.0 48.0 135 15.0 15.0 30.0 15.0 175 50.0 50.0 50.0 50.0 136 14.0 14.0 28.0 14.0 176 52.0 52.0 52.0 52.0 137 13.0 13.0 26.0 13.0 177 54.0 54.0 54.0 54.0


178 56.0 56.0 56.0 56.0 218 41.0 52.0 49.0 41.0 179 58.0 58.0 58.0 58.0 219 40.5 51.0 49.5 40.5 180 60.0 60.0 60.0 60.0 220 40.0 50.0 50.0 40.0 181 59.5 60.0 59.5 59.5 221 39.5 49.0 50.5 39.5 182 59.0 60.0 59.0 59.0 222 39.0 48.0 51.0 39.0 183 58.5 60.0 58.5 58.5 223 38.5 47.0 51.5 38.5 184 58.0 60.0 58.0 58.0 224 38.0 46.0 52.0 38.0 185 57.5 60.0 57.5 57.5 225 37.5 45.0 52.5 37.5 186 57.0 60.0 57.0 57.0 226 37.0 44.0 53.0 37.0 187 56.5 60.0 56.5 56.5 227 36.5 43.0 53.5 36.5 188 56.0 60.0 56.0 56.0 228 36.0 42.0 54.0 36.0 189 55.5 60.0 55.5 55.5 229 35.5 41.0 54.5 35.5 190 55.0 60.0 55.0 55.0 230 35.0 40.0 55.0 35.0 191 54.5 60.0 54.5 54.5 231 34.5 39.0 55.5 34.5 192 54.0 60.0 54.0 54.0 232 34.0 38.0 56.0 34.0 193 53.5 60.0 53.5 53.5 233 33.5 37.0 56.5 33.5. 194 53.0 60.0 53.0 53.5 234 33.0 36.0 57.0 33.0 195 52.5 60.0 52.5 52.5 235 32.5 35.0 57.5 32.5 196 52.0 60.0 52.0 52.0 236 32.0 34.0 58.0 32.0 197 51.5 60.0 51.5 51.5 237 31.5 33.0 58.5 31.5 198 51.0 60.0 51.0 51.0 238 31.0 32.0 59.0 31.0 199 50.5 60.0 50.5 50.5 239 30.5 31.0 59.5 30.5. 200 50.0 60.0 50.0 50.0 240 30.0 30.0 60.0 30.0 201 49.5 60.0 49.5 49.5 241 29.5 29.5 58.5 31.0 202 49.0 60.0 49.0 49.0 242 29.0 29.0 57.0 32.0 203 48.5 60.0 48.5 48.5 243 28.5 28.5 55.5 33.0 204 48.0 60.0 48.0 48.0 244 28.0 28.0 54.0 34.0 205 47.5 60.0 47.5 47.5 245 27.5 27.5 52.5 35.0 206 47.0 60.0 47.0 47.0 246 27.0 27.0 51.0 36.0 207 46.5 60.0 46.5 46.5 247 26.5 26.5 49.5 37.0 208 46.0 60.0 46.0 46.0 248 26.0 26.0 48.0 38.0 209 45.5 60.0 45.5 45.5 249 25.5 25.5 46.5 39.0 210 45.0 60.0 45.0 45.0 250 25.0 25.0 45.0 40.0 211 44.5 59.0 45:5 .44.5 251 24.5 24.5 43.5 41.0 212 44.0 58.0 46.0 44.0 252 24.0 24.0 42.0 42.0 213 43.5 57.0 46.5 43.5 253 23.5 23.5 40.5 43.0 214 43.0 56.0 47.0 43.0 254 23.0 23.0 39.0 44.0 215 42.5 . 55.0 47.5 42.5 255 22.5 22.5 37.5 45.0 216 42.0 . 54.0 48.0 42.0 256 22.0 22.0 36.0 46.0 217 41.5 53.0 48.5 41.5 257 21.5 21.5 34.5 47.0

·•


258 21.0 21.0 33.0 48.0 280 10.0 10.0 10.0 40.0 259 20.5 20.5 31.5 49.0 281 9.5 9.5 9.5 38.0 260 20.0 20.0 30.0 50.0 282 9.0 9.0 9.0 36.0 261 19.5 19.5 28.5 51.0 283 8.5 8.5 8.5 34.0 262 19.0 19.0 27.0 52.0 284 8.0 8.0 8.0 32.0 263 18.5 18.5 25.5 53.0 285 7.5 7.5 7.5 30.0 264 18.0 18.0 24.0 54.0 286 7.0 7.0 7.0 28.0 265 17.5 17.5 22.5 55.0 287 6.5 6.5 6.5 26.0 266 17.0 17.0 21.0 56.0 288 6.0 6.0 6.0 24.0 267 16.5 16.5 19.5 57.0 289 5.5 5.5 5.5 22.0 268 16.0 16.0 18.0 58.0 290 5.0 5.0 5.0 20.0 269 15.5 15.5 16.5 59.0 291 4.5 4.5 4.5 18.0 270 15.0 15.0 15.0 60.0 292 4.0 4.0 4.0 16.0 271 14.5 14.5 14.5 58.0 293 3.5 3.5 3.5 14.0 272 14.0 14.0 14.0 56.0 294 3.0 3.0 3.0 12.0 273 13.5 13.5 13.5 54.0 295 2.5 2.5 2.5 10.0 274 13.0 13.0 13.0 52.0 296 2.0 2.0 2.0 8.0 275 12.5 12.5 12.5 50.0 297 1.5 1.5 1.5 6.0 276 12.0 12.0 12.0 48.0 298 1.0 1.0 1.0 4.0 277 11.5 11.5 11.5 46.0 299 0.5 0.5 0.5 2.0 278 11.0 11.0 11.0 44.0

:} 0.0 279 10.5 10.5 10.5 42.0 0.0 0.0 0.0

Chart of Drishti Kendra of example horoscope.

Aspected planets

.t' Planet Sun Moon Mars Mer Jup Ven Sat '1S 37.93 243.58 37.82 12.75 343.35 80.32 152.43 i

o"" or or or or or or Oo,J 397.93 603.58 397.82 372.75 440.32 512.43

37.93 Sun - 205.65 359.89 334.82 305.42 42.39 114.50

243.58 Moon 154.35 - 154.24 129.17 99.77 196.74 268.85

37.82 Mars 0.11 205.76 - 334.93 305.53 42.50 114.61

12.75 Mer 25.18 230.83 25.07 - 330.60 67.57 139.68

343.35 Jup 54.58 260.23 54.47 29.40 - 96.97 169.08

80.32 Ven 31'7.61 163.26 317.50 292.43 263.03 0- 72.11

152.43 Sat. 245.50 91.15 245.39 220.32 190.92 287.89 -


Aspected Planets

Planet Sun Moon Mars Mercury Jupiter Venus Saturn

Moon 8.70 - 8.48 20.83 40.12 51.63 15.58

Mercury - 34.59 - - - 22.57 10.32

Jupiter 12.29 29.66 12.24 - - 48.49 38.16

Venus - 26.52 - 3.79 18.49 - 27.11

Total Shubha 20.99 90.77 20.72 24.62 58.61 122.69 9Ll7

Drishti Value

Sun - 47.18 - - - 6.20 32.75

Mars - 60.00 - - - 6.25 35.39

Saturn 35.50 44.43 35.39 39.84 54.54 24.22 -

Total Ashubha Drishti Value 35.50 151.61 35.39 39.84 54.54 36.67 68.14

Drishti Pinda Net Aspect Value (-)14.51 (-)60.84 (-)14.67 (-)15.22 4.07 86.02 23.03

Drishti or

Drik Bala in sh (-)3.63 (-)1521 (-)3.67 (-)3.81 +1.02 +21.51 +5.76

25.47 Calculation of Aspect value without table:

(i) For Mar's special aspect value is 15 sh. at goo and 210°

It increases or decreases in 300, so for every degree its increase or decrease is 15 + 30 = 0.5 sh.

(a) Mars aspect angle on Moon is 205°.76. Mars special aspect at 180° is nil and at 210° is 15 sh.

Its special aspect on Moon = (205. 76 - 180) X 0.5

= 25.76 X 0.5

= 12.88sh.

Its nonnal aspect value at Moon = 47.12 sh.

Its total aspect value at Moon = 60.00 sh.

(b) Mars aspect angle at saturn is 114°.61 which is within 30° of goo. Its special aspect at 120° is zero and at goo it is 30 sh.

Its sper.ial aspect value on sat. = (120- 114.61) x 0.5

= 5.3g X 0.5.

= 2.6gsh.


Its normal aspect value of saturn = 32.70 sh.

Its total aspect value at saturn = 35.39 sh.

25.48 (ii) For Jupiter's a special aspect value at 120° and 240° is 30sh.lt increases or decreases in 30°, for every degree there is increase or decrease of 1 sh.

(a) Jupiter's aspect angle on Moon is 260°.23. So at 240+30 = 270 its special aspect value is nil

Its special aspect value on Moon= 270-260.23 = 9.77

Its normal aspect value on Moon

Its total aspect value at Moon

= 19.89

=29.66

(b) Jupiter's aspect angle on Venus is 96.97 which is within 300 of 120°.

Its special aspect value on Venus = 96.97- 90

Its normal aspect value on Venus

= 6.97 sh.

= 41.52 sh.

Its total aspect value at Venus = 48.49

25.49 (iii) Saturn's special aspect value at 60° or 270° is 45 sh. In 30° before after these, it is nil. So the increase or decrease. per degree from 30° earliar or upto 30° after is 45 + 30 = 1.5 sh.

(a) Saturn's aspect angle on sun = 245°.50 which is within 30° from 270° or its special aspect starts from 270- 30 = 240°

Saturn's special aspect value at sun = (245.50- 240) X 1.5

= 5.50 X L5

= 8.25 sh.

Saturn's normal aspect value at sun = 27.25sh.

Its total aspect value on sun = 35.50 sh.

(b) Saturn's aspect angle on Mars = 245.39 which is within 30° from 270° or its special aspect starts from 270- 30 = 240°

Saturn's special aspect value on Mars (245.39 - 240) x 1.5

= 5.39 X 1.5

= 8.09 sh.

Saturn's normal aspect value on Mars = 27.30 sh.

Its total aspect value on Mars = 35.39

(c) Saturn's aspect angle on Venus = 287°.89 which is within 30° of 270° or its special strength ends at 270 + 30 = 300o

.. Elements of Astronomy and Astrological Calculations 219

Saturn's special aspect value on Venus = (300- 287.89) X 1.5

= 12.11 X 1.5

= 18.16sh.

Saturn's normal aspect value on Venus = 6.06 sh.

Saturn's total aspect value on Venus = 24.22 sh.

Total shadbala of the Planets of example horoscope

Bala Sun Moon Mars Mercury Jupiter Venus Saturn

Positional 238.19 130.19 199.2~ 191.12 232.78 214.10 160.39

Directional 29.62 21.07 29.65 46.48 36.68 44.51 33.04

Temporal 166.60 251.66 93.55 263.56 175.73 141.48 95.34

Motional 0.00 0.00 1.58 28.10 18.93 32.06 38.15

Natural 60.00 51.43 17.14 25.71 34.29 42.86 8.57

Aspectual (-)3.63• (-)15.21 (-)3.6C (-)3.81 1.02 21.51 5.76

Total in

Shashtiamsa 490.78 439.14 337.4~ 551.16 499.43 496.52 341.25

In Rupa 8.18 7.32 5.62 9.19 8.32 8.28 5.69

Gradation of planets according to their strength. If the strength exceeds the following limit, it is deemed to be strong.

Sun Moon Mars Mercury Jupiter Venus Saturn

5 6 5 7 6.5 5.5 5

Planet Shadbala Minimum Strength Rank inRupa requirement

Sun 8.18 +5 1.64 I

Moon 7.32 +6 1.22 v Mars 5.62 +5 1.12 VII

Mere - 9.19 +7 1.31 lll

Jupiter 8.32 +6.5 1.28 IV

Venus 8.28 +5.5 1.51 II

Saturn 5.69 +5 1.14 VI

Sun is considered strong after dividing its shadbala by 5, but as per Parasar its shadbaia is to be divided by 6.5. We are following as narrated by Shri B.V. Raman.


The planets are strong if their Sthana bala, Digbala, Kalbala Chestabala and Ayan bala exceed the strength in shashtiamsas given below.

Planet Sthana Digbala Kal bala Chesta Ayan Bala Bala bala bala bala

Sun 165 35 112 50 30

Moon 133 50 100 30 40

Mars 96 30 67 40 20

Mercury 165 35 112 50 30

Jupiter 165 35 112 50 30 Venus 133 50 100 30 40

Saturn 96 30 67 40 20

Ayanbala has been shown separately in the above table. It is normally included in Kalabala. For considering the strength for separate balas, the Kalabala should not include Ayanbala as it has been shown separately in the above table.

lXXVII BhavaBala

26.1 There are certain significations or functions of a Bhava. Each Bhava represent some specific things. If a bhava is strong, the native will enjoy the results of the Bhava fully. In case it is weak, the native may not be in a position to get the results and enjoy the significations of the Bhava. The strength of a Bhava is determined by the following five factors. These factors are as per Parashar. Mostly the first three factors are used.

(i) Bhavadhipati bala is the strength of the lord of the Bhava madhya as determined by shad bala of the planets.

(ii) Bhava Dig bala is the strength gained by a Bhava due to its sign, whether it is Nar, Chatuspada, Jalchara or Keeta.

(iii) Bhava Drishti Bala or aspectual strength obtained due to aspect of the planets on it.

(iv) Bhava's strength due to accupancy of a planet is the strength gained or lost by a Bhava due to placement of benefic or malefic planets in it.

(v) Diva Ratri Bala is the strength gained by a Bhava due to the birth of the native in day or night.

26.2 Bhavadhipati bala is the strength of the sign lord of the bhava madhya as calculated by Shad bala.

26.3 (il) Bhava Dig Bala :

It is strength gained by the various Bhavas due to their Bhava Madhya being in different signs. Signs of the wdiac have been classified into four types of signs namely (a) Nar-rashi or human signs, (b) Jalchara rashis or watery or aquatic signs (c) Cbatuspada rashis or quadrupad signs (d) Keeta rashis or insect signs.

(a) Nar-rashis or Human signs : Rashi numbering 3, 6, 7, 1st half of 9 and 11 are Nar-Rashis. Gemini (Mithuna), Virgo (Kanya), Ubra (Tula), first half of Sagittarius (Dhanu) and Aquarius (Kumbha) are Nar rashis. They acquire strength of 60 sh in I house and 0 (zero) in Vll house. They gain 10 sh per Bhava from VII house, till it becomes 60 in the I Bhava. The decrease


orincrease is at the rate of 10 sh. per Bhava from I or VII respectively.

(b) Jalchara rashis or Watery signs are Cancer (Karkata) second half of Capricorn (Makar) and Pisces (Meena). Their Rashi numbers are 4,_2nd half of 10 and 12.

If the Bhava Madhya falls in these signs and in X house, the dighala of the Bhava will be 0 (zero) and increases at the rate of 10 sh per Bhava till it becomes 60 sh. in IV Bhava afterwards it starts declining at the rate of 10 sh per Bhava till it reaches 0 (zero) in X Bhava.

(c) Keeta Rashis or insect signs : There is only one Rashi numbering 8 or Vrischika (Scorpio) in this catageory. When this sign is in VII Bhava its strength is 60 sh and at I Bhava it is 0 (zero). The increase or decrease is at the rate of 10 sh. per Bhava on either side (earlier or after).

(d) Chatuspada Rashis or Quadruped signs are numbering 1, 2, 5, 2nd half of 9 and 1st half of 10. If the X Bhava Madhya falls in such a Rashi that Bhava gets 60 sh bala which is maximum and if IV Bhava falls in such a Rashi it gets 0 (zero) bala. The increase or decrease is at the rate of 10 sh per Bhava on either side of IV or X Bhava.

Directional strength in shashtiamsas of Bhavas are according to Bhava Madhya falling in the Rashis as per table given below :

Rashi"" Bhava I II Ill IV v VI VII VIII IX X XI XII

NarRashi 3, 6, 7, 11 and 1st half of 9 60 50 40 30 20 10 0 10 20 30 40 SQ.

Jalchar sign 4, 12 and II half oflO 30 40 50 60 50 40 30 20 10 0 10 20

Chatuspada Sigl) 1, 2, 5 II half"of 9 and I half of 10 30 20 10 0 10 20 30 40 50 60 50 40

Keetasign 8 0 10 20 30 40 50 60 50 40 30 20 10

26.4 (iii) Bhava Drishtibala or Bhavas aspectual strength :

A Bhava gains or loses certain amount of strength by the aspect of benefics or malefics. This strength is found as done for the Drishti

Elemenls of Astronomy and Astrological Calculations 223

bala of the planes with the following changes :

(i) Mercury is always considered benefic, irrespective of its association with malefic.

(ii) Drishtibalas of Mercury and Jupiter including their special aspect, are taken as obtained that is full. The aspectual strengths of other planets are divided by 4.

(iii) Bhava Madhya may be considered in place of a planet for calculating Dristibala of a Bhava.

(iv) Drishtibala of shubhas are positive, while that of malefics are negative. The sum total is added if positive or subtracted if negative from the other Bhava balas.

26.5 (iv) Bhavas strength due to occupancy of a planet:

If the Bhava is occupied by Mercury or Jupiter, it will get an addition of 1 Rupa or 60 shashtiamsa bala. In case it is occupied by Sun or Mars or Saturn, it loses one Rupa bala.

26.6 (v) Bhava Diva-Ratri Bala:

The Bhavas in sheershodaya signs (the signs rising by head) namely 3, 5, 6, 7, 8 and 11, if the birth is of day time, the Bhavas get 15 sh. bala, otherwise zero. . ..

If the birth time is of night and the Bhava Madhya is falling in Pristodaya signs that is sign numbers 1, 2, 4, 9 and 10 the Bhavas get 15 sh. bala otherwise zero.

If the time of birth happens to be in twilight, the Bhava falling in ubhyodaya sign 12 (Pisces) get 15 sh. bala. There is difference of openion. ·Some authors take Gemini also in this category but we shall take Pisces only as ubhyodaya Rashi.

"' :>

"' .c ..al

I

II

III

Calculation of Bhava Sal of (he example horoscope :

I Bhava Madhya 53.30 IV Bhava Madhya 126.78

VII Bhava Madhya 233.30 X Bhava Madhya 306.78 Aspecting Planets .

Bhava Sun Moon Mars Mercury Jupiter Venus Madya 37.93 243.58 37.82 12.75 343.35 80.32

53.30

or 413.30 15.37 169.72 15.48 40.55 69.95 332.98

77.79

or 437.79 39.86 194.21 39.97 65.04 94.44 357.47

102.28

or 462.28 64.35 218.70 64.46 89.53 118.93 21.96

Saturn 152.43

260.87

285.36

309.85


IV 126.78

or 486.78 88.85 243.20 88.96 114.03 143.43 46.46 334.35

v 162.29

or 522.29 124.36 278.71 124.47 149.54 178.94 81.97 9.86

VI 197.80

or 557.80 159.87 314.22 159.98 185.05 214.45 117.48 45.37

Vll 233.30

or 593.30 195.37 349.72 195.48 220.55 249.95 152.98 .80.87

Vlll 257.79

or 617.79 219.86 14.21 219.97 245.04 274.44 177.47 105.36

IX 282.28

or 642.28 244.35 38.70 244.46 269.53 298.93 201.96 129.85

X 306.78

or 666.78 268.85 63.20 268.96 294.03 323.43 226.46 154.35

XI 342.29

or 702.29 304.36 98.71 304.47 329.54 358.94 261.97 189.86

Xll 17.80

or 377.80 339.87 134.22 339.98 5.05 34.45 297.48 225.37

Aspecting Planets

Shubha Drishti Bala Ashubh Drishti Bala Net

Drishti -Ei;;j~

~ I 2 3 4 5 6 7 8 9 10 II

> Moon Venus l/4of Mer Jup 3+4+5 Sun Mars Sat 1/4of 6-10 ~ .<:

1+2 =6 7+8+9 =II Ill

I =10

I 39.44 - 9.86 5.28 24.95 40.09 - - 50.87 12.72 27.37

I 52.90 - !3.23 20.04 4722 80.49 4.93 4.99 29.28 9.80 70.69

m 40.65 - 10.16 44.53 59.47 114.16 19.35 21.69 - !0.26 !03.90

IV 28.40 8.23 9.16 32.99 13.14 55.29 43.85 58.44 - 25.57 29.72

v 10.65 36.97 11.91 0.54 57.88 70.33 25.64 25.53 - 12.79 57.54

VI - 31.26 7.82 57.48 47.23 112.53 19.74 19.% 30.74 17.61 94.92

\Ill - 5.% I.@ 39.73 45.08 86.30 52.32 60.00 49.56 40.47 45.83

\/Ill - 54.94 13.74 27.48 12.78 54.00 40.07 50.03 3732 31.86 22.14

IX 4.35 49.02 13.34 15.24 0.54 29.12 27.83 27.77 20.15 18.94 !0.18

X 18.20 36.77 13.74 2.99 - 16.73 15.58 !5.52 8.70 9.95 6.78

XI 40.65 19.02 14.92 - - 14.92 - - 55.07 13.77 1.15

XII 15.78 1.26 4.26 - 2.23 6.49 - - 37.32 9.33 (-)2.84


Total Bhava Bala

Net Drishti Dig Bhavadi- Strength Dive Total Bhava Rank Bala Bala pati Bala due to Ratr in Sh. Bala

occupancy Bala in Rupa

I 27.37 30 496.52 - 120 - 433.89 7.23 X

II 70.69 50 551.16 - 15 686.85 11.45 I

Ill 103.90 50 439.14 - - 593.04 9.88 Ill

IV 29.72 0 490.78 - 15 535.50 8.93 VII

v 57.54 20 551.16 -60 15 583.70 9.73 IV

VI 94.92 10 496.52 - 15 616.44 10.27 II

VII 45.83 60 337.48 - 15 458.31 7.64 VIII

VIII 22.14 40 499.43 - - 561.57 9.36 VI

IX 10.18 50 341.25 - - 401.43 6.69 XI

X 6.78 30 341.25 - 15 393.03 6.55 XII

XI 1.15 10 499.43 +60 - 570.58 9.51 v XII (-)2.84 40 337.48 + 60 - 434.64 7:24 IX

As the VIII Madhya is in II half of Dhanu, so it is Chatuspada sign, and IX Madya is in I half of Makar, so it is also Chatuspada sign.

1 bhava is occupied by Sun and Mars, so it gets - 60 - 60 == -120 sh, as occupancy strength, similarly Vis occupied by Saturn, XI by Jupiter and XII by Mercury, get occupancy strength of- 60, 60 and 60 sh. respectively.

The birth of the native is in day time, so the Bhava Madhyas falling in sheershyodya signs get 15 sh. Bala as Diva-Ratri Bala.

26.7 lshta Phala and Kashta Ph ala :

lshta Phala and Kashta Phala indicate the nature of results in the Dasha and Autar Dasa of the planets. If lshta Phala is more than the Kashta Phala, the native may expect good results in the planets periods and if the Kashta Phala is more than lshta Phala, the native may expect adverse results.

lshta Phala and Kashta Phala are calculated as under :

lshta Phala = J Uchcha bala X Chesta Bala

Kashta Phala == J (60- Uchcha bala) x (60- Chesta bala)

Chesta balas of the planets other than the Sun and the Moon have been worked out earlier, while those of the Sun and the Moon were not calculated as they are never retrograde. But for Ishta ph ala


and Kashta Phala, the same are calculated as below:

Sun's Chesta bala:

(i) Convert the longitude of Sun into Sayana one.

(ii) Add 90° in the sayana longitude of Sun.

(iii) If the result of (ii) is more than 180° deduct it from 360°, so that it may be less than 180° arc.

(iv) Dividing the result of (iii) by 3, Chesta bala of the Sun is known.

For the example horoscope :

Sun's Nirayana longitude = 37.93

Aynamsa = + 23.18

Sun's sayana longitude = 61.11

+ 90.00

Total = 151.11

As it is less than 180°, so these no necessity of deducting it from 360°.

Sun's Chesta bala = 151.11 + 3 = 50.37 sh.

Moon's Chesta bala:

Moon's Chesta bala is the same as the Paksha bala of subhas.lt is again calculated.

(i) Moon's longitude-Sun's longitude if less than 180°, otherwise deduct it from 360°.

(ii) Dividing the result of (i) by 3, we get Chesta bla of the Moon.

For example horoscope.

243.58- 37.93 = 205.65 which is more than 180°, so 360-205.65 = 154.35

Chesta bala of the Moon = 154.35 + 3 = 51.45

Planet lshta Phala Kashta Phala

Sun J 50.69 X 50.37 = 50.53 J9.31 X 9.63 = 9.47

Moon )10.19 X 51.45 = 22.90 J 49.81 X 8.55 = 20.64

Mars )26.73 X 1.58,: 6.S0 J33.27 X 58.42 = 44.09

Mercury )9.25 X 28.10 = 16.12 J5o.75 x 31.90 = 40.24

Jupiter )22.78 X 18.93 = 20.77 J37.22 X 41.07 = 39.10

Venus )32.23 X 32.06 = 32.14 J27.77 x 27.54 = 27.65

Saturn J 44.14 X 38.15 = 41.04 J15.86 X 21.85 = 18.62

XXVII Annual Horoscope

Janama Kundli or birth horoscope or natal horoscope is cast at the time of birth {)f a native and is used for the results of whole life. Annual Horoscope or Varsa horoscope is used for the predictions for one year which is normally from the previous birth day to the next one. In natal horoscope Dasa, Antardasa, Pratyanter dasa are used but for precise predictions one will have to use Sukshma and Pran Dasas and these are not possible without correct time of birth. Astrologers differ on the time of birth. ~me consider the time of birth, the time when head comes out, others think it when the whole body is out and many take the time of first cry of the child. These time differ by 1.5 to 20 minutes and it is sufficient to make difference in Sukshma or Pran Dasas. Therefore, to analyse the events during one year Varsh Kundli along with the Janam-kundli is essential. Varsh-Kundli cannot be p~epared without Janam kundli.

The time of solar return on the same longitudes as in birthchart is taken as the beginning of the year and Varsh-kundli is prepared .for that time. Pridictions by this Varsh-Kundli are called varshphal. These predictions are done by Tajic shastra (V arshphal shastra).

In Tajic Western aspects are used. Third, fifth, ninth and eleventh aspects are friendly ones and first, fourth, seventh and Tenth aspects are enemical; second, sixth, eighth and twelfth are neutral ones.

Here we s}l,all deal with the casting ofVarsh-kundli and other calculations required for its deliniation.

27.2 Casting of Annual horoscope

Following are the require~ents (a) Ista ghati, Birth Tithi, Masa, Day of week and Samvat

or Date of birth, birth time and bith place. (b) Natal horoscope alongwith the degrees of planets. (c) Sun's degrees, minutes and seconds if possible in the

natal chart. (d) DhruvankasTableisrequired to find thetimeofVarsh

Pravesh.

27.3 Dhruv .. loKa Table

Traditionally the duration of one year is 365 days, 15 ghatis, 31 pals and 30 vi pals. When it is divided by 7 remainder after complete weeks is 1 day 15 ghati, 31 pal and 30 vipal or say 1 day 6 hours. 12 minutes and 36 seconds. Bhaskaracharya has given this figure as 1 day, 6 hours, 12 minutes_9 seconds. According to


modern astronomers it is 1 day, 6 hours, 9 minutes and 9.8 seconds approximately.

Now-a-days Varsh-Kundli is prepared according to latest method in which duration of the year is 1 day, 6 hours, 9 minutes and nearly 9.8 sec. more than complete weeks and we will also follow the same for which Table of Dhruvanka is required. This table gives the time (No of day, hour, and minutes) to be added in birth day and time to get the varsh pravesh time and day for a particular Varsh-Pravesh.

Year Day Hour Min Year Day Hour Min

1 1 6 9.2 27 5 22 7.4 2 2 12 18.3 28 0 4 16.5 3 3 18 27.5 29 1 10 25.7 4 5 0 36.6 30 2 16 34.9 5 6 6 45.8 31 3 22 44.0 6 0 12 55.0 32 5 4 53.2 7 1 19 4.1 33 6 11 2.4 8 3 1 13.3 34 0 17 11.5 9 4 7 22.5 35 1 23 20.7

10 5 13 31.6 36 3 5· 29.8 11 6. 19 40.8 37 4 11 39.0 12 1 1 49.9 38 5 17 48.2 13 2 7 59.1 39 6 23 57.3 14 3 ' 14 8.3 40 1 6 6.5 15 4 20 17.4 41 2 12 15.7 16 6 2 26.6 42 3 18 24.8 17 0 8 35.8 43 5 0 34.0 18 1 14 44.9 44 6 6 43.1 19 2 20 54.1 45 0 12 52.3 20 4 3 3.2 46 1 19 1.5 21 5 9 12.4 47 3 1 10.6 22 6 15 21.6 48 4 7 19.8

' 23 0 21 30.7 49 5 13 I 29.0 24 2 3 39.9 50 6 19 38.1 25 3 9 49.1 51 1 1 47.3 26 4 15 58.2 52 2 7 56.4


Year Day Hour min Year Day Hour min 53 3 14 5.6 87 4 7 17.1 54 4 20 14.8 88 5 13 26.3 55 6 2 23.9 89 6 19 35.4

56 0 8 33.1 90 1 1 44.6 s7 1 14 42.3 91 2 7 53.8

58 2 20 51.4 92 3 14 2.9

59 4 3 0.6 93 4 20 12.1 60 5 9 9.7 94 6 2 21.3 61 6 15 18.9 95 0 8 30.4 62 0 21 28.1 96 1 14 39.5 63 2 3 37.2 97 2 20 48.7 64 3 9 46.4 98 4 2 57.9

65 4 15 55.6 99 5 9 7.1

66 5 22 4.7 100 6 15 16.2 67 0 4 13.9 10J. 0 21 25.4 68 1 10 23.0 102 2 3 34.5 69 2 16 32.2 103 3 9 43.7

70 3 22 41.4 104 4 15 52.8 71 ~-

5 4 50.5 105 5 22 2.0 72 6 10 59.7 -106 0 4 11.2 73 0 17 8.9 107 1 10 20.3 74 1 23 18.0 108 2 16 29.5 75 3 5- 27.2 109 3 22 38.7 76 4' -11 36.3 110 5 4 47.8 77 5 17 45.5 111 6 10 57.0

~

78 6 23 54.7 112 0 17 6.1 79 1 6 3.8 113 1 23 15.3

80 2 12 13.0 114 3 5 24.5 81 ( 3 18 22.1 115 4 11 33.6 82 5 0 31.3 116 5 17 4;s 83 6 6 40.5 117 6 23 _./52.0

84 0 12 49.6 118 1 6 1.1

85 1 18 58.8 119 2 12 10.3

86 3 1 8.0 120 3 18 19.4

:30 Elements of Astronomy and Astrological Calculations

Note:- Longitudes of the Sun in the annual horoscope should be the same as that of Natal-Sun. These may differ by a few minutes due to attraction of other planets on the Sun.

27.4 We take an example of horoscope for casting Varsh-Kundli.

The native was born on Tuesday the 8th January, 1980 at 22 hrs 28 minutes at latitude 28° 39'{N) and longitude 770 13' (E)

Natal Horoscope is : Asc Leo 26° 51' 0"

Sun Sagittarius 23° 59' 49"

Moon Virgo 4° 37' 18"

Mars Leo 2e 25' 55"

Mercury Sagittarius 16° 19' 34"

Jupiter (R) Leo 16° 23' 54"

Venus Capricorn 2r 18' 48"

Saturn (R) .

Virgo 3° 26' 18"

Rahu (R) Leo 6° 16' 5"

Ketu (R) Aquarius 6° 16' 5"

X cusp Taurus 26° 25' 46''

Ketu (-)

Rahu(-) Venus Jup.

Mars

Sun Sat(-) Mercury Moon(-)

(-) indicate that the planet has gone to previous house in Bhava chalit.

27.4.1 Casting of Annual Horoscope

Following procedure is to be followed. (1) Write the number of week day of birth along with this


time of birth one for Sunday, 2 for Monday, 3 for Tuesday, 4 for Wednesday, 5 for Thursday, 6 for Friday and 7 for Saturday.

(2) Add Dhruvankas for the number of years completed on that birth-day. It shows the name of weak-day and time of Varsh pravesh.

(3) The week-day thus attained should be nearest to the birth-date and will give the date of varsh-pravesh.

We are preparing the Annual Horoscope for the year starting in Jan 2006. Completed number of years up to Jan 2006 = 2006-1980=26 years.

Date and time birth was 8.1.1980 Tuesday at 22 hr 28 min

Day H M

= 3 22 28

Dhruvanka for 26 years = 4 15 58.2

= 8 14 26.2

deducting 7 = -7 0 0

(number of days in a week) 1 14 26.2

Moon Asc Mars

A

Rahu Saturn

Venus

Sun Jup .Ketu Mercury Muntha

i.e. 27 year starts on sunday at 14 hrs 26 Min 12 sec. as Sunday is on 8.1.2006, the date of starting new year is taken 8.1.2006.

If Sunday would have been on 7.1.2006 or 9 .1.2006., Varsh Pravesh would have been on that date.

Cast an horoscope of 8th January, 2006 at 14 hrs 26 minutes 12 seconds at the Lat 28° 39' (N) Longitude 7JO 13' (E)


Annual Horoscope for 27'h year

s D 1 " Asc 1 9 07 -

Sun 8 23 59 49

Moon 0 13 41 25

Mars 0 19 10 05

Mer 8 12 53 27

Jup 6 20 30 02

Ven (R) 9 03 04 46

Sat (R) 3 15 28 12

Rahu 11 14 20 28

Ketu 5 14 20 28

X cusp 9 22 10 -Muntha has also been given in VI house, its calculation will

be given in para 27.4.2 +sign indicates that the planet has gone in the next house in Bhava Chalit.

Bhava Chart

Bhava start Bhavacusp

s 0 s 0

'

I ·o 21 18 1 9 7

II 1 21 18 2 3 28

III 2 15 39 2 27 49

IV 3 10 00 3 22 10

v 4 10 00 4 27 49

VI 5 15 39 6 3 28

VII 6 21 18 7 9 7

VIII 7 21 18 8 3 28

IX 8 15 39 8 27 49

X 9 10 00 9 22 10

XI 10 10 00 10 27 49

XII 11 15 39 0 3 28


27.4.2 Muntha

A mathematical point called Muntha is taken to establish relationship between the Natal Horoscope and Armual chart. At the time of birth its longitudes are equal to that of Ascendant and Muntha progresses every year by one sign i.e. 2° 30' every month. Muntha adopts the characteristics of the Rashi in which it is located. Its lord is also one of the five office-bearers in the annual chart.

Muntha at the time of birth = Ascendant or 26° 51' of Leo. After completion of 26 years it has moved 26 signs. 26/12 = 2 Quotient and remainder is 2. Which shows that it will be in 5+2= 7th sign i.e. Libra of 26° 51'. It has been shown in the Libra sign in Anuual chart.

27.5 Dasha. used in Varshphal

For timing the events during the year Dasha systems are used. Three types of Dashas are more popular and these are:

(1) Vimshotri Mudda Dasha.

(2) Yogini Mudda Dasha

(3) Pratyayini Dasha

They are reckoned as follows:

27.51 Vimshotri Mudda Dasha

In Parashari Vimshotri Dasha system starts from Ashwini Nakshtra but here the starting Nakshatra is Kritika whose lord is Sun. It is the reason of deducting two in the formula given below:

The remainder which comes after [Natal Nakshtra of moon + completed years form birth

-two] divided by nine will show the dasha of the planet counted from Sun onwards as in Parashari system.

Total period of Vimshotri Dasha in Parashari is 120 years, while here it is one year= 360 days. 360/120=3. So the period of Vimshotri Mudda Dasha of the planets will be three times of Parashari Vimshotri Dasha but for years it will show the number of days.

It is shown below.

Planet No. of days Months Days.

Sun 6x3 = 18 = 0 18

Moon 10x3 = 30 = 1 0

Mars 7x3 = 21 = 0 21


Rahu 11>x3 =54 = 1 24

Jupiter 16x3 =48 = 1 18

Saturn 19x3 =57 = 1 27 Mercury 17x3 =51 -- 1 21

Ketu 7x3 = 21 = 0 21

Venus 20x3= 60 = 2 0

Total = 7 150 or 12 0 =1 year.

in the example horoscope the Moon is in Uttraphalguni Nakshatra whose number is 12 counted from Ashwini. So (12+26-2)/9 = 4 as quotient and remainder is 0 which means that planet is 9th from the Sun is Venus" Mudda Dasha is running at the start of the year.

At the time of birth Moon was of virgo 4° 37' but Uttraphalguru started from Leo 26° 40' showing that Moon had travelled 3° 20' + 4° 37' = 7D 57' = 477' in Uttraphalguni. Every Nakshatra is of 13° 20' = 800 showing that it has to pass 800-477 = 323 in Uttraphalguru.

Balance of Mudda Dasha of Venus= 323x60 (no of days for Venus) I 800 = 24.225 days.

Year started from 8th january 2006, so Venus Dasa is upto2 nd February, 2006.

Planets Months Days from 8.1.2006

Venus 0 24 upto 2.2.2006

Sun 0 18 upto 20.2.206

Moon 1 - upto 20.3.2006

Mars 0 21 u_pto 11.4.2006

Rahu 1 24 upto 5.6.2006

Jupiter 1 18 l,lEtO 23.7.2006

Saturn 1 27 upto 20.9.2006

Mercury 1 21 upto 11.11.2006

Ketu 0 21 upto 2.12.2006

Venus 1 6 upto 8.1.2007

Total 12 0


Total of Venus Dasha is of 60 days out of which 24 days have been in the beginning of the year and rest 1 month 6 days in the end.

27.52 Yogini Mudda Dasha

It consists of Eight Dashas namely: Mangla, Pingla, Dhanya, Bhramari, Bhadri.ka, Ulka, Siddha and Sankata. The duration of each Dasha is:

S.No. Dash a DashaLord duration in days

1 Mangla Moon 10

2 Pingla Sun 20

3 Dhanya Jupiter 30

4 Bhramasi Mars 40

5 Bhadri.ka Mercury 50

6 Ulka Saturn 60

7 Siddha Venus 70

8 Sankata RahuiKetu 80

Total 360

Sum of completed years and number of birth Nakshatri! from Ashwini + 3 is to be divided by eight. The remainder will tell the number of Dasha runing at the time of start of the year. In the example horoscope it is (26+12+3) I 8 = 4118 = 5 is quotient and 1 is remainder showing that the 1st Dasha of Mangla is running Uttraphalguni Nakshtra has passed = 3° 20' + 4° 37' = 7057' = 477'

Total duration of Nakshatra is 800'

Bal of Nakshtra = 800'-477' = 323'

Balance of Mangla = (10x3Z3) I 800

= 4.04 days = 4 days


Dasha Month Day!:f from 08.1.2006

Mangla 0 4 upto 12.1.2006

Pingla 0 20 up to 2.2.2006

Dhanya 1 0 upto 2.3.2006

Bhramri 1 10 upto 12.4.2006

Bhadrika 1 20 upto 2.6.2006

Ulka 2 0 upto 2.8.2006

Siddha · 2 10 upto12.10.2006

Sankata 2 20 upto 02.01.2007

Mangla 0 6 upto 8.1.2007

Total 12 00

27.53 Patyayini Dasha

(a) The I<rishamshas -This dasha is not calculated as Vinshotri Mudda or Yogini Mudda Dasha, but it is calculated by the degrees, minutes of Lagna and all the seven planets (excluing Rahu\Ketu)

Arrange the langna and the planets in the ascending order of their Degrees and Minutes (leaving their signs). These are known as I<rishamshas.

Krishamshas table of the example horoscope is gi Jen below by taking their longitudes upto the nearest minute and ignoring the signs.

Ven Asc Mer Moon Sat Mars Jup. Sun ..

Krishamsha 3°05' 9"07' 12°53' 13°41' 5D28' 19"10' 20030' 24000'

Krishamsha 3°.08 9".12 12°.88 13°.68 5°.4? 19".17 200.50 24°.00 in decimals

(b) Patyamsa- Patyarnsas are found out by deducting the I<rishamsha of the previous column from its I<risharnsa. In case of the minimum I<rishamsha 0 (zero) is substracted as-

Patyamsa of Venus = 3.08 - 0.00 = 3.08

Patyarnsa of Lagna = 9.12-3.08 = 6.04

Patyamsa of Mercury = 12.88 - 9.12 = 3.76

Patyarnsa of Moon = 13.68 - 12.88 = 0.80

Elements of Astrortomy and Astrological Calculations 237

Similarly the Patyamsa of Lagna and all the planets will be found out. The sum total of all the Patyamsas will be equal to the Krishamsha of the plenet or lagna having maximum degrees and minutes.

Patyamsas of the example horoscope -

Planet Yen Lagna Mer Moon Sat Mars Jup Sun

Patyamshas 3.08 6.04 3.76 0.80 1.79 3.70 1.33 3.50

As already told that the sum total of the Patyamsas will be equal to the maximum Krishamsha. In this Annual horoscope it is of sun = 24°. There are 365.25 days in a year. Each planet and langna will get the dasha in proportion to their Patyamsa and the seriatum will be as in Patyamsa table. Thus the formula is -

Dasha = Patyamsa +sum total of all the Patyamsas which is equal to Maximum I<rishansha.

Here the Patymnsa x 365.25 + 24 which is sum of all the patyansas

The table of patyayini Dasha of example horoscope is -

Graha Patyarnsha Dasha Dasha period from period in months 8.1.2006

in days in days and days

Venus 3.08 46.87 1-17 upto 24.2.2006

Lagna 6.04 91.92 3-02 upto 27.5.2006

Mereu!) 3.76. 57.22 1~27 upto 23.7.2006

Moon 0.80 12.18 0-12 upto 4.8.2006

Saturn 1.79 27.24 ()..27 upto 31.8.2006

Mars 3.70 56.31 1.27 upto 27.10.2006

Jupiter 1.33 20.24 0-20 upto 16.11.2006

Sun 3.50 53.27 1-23 upto 8.1.2007

Total 24.00 365.25 12.05

I

The days of January, February, March, etc have been taken as 31, 28, 31 etc.

27.6 Graha BaJa

In Parashari Graha Bala is obtained from the Shad-bala. In Varshphala it is calculated by three ways given below:-


1. Harsh bala, 2. Panch Vargiya bala, 3. Dwadash Vargiya !Jala.

27.6.1 Harsh Ba1a

Harsh means happy. It is the sum total of four kinds of strengths. Every one contributes 5 units or Viswa bala (V.B.)

(a) First Bala-Positional Strength/Sthana Bala- In case a planet is posted in a particular house, it gains strength of 5 V.B. When Sun is in IX house, Moon in third, Mars in sixth, Mercury in Ascendant, Jupiter in XI, Venus in V and Saturn in XII, they gain 5 V.B. each otherwise zero.

(b) Second Bala- Uchcha or Swa-kshtriya BaJa- In case a planet is in its own sign or its exalted sign, it obtains 5 V.B. otherwise zero.

(c) Third Bala - Male or Female strength - If the female planets (Moon, Mercury, Venus and Saturn) are in 1, 2, 3, 7, 8 or 9th Bhawa and Male planets in 4, 5, 6, 10, 11 or 12th Bhawa in annual horoscope they secure 5V.B. strength otherwise zero.

(d) Fourth Bala- Diva RatTi Bala- If the year starts during night, the female planets and in case the year starts within day time, the male planets get 5 V.B. otherwise zero.

Any planet can get maximum Harsh-Bala 5 x 4 = 20 V .B. In case a planet get zero Harsh Bala it is having no strength in 5 V.B. it is weak in ten VB medium strong, in 15 to 20 VB fully strong.

Harsh BaJa of the example horoscope

Strength Sun Moon Mars Mer ]up Ven Sat.

Positional 0 0 0 0 0 0 0 Strength

Own signor 0 0 5 0 0 0 0 exaltation sign strength

· M/female bala 0 0 5 5 5 5 5

Day or night 5 0 5 0 5 0 0 Strength

Total 5 0 15 5 10 5 5


27.6.2 Panch Vargiya Bala

As the name suggests it is the sum total of five kind of Balas. These are obtained by being posted in the Rashi of a planet, Hadda, Drekkana, Navarnsa and Exaltation bala. Uchcha Bala is proportionate to its distance from debilitation point.

They are calculated as under:-

Name Maximum Own Friend Neutral Enemy ofBala Sign Sign Sign Sign

Kshetra Bala 30 30 22.5 15 7.5

Hadda BaJa 15 15 11.25 7.5 3.75

Drekkana BaJa 10 10 7.5 5 2.5

Navamsa Bala 5 5 3.75 2.5 1.25

Uchcha Bala 20 - - - -

Total 80

After dividing the maximum strength 80 by 4 we get 20. This the reason that when the sum total of these· five balas is divided by 4 we get the balain V.B.

(a) Kshtriya Bala- The strength gained by a planet owing to its position in own sign, friend's sign, neutral's sign or enemy's sign is known as I<shtriya Bala.

Relation of the planets in annual horoscopy-Planets posted in the 3,5, 9 and 11 Bhawas from any planet

are its Friends. Planets in 1, 4, 7 and 10 Bhawas are Enemy. Planets in 2, 6, 8 and 12 Bhawas are Neutral.

Relation of the planets in the example Horoscope:-

Planets. Friends Neutral Enemy

Sun Moon, Mars, ]up. Ven., Sat. Mercury

Moon Sun, Mercury - Mars, Jup.,Ven., Sat.

Mars Sun, Mercury - Moon, Jup., Ven., Sat.

Mer. Moon, Mars, Jup. Ven., Sat. Sun

Jup. Sun, Mer. - Moon, Mars, Ven., Sat.

Ven. - Sun, Mer. Moon, Mars, Jup., Sat.

Sat. - Sun, Mer. Moon, Mars, Jup., Ven.


Relationship of Planets in Horoscope:-

Planet Rashi Lord Relation Kshetra Bala

Sun Jup. Friend 22.5

Moon Mars Enemy 7.5

Mars Mars Own Sign 30

Mer Jup. Friend 22.5

Jup. Ven. Enemy 7.5

Ven. Sat. Enemy 7.5

Sat. Moon Enemy 7.5

(b) Uchcha Bala-Exaltation and deblitation points of planets have already been given in Shad-Bala. They are as under:

Sun Moon Mars Mer Jup Ven Sat

Exaltation 0/10° 1/3° 9/28° 5/15° 3/5° 11/27" 6/20 point 100 330 298° 165° 95° 357" 200°

Deblitation 6/100 7W 3/28° 11/15° 9/5° 5/27" 0/20° point 1900 213°. 118° 345° 275° 177" 200

In Shad BaJa exaltation strength or Uchcha Bala at exaltr.tion point is 60 and at deblitation point it is zero while here they are 20 and 0. In 180° difference the bala is increased/ decreased by 20 therefore, the formula becomes the difference of longitudes from the deblitation point +,9 will give lh.is bala.

Uchcha bala of example Horoscope:-

Planets Longitudes Long of Diff. If the diff. is Uchcha in Decimals Debilitation more than 180° Bala

point deduct from 360•

Sun 264.0 190 74.00 - 8.22

Moon 13.68 213 199.32 160.68 17.85

Mars 19.17 118 261.17 98.83 10.98

Mer. 252.88 345 267.88 92.12 10.23

Jup. 200.50 275 285.50 74.50 8.28

Ven. 273.08 177 96.08 - 10.68

Sat. 105.47 20 85.47 - 9.50

•


(c) Hadda bala-Hadda means territory. In the following table the territory in degrees in a Rashi has been shown below. The lords of the territories are given there. Sun and Moon the Luminaries have not been included in this system.

Hadda BaJa Table:-

ifiuddo Aris Tau Gem Can Leo Vir Lib Sagi Scor Capri AcqL Pisc

1 (H) 0-8 (H) 0-7 (H) 0-7 (H) 0-7 0-12 0-7 0-1 0-1; Ju v Me Ma J Me Sa Ma J Me v v

11 &-12 8-14 &-12 7-13 &-11 b'-17 &-14 7-11 12-17 7-14 7-13 12-16 v Me v v v v Me v v J Me J

m 12-20 14-2< 12-1 1:>--1~ u-18 ~7-21 4-21 11-19 17-21 1'4-22 1:>--2( 16-19 Me J J Me Sa J J Me Me v J Me

N 20-25 22-21 17-2 19-2 18-2 21-2 21-28 19-24 21-26 122-26 20-25 19-28 Ma sa Ma Ju Mer Ma Ve Ju Ma Sa Ma Ma

v 25-30 27-3( 2 "' "' "' "' •o 30 24-,30 2&-30 2&-30 2$-3(] 28-3C Sa Ma Sa Sa Ma Sa Ma Sa Sa Ma Sa Sa

A planet obtains 15 BaJa in own Hadda, in Friend's hadda 11.25, in Neutral's Hadda 7.5 and in enemy's hadda 3.75 BaJa.

Hadda BaJa of the example Horoscope is:-

Planet In Annual Horoscope Hadda Relation Hadda

Sign Degrees Lord Bala

Sun Sagittarius 24° Mars Friend 11.25

Moon Aries 13.68° Mer. Friend 11.25

Mars Aries 19.17" Mer. Friend 11.25

Mer Sagittarius 12.88° V~n. Neutral 7.50

Jup. Libra 20.50° Jup. Own 15

Ven. Capricorn 3.08° Mer. Neutral. 1:'.50

Sat. Cancer 15.47" Mer. Neutral 7.50

Drekkana BaJa- Lords of Drekkanas are different than those of Pa rashari.


Table showing li-te lords of Drekhanas-

Drekkanas Aries Tau Gemi Can. Leo Vir. Lib. Scor lsagi. Capr Acqu. Pisce and degrees

I Ma Me J v Sa Su Mo Ma Me J v Sa 0-10°

II Su Mo Ma Me J v Sa Su Mo Ma Me J 10°- 20"

III v Sa Su Mo Ma Me J v Sa Su Mo Ma 20°- 30"

The observation of the table will reveal that the Drekkana Lords of Aries, Taurus etc. start from Mars and are in the order of day lords of a week after the I drekhana continue it to II and then to Ill.

As already described that in own drekkana the strength obtained is 10, in friend's it is 7.5 in neutral's 5 and in enemy's 2.5 bala.

Drekkana-Bala Table of example Horoscope:-

Planet Rashi Degrees Lord of Relation Drekkana Drekkana Bala

Sun Sagittarius 24° Sat. Neutral 5.0

Moon Aries 13.68° Sun Friend 7.5

Mars Aries 19.17" Sun Friend 7.5

Mer Sagittarius 12.88° Moon Friend 7.5

Jup. Libra 20.50° Jup. Own Sign 10.0

Ven. Capricorn 3.08° Jup. Enemy 2.5

Sat. Cancer 15.47" Mer. Neutral 5.0

Navamsa BaJa:- Navamsa Chart is casted as in Parashari. In case a planet is in own, friend, neutral or enemy's navamsa it gets 5, 3.75, 2.5 or 1.25 bala respectively.

Asc Jup

Mereu!)

Ven Moon

Sun Mars Sat


Planet Navamsa Lord Relation Navamsa BaJa

Sun Mars Friend 3.75

Moon Sun Friend 3.75

Mars Mercury Friend 3.75

Mer Moon Friend 3.75

Jup. Mars Enemy 1.25

Ven. Saturn Enemy 1.25

Sat. Mars Enemy 1.25

Panchvargiya BaJa of example Horoscope:-

.Bala Sun Moon Mars Mer. ]up. Ven. Sat.

Kshtara 22.50 7.50 30.00 22.50 7.50 7.50 7.50

Uchcha 8.22 }7.85 10.98 10.23 8.28 10.68 9.50

Hadda 11.25 11.25 11.25 7.50 15.00 7.50 7.50

Darkkana 5.00 7.50 7.50 7.50 10.00 2.50 5.00

Navamsa 3.75 3.75 3.75 3.75 1.25 1.25 1.25

Total 50.72 47.85 63.48 51.48 42.03 29.43 30.75

V.B. 12.68 11.% 15.87 12.87 10.51 7.36 7.69

In case Panchvargtya Bala IS more than 15 V.B., 1t IS called Parakrami or brave, between 10 to 15 fully strong, between 5 to 10 medium strong and less than 5 V.B. week.

In this horoscope Mars is Parakrami, Mercury, Moon, Jupiter and Sun are fully strong (Puran Bali) Venus and Saturn are medium strong (Madhya bali)

27.6.3 Dwadash Vargiya Bala

A sign is divided into equal parts, those parts of zodiac are called divisions. In case they are divided into 3 equal parts and the chart framed in this division is called Drekhana Chart. Similarly other divisional charts are prepared.

The tweleve vargas are (1) Rashi Chart, (2) Hora, (3) Dral<hana, (4) Chaturthamsa, (5) Panchmansa (6) Sashthamsa, (7) Saptamansa, (8) Ashtamansa, (9) Navamsa, (10) Dashamansa, (11) Akadshamsa, (12) Dwadasmsa.

The method of casting Hora, Drekkana, Chaturthamsa, Saptamansa, Navamsa, D.shamansa and Dwadshamsa has been described in CJ:lapter XVIII. Others are as under:-

Panchmansa:- Each Rashi (30") is divided into five equal parts. Each part is of 6°. In odd signs the lords of 1st to 5th part are Mars,


Saturn, Jupiter, Mercury and Venus respectively. In even signs the lords of the parts 1 to 5 are in reverse order i.e. Venus, Mercury, Jupiter, Saturn and Mars.

Panch.mansa Table of Example Horoscope

Degrees Odd Signs Even Signs (1, 3, 5, 7, 9 & 11) (2, 4, 6, 8, 10 & 12)

0-6 1 2

6-12 11 6

12-18 9 12

18-24 3 10

24-30 7 8 Sashthamsa :-Each sign is divided into six equal parts and each

part is of 5°

Degrees Odd Signs Even Signs (1, 3, 5, 7, 9 & 11) (2, 4, 6, 8, 10 & 12)

0-5 1 7

5-10 2 8

10-15 3 9

15-:20 4 10

20-25 5 11

25-30 6 12

Ashtamansa Chart:- Each Rashi is divided into eight equal parts of 3° 45'. The parts of movable signs are started from 1, in fixed signs from 9, in dual sign from 5.

Asthamsa Table

Degrees Movable Signs Fixed Signs Dual Signs (1, 4, 7 & 10) (2,5,8 & 11) (3, 6, 9 & 12)

0°-3° 45 1 9 5

3° 45°-r30' 2 10 6

7': 30' - 11° 15' 3 11 7

·11 ° 15°- 15° 0' 4 12 8

15° 0'- 18° 45' 5 1 9

18° 45' - 22° 30' 6 2 10

22° 30'- 26° 15' 7 3 11

26° 15' - 30° 00' 8 4 12


Ekadshamsa:-Each sign is divided into eleven equal parts and each part is of 30" + 11 = 2° 43' 38". In this the 1st part of Aries starts from Aries, of Taurus from Pisces, of Gemini from Acquaries etc.

Ekadshamsa Table

Ekadshamsa Rashi 1 2 3 4 5 6 7 8 9 10 11 12

0"0'0"-2"43'38" 1 12 11 10 9 8 7 6 5 4 3 2

2" 43' 38"- 5" 27' 16" 2 1 12 11 10 9 8 7 6 5 4 3

5"27' 16" -8"10' 54" 3 2 1 12 11 10 9 8 7 6 5 4

8" 10' 54"- 10° 54' 32" 4 3 2 1 12 11 10 cj 8 7 6 5

10" 54' 32"- 13° 38' 11" 5 4 3 2 1 12 11 10 9 8 7 6

13"38' 11" -16"21' 49" 6 5 4 3 2 1 12 11 10 9 8 7

16"21' 49" -19" 5' 27" 7 6 5 4 3 2 1 12 11 10 9 8

19"5' 27" -21"49' 5" 8 7 6 5 4 3 2 1 12 11 10 9

21"49' 5" -24"32' 44" 9 8 7 6 5 4 3 2 1 12 11 10

24° 32' 44"- 27" 16' 22" 10 9 8 7 6 5 4 3 2 1 12 11

27" 16' 22"- 30" 0' 0" 11 10 9 8 7 6 5 4 3 2 1 12

as 1 0 R h'L rdPI 'th anetsm I V etwe ve aiKas

S.No. Varga Sun Moon Mars Mer )up Ven. Sat.

1. D/1 )up. Mars Own )up. Ven. Sat. Moon

2. D/2 Moon Sun A Moon Sun BMoon Moon Sun

3. D/3 Own Sun Sun Mars Mer Sat Mars

4. D/4 Mer Own Ven A)up Mars Sat Own

5. D/5 Mer )up Mer )up Mer Own )up

6. D/6 Own Mer A Moon Own Sun Own Own

7. D/7 Ven Own Sun A)up Sat MoonB Mars

8. D/8 Sat Own Mer Mars Mer Mars Sun

9. D/9 Mars Sun Mer Moon Mars Sat Mars

10. D/10 Moon Sun Ven Mars Mars Own Sun

11. D/11 BMars Mer Own )up Ven Sun Mer

12. D/12 Mer Mer Own Ven Mer Sat Own

A~ Deblitation Sign; B =Exaltation Sign. (for above chart only) If a planet is in exaltation sign, own sign or friend's sign it is

Benefic (B); in case it is in deblitation sign, enemy's sign it is rna. lefic (M) and in neutal's sign it is in neutral (N).


In Para 27.6.2 the friendship chart is given. In the following table of Dwadash Vargiya table the letters represent:

F= Friendship, E = Enemy; N = Neutrals; 0 = Own sign; U = Uchcha sign; D= Deblitation B = Benefic; M = Malefic; N =Neutral

S.No. Chart Sun Moon Mars Mercury Jupiter

1. D/1 FB EM OB FB EM

2. D/2 FB FB DM EM FUB

3. D/3 OB FB FB FB FUB

4. D/4 EM OB EM F-DN EM

5. D/5 EM EM FB FB FB

6. D/6 OB FB EM OB FB

7. D/7 NN OB FB F-DN EM

8. D/8 NN OB FB FB FB

9. D/9 FB FB FB FB EM

10. D/10 FB FB EM FB EM

11. D/11 FB FB OB FB EM

12. D/12 EM FB OB NN FB

13. Benefic 7 10 8 8 6

14. Malefic 3 2 4 1 6

15. Neutral 2 - - 3 -

27.7 Year Lord

There .are five elElffi:ents of year lord:-( a) LOrd of Ascendant in the Natal Chart. (b) Lord of Ascendant of the Varsha Kundli. (c) Lord of the sign where Muntha is located. (d) Tri Rashi Pati. (e) Rashi Pati.

Venus. Sat.

EM EM

EM NN

EM EM

EM OB

OB EM

OB OB

EM EM

EM NN

EM EM

OB NN

NN NN

EM OB

3 3

8 5

1 4

As regards the 1st three are concerned, they can be found out from the Natal Chart and Varsh Kundli.

(4) Tri Rashi Pati varies from sign to sign. It varies with the Varshapravesh (Start of the year) Ac.cording to the sign of Lagna of annual horoscope the table

is given below:

Sign

Day


Tri-Rashi Pati chart

1 2 3 4 5 6 7 8 9 10 11 12

Su v Sa v J Mo Me Ma Sa Ma J Mo

Night J Mo Me Ma Su v Sa v 'Sa Ma J Mo

(5) Rashi Pati:- In case the year starts during day time sign lord of Sun, otherwise (start of the year during night) sign lord of Moon is the Rashi Pati.

Following five are the elements for the year lord in the example Chart:-

(a) Ascendant Lord of Natal Horoscope - Sun (b) Ascendant Lord of Annual Horoscope - Venus (c) Munthosh- Lord of the sign of Muntha - Venus (d) Tri-Rashi Pati (of Day) - Venus (e) Rashi Pati - Jupiter

The Year Lord is judged with the following conditions:(1) The Planet out of the above five aspecting the Ascen-

dant of annual horoscope and strongest among these planets is the year lord. In case a planet is not aspecting ascendant, cannot be a claimant for the year lord, howsoever strong it may be.

(2) lf two or more planets are aspecting the lagna, the strongest will be l:t'le year lord.

(3) If the two or more plaP.ets aspecting the lagna are equally strong, the planet which is claimant more times in the above 5 conditions, becomes the year lord. Some astrologers are of the view that in case the aspecting planets are equally strong, Munthesh becomes year lortl.

(4) lf none of the claimantaspects lagna or strength is lPss than 5 V.B., the Muntha lord becomes year lord. In the example horoscope, Venus has appeared thrice and aspecting the lagna with fifth aspect. Sun and Jupiter are in II and VIII house and do not aspect the iagna. Though their Panch Vargiya bala is more yet they cannot become year lord and the Venus having lesser Panchvargiya BaJa than Sun & Jupiter but aspecting lagna becomes the year lord.

27.8 Tripataki Chakra:-

In this chakra there are three flags (PatakJ.) over the three lines and as such it is called Tri-Pataki chakra. It is prepared with the planets in the Natal Chart and Ascendant of annual horoscope.

:.!48 Elements of Astronomy and·Astrological Calculations

Preparation of Tri~Patilki Chakra:

Draw three parallel vertical lines and the same are intersected by the three hoi:izontallines. On the top of vertical lines flags are

· drawn. The ends of these lines are joined as shown in the figure. The number of sign of ascendant of annual horoscope may be writ-. ten at the joint of middle flag. The number of signs may be written in ascending order on the )ofuts in anti-clock-wise direction. Lagna of Varsha Kundli is Taui:as so 2 is wirtten at the joint under middle flag. The rest rashl.s are written in ascending order as shown in the figure.

Method of pos~g the grahas in Tri Ch:~.kra.

Moon: Find· olitf the number of year running since birth. It can be obtained by'adding· 1 to the number of years completed. Divide this nt.imber by 9 and find out remainder. Moon is placed forward of that number ofnatal chart. In the example horoscope 26 years have been completed and 27th is current. Divide 27+ 9, 3 as quotient and leaving 0 or 9 as remainder. Place the Moon in the 9th sign counted from the natal moon (virgo), which is taurus in Tri pataki Chakra;

Sun, Mercury, Jupiter, Venus and Saturn:

The number ~f currentyeads divided by four and the_planet is placed in the Rashi .which is ahead of the remainder of the sign from the respective natal planet. !n case the planet is retrograde, the counting is _done backward. In the example 27 + 4 = 6 as quotient leaving 3 as remainder. In natal horoscope, Sun, Moon and Venus are in Sagitt(\rius, Sagittarius and Capricorn ·signs. They are to be placed in the 3rd sign from these i.e, Acquarius, Aquarius arid Pisces respectively. Jupiter and Saturn are retrograde, so the counting will be backward; they are in Leo and Virgo and

. counting 3rd in the reverse direction, they are placed inJemini and Cancer resp~ctively

.· Mars;.Rahu and Ketu

' · -. ·. Find out remainder after dividing the number of current year . .by6, The direct '!Jlanei. will move the same number of rashi ahead ·: and ~trograde backwards. Rahu and Ketu are taken retrograde

always. : .For example horoscope the number of current year 27, when

dividedby 6, leaves 3 remainder. Mars, Rahu and Ketu are in Leo, . Leo· ~d. Acquari.us. respectively. They· are to be placed in Libra, Jaminl.and Saggitaril.i's signs respectively. .


Tri-Pataki Chakra

In case the Vedha of Moon is by the benefics, benefic results arf' 0btained during the year and by the Vedha of Malefics, unfavourable results are got during the year. In case of Vedha by beneficial and malefics both, mixed results are obtained.


Appendix -I

Table of Equation of time to nearest minute

Date Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

1 +3 +14 +13 +4 -3 -2 +3 +6 0 -10 -16 -11

2 4 14 12 4 3 2 4 6 0 10 16 11

3 4 14 12 4 3 2 4 6 -1 11 16 10

4 5 14 12 3 3 2 4 6 1 11 16 10

5 5 14 12 3 3 2 4 6 1 11 16 10

6 6 14 12 3 3 2 4 6 1 12 16 10 .

7 6 14 12 2 4 1 ·5 6 2 12 16 9

8 7 14 11 2 4 1 5 6 2 12 16 9

9 7 14 11 2 4 1 5 5 2 13 16 8

10 7 14 11 2 4 1 5 5 3 13 16 7

11 8 14 10 1 4 1 5 5 3 13 16 7

12 8 14 10 1 4 1 5 5 3 13 16 7

13 9 14 10 1 4 0 5 5 4 14 16 6

14 9 ' 14 10 0 4 0 6 5 4 14 16 6

' 15 9 14 9 0 4 0 6 4 5 14 15 5

16 10 14 9 0 4 0 6 4 5 14 15 5

17 10 14 9 0 4 0 6 .4 5 14 15 4

18 10 14 8 0 4 +1 6 4 6 15 15 4

19 11 14 8 -1 4 1 6 4 6 15 15 3

20 11 14 8 1 4 1 6 3 6 15 14 3

21 11 . 14 8 1 4 1 6 3 7 15 14 2

22 2 14 7 1 4 2 6 3 7 15 14 2

23 12 13 7 2 3 2 6 3 7 16 14 1

24 12 13 7 2 3 2 6 2 8 16 13 1

25 12 13 7 2 3 2 6 2 8 16 13 0

26 13 13 .6 2 3 2 6 2 8 16 13 (J

2? 13 13 6 2 3 3 6 2 9 16 13 +1

28 13 13 5 2 3 3 6 1 9 16 12 1

29 13 13 5 3 3 3 6 1 9 16 12 2

30 13 - 5 3 3 3 6 1 10 16 1~ 2

31 14 - 4 - 3 - 6 0 - 16 - 3

Elements of Astronomy and Astrological Calculations

Sl.No. Lord

I Dewta

2 Pi tar

Rasi

0'-15'

15'-30'

Appendix - II Hora chart (D/2)

1 2 3 4 5 6

5 4 5 4 5 4

4 5 4 5 4 5

7

5

4

Drekhana Chart (D/3)

8

4

5

S.No. Lord ~i 1 2 3 4 5 6 7 8 . 1 Narad 0'-10' 1 2 3 4 5 6 7 8

2 Agasta 10'-20' 5 6 7 8 9 10 11 12

3 Durvasa 20'-30' 9 10 11 12 1 2 3 4

Chaturthamsa Chart (D/4) Sl. Lord ~ 1 2 3 4- 5 6 7 8 No 0

1 Sanak 7'-30 1 2 3 4 5 6 7 8

2 5annadan 15-00 4 5 6 7 8 9 10 11

3 Sana! 22-30 7 8 9 10 11 12 1 2 Kumar

4 Sana tan 30-00 10 1i 12 1 2 3 4 5

Trimshamsa chart (D/30) Odd signs even signs

9

5

4

9

9

1

5

9

9

12

.3

6

Lord Degrees. Rasi ·Lord Degrees Rasi Lord

Agni 0'-5' 1 Mars 0-5 2 Venus

10

4

5

10

10

2

6

10

10

1

4

7

Vayu 5-10 11 Saturn 5-12 6 Mercury

lndra 10-18 9 Jupiter 12~20 . 12 Jupiter

Dhanda 18-25 3 Mercury 20-25 10 Saturn

Jalad 25-30 7 Venus 25-30 8 Mars

Saptmansa Chart (D/7) . Sl. Lord Signs 1 2 3 4 5 6 7 8 9 10 No. Degr•es

up to

1 Kchar 4'-17' 1 8 3 10 5 12 7 2 9 4

2 Kcheer 8-34 2 9 4 11 6 1 8 3 10 5

3 Dadhi 12-51 '3 10 5 12 '7' 2 9 4 11 6

4 Aajya, 17-08. 4 11 6 1 8 3 10 5 12 7

5 Ikshuras 21-25 5 12 7 2 9 4 11 6 1 8 6 Madya 25-42 6 1 8 3 10 5 12 7 2 9

7 Sudhjal 30-00 7 2 9 4 11 6 1 8 3 10

251

11 12

5 4

4 5

11 12

11 12

3 4

7 8

11 12

11 12

2 3

5 6

8 9

Lord

Jalad

Dhanad

lndra

Vayu

Agni

11 12

11 6

12 7

1 8

2 9

3 10

4 11

5 12


Navamsa Chart D/9

Sl. Lord

~ 1 2 3 4 5 6 7 8 9 10 11 12

No.

0

.

1 Devta 3'-20' 1 10 7 4 1 10 7 q 1 10 7 4

2 Nara 6-40 2 11 8 5 2 11 8 5 2 11 8 5

3 Rakchas 10-00 3 12 9 6 3 12 9 6 3 12 9 6

4 Oevta 13-20 4 1 10 7 4 1 10 7 4 1 10 7

5 Nara 16-40 5 2 11 8 5 2 11 8 5 2 11 8

6 Rakchas 20-00 6 3 12 9 6 3 12 9 6 3 12 9

7 Devta 23-20 7 4. 1 10 7 4 1 10 7 4 1 10

8 Nara 26-40 8 5 2 11 8 5 2 11 8 5 2 11

9 Rake has 30-00 9 6 3 12 9 6 3 12 9 6 3 12

Dashmansha Chart (D/10)

Sl. Lord

~ 1 2 3 4 5 6 7 8 9 10 11 12 Lords No. of . ol

Odd sign B.ensiJ!

1 lndra 0'- 3' 1 10 3 12 5 2 7 4 9 6 11 8 Anania

2 Agni 3-6 2 11 4 1 6 3 8 5 10 7 12 9 Brahrna

3 Varna 6-9· 3 12 5 2 7 4 9 6 11 8 1 10 !shan

4 Rakshas 9-12 4 1 6 3 8 5 10 7 12 9 2 11 Kuber

5 Varun 12-15 5 2 7 4 9 6 11 8 1 10 3 12 Vayu

6 Vayu 15-18 6 3 8 5 10 7 12 9 2 11 4 1 Varun

7 Kuber 18-21 7 4 9 6 11 8 1 10 3 12 5 2 Rakshas

8 Eshan 21-24 8 5 10 7 12 9 2 11 4 1 6 3 Varna

9 Brahrna 24..:27 9 6 11 8 1 . 10 3 12 5 2 7 4 Agni

10 Anania 27-30 10 7 12 9 2 11 4 1 6 3 8 5 lndra

Elements of Astronomy and Astrological Calculations

Dwadshamsa Chart (D/12)

Sl. Lord I~ 1 2 3 4 5 6. 7 8 9 10 No.

IgnS

0

1 Ganesh 2'- 30' 1 2 3 4 5 6 7 8 9 10 2 Ashwini 5-00 2 3 4 5 6 7 8 9 10 11

Kumar

3 Varna 7-30 3 4 5 6 7 8 9 10 11 12

4 Sarpa 10-00 4 5 6 7 8 9 10 11 12 1

5 Ganeshc 12-30 5 6 7 8 9 10 11 12 1 2

6 Ashwini 15-00 6 7 8 9 10 11 12 1 2 3 Kumar .

7 Varna 17-30 7 8 9 10 11 12 1 2 3 4

8 Sarpa 20-00 8 9 10 11 12 1 2 3 4 5.

9 Ganesh 22-30 9 10 11 12 1 2 .3 4 5 6

10 Ashwini 25-00 10 11 12 1 2 3 4 5 6 7 Kumar

11 Varna 27-30 11 12 1 2 3 4 5 6 7 8

12 Sarpa 30-00 12 1 2 3 4 5 6 7 8 9

Shodshamsa Chart (D/16) Brahma = B Vishnu = V, Hora = H, Sun = S

51. Odd ~Signs 1 2 3 4 5 6 7 8 9 10 11 12

No. ~~ ~:~~"" 1 B 1 '/52'/30 1 5 9 1 5 9 1 5 9 1 5 9

2 v 3/45/00 . 2 6 10 2 6 10 2 6 10 2 6 10

3 H 5/37/30 3 7 11 3 7 11 3 7 11 3 7 11

4 s 7/30/00 4 8 12 4 8 12 4 8 12 4 8 12

5 . B 9/22/30 5 9 1 5 9 1 5 9 1 5 9 1

6 v 11/15/00 6 10 2 6 10 2 6 10 2 6 10 2.

7 H 13nt30 7 11 3 7 11 3 7 11 3 7 11 3

8 s 15/0/00 . 8 12 4 8 12 4 8 12 4 8 12 4

9 B 16/52/30 9 1 5 9 1 5 9 1 5 9 1 5

10 v 18/45!00 10 2 6 10 2 6 10 2 6 10 2 6

11 H 20/37/30 11 3 7 11 3 7 11 3 7 11 3 7

12 s 22/30/00 12 4 8 12 4 8 12 4 8 12 4 8

13 · B 24/22/30 1 5 9 1 5 9 1 5 9 1 5 9

14 v 26/15/00 2 6 10 2 6 10 2 6 10 2 6 10

15 1'1 28/7/30 3 7 11 3 7 11 3 7 11 3 7 11

16 s 30/0/00 4 8 12 4 8 12 4 8 12 4 8 12

253

11 12 !

11 12

12 1

1 2

2 3

3 4

4 5

5 6

6 7

7 8

8. 9

9 10

10 11

Even sign Lord

s H

v B

5

H

v B 5 H

v B

s H

v B

I

!


Vimshamsa Chart (D/20)

Sl. Odd s: 1 2 3 4 5 6 7 8 9 10 11 12 Even No. sign sign

Lord De g.

Lord up to

~ Kali 1°/30' 1 9 5 1 9 5 1 9 5 1 9 5 Daya

2 Gauri 3/00 2 10 6 2 10 6 2 10 6 2 10 6 Megha

3 Jay a 4/30 3 11 7 3 11 7 3 11 7 3 11 7 Chinnashi

4 Laxmi 6/00 4 12 8 4 12 8 4 12 8 4 12 8 Pishachi

5 Vijya 7/30 5 1 9 5 1 9 5 ] 9 5 1 9 Dhumavati

6 Vimla 9!00 6 2 10 6 2 10 6 2 10 6 2 10 Matangi

7 Sati 10/30 7 3 11 7 3 11 7 3 11 7 3 11 Bala

8 Tara 12/00 8 4 12 8 4 12 8 4 12 8 4 12 Bhadra

9 Jawalamu 13/30 9 5 1 9 5 1 9 5 1 9 5 1 Aruna

10 Sweta 15/00 10 6 2 10 6 2 10 6 2 10 6 2 Anala

11 Lalita 16/30 11 7 3 11 7 3 11 7 3 11 7 3 Pingla

12 Bag ala 18/00 12 8 4 12 8 4 12 8 4 12 8 4 Cl-luti1.J<I

13 ~ 19/30 1 9-~- 1 9 5 1 9 5 1 9 5 Ghora

14 Shachi 21/00 2 10 6 2 10 6 2 10 6 2 10 6 Varahi .

15 Randri 22/30 3 11 7 3 11 7 3 11 7 3 11 7 Vashnavi

16 Bhawani 24/00 4 12 8 4 12 8 4 12 8 4 12 8 Sita

.. 17 Varda 25/30 5 1 9 5 1 9' 5 1 9 5 1 9 Bh\MleShwari

18 Jaya 27/00 6 2 10 6 2 10 6 2 10 6 2 10 Bharvi

19 Tripura 28/30 7 3 11 7 3 11 7 3 11 7 3 11 Mangla

20 Sumukhi 30/00 8 4 12 8 4 12 8 4 12 8 4 12 Apraji


Chaturvimsamsa Chart (D/24)

Sl. Odd ~ 1 2 3 4 5 6 7 8 9 10 11 12 Even No. sign sign

Lord D~g.

Lord up to

1 Skanda 1/15 5 4 5 4 5 4 5 4 5 4 5 4 Bhirna

2 Parusdha 2/30 6 5 6 5 6 5 6 5 6 5 6 5 Madan a

3 Anala 3/45 7 6 7 6 7 6 7 6 7 6 7 6 Govit\da

4 Vishwaka 5/00 8 7 8 7 8 7 8 7 8 7 8 7 Vrish dhawja

5 Bhaga 6/15 9 8 9 8 9 8 9 8 9 8 9 8 An taka

6 Mittra 7/30 10 9 10 9 10 9 10 9 10 9 10 9 Varna

7 Varna 8/45 11 10 11 10 11 10 11 10 11 10 11 10 Mittra

8 An taka 10/10 12 11 12 11 12 11 12 11 12 11 12 11 Bhaga

9 Vrish 11/15 1 12 1 12 1 12 1 12 1 12 1 12 Vishwaka dhwaja

10 Govinda 12/30 2 1 2 1 2 1 2 1 2 1 2 1 Anata

11 Madan a 13/45 3 2 3 2 3 2 3 2 3 2 3 2 Parusdhar

12 Bhirna 15/00 4 3 4 3 4 3 4 3 4 3 4 3 Skand

13 Skanda 16/15 5 4 5 4 5 4 5 4 5 4 5 4 Bhirna

14 Parush 17/30 6 5 6 5 6 5 6 5 6 5 6 5 Madan a dhara

15 An ala 18/45 7 6 7 6 7 6 7 6 7 6 7 6 Govinda

16 Vishwaka 20/00 8 7 8 7 8 7 8 7 8 7 8· 7 Vrish dhwaja

17 Bhaga 21/15 9 8 9 8 9 ~ 9 '8 9 8 9 8 An taka

18 Mittra 22/30 10 9 10 9 10 9 10 9 10 9 10 9 Varna

19 Varna 2~/45 11 10 11 10 11 10 11 10 11 10 11 10 Mittra

20 An taka 25/00 12 11 12 11 12 11 12 11 12 11 12 11 Bhaga

21 Vrish 26/15 1 12 1 12 1 12 1 12 1 12 1 12 Vishwaka dhawaja

22 Govinda 27/30 2 1 2 1 2 1 2 1 2 1 2 1 Anala

23 Madna. 28145 3 2 3 2 3 2 3 2 3 2 3 2 Parusdhar

24 Bhirna 30100 4 3 4 3 4 3 4 3 4 3 4 3 Skanda


Bhashansha (Saptvimsansh) (D/27)

Sl. I~ up to 1 2 3 4 5 6 7 8 9 10 11 12

No 0 I II

rd

1 Aswini Kr 1/6/40 1 4 7 JO 1 4 7 10 1 4 7 10

2 Yam a 2/13/20 2 5 8 11 2 5 8 11 2 5 8 11

3 Agni 3/20/00 3 6 9 12 3 6 9 12 3 6 9 12

4 Brahma 4/26/40 4 7 10 1 4 7 10 1 4 7 10 1 .

5 Chandra 5/33/20 5 8 11 2 5 8 11 2 5 8 11 2

6 Shanker 6/40/00 6 9 12 3 6 9 12 3 6 9 12 3

7 Aditi 7/46/40 7 10 1 4 7 10 1 4 7 10 1 4

8 Jeeva 8/53/20 8 11 2 5 8 11 2 5 8 11 2 5

9 Ahi 10/0/00 9 12 3 6 9 12 3 6 9 12 3 6

10 Pi tar 11/6/40 10 1 4 7 10 1 4 7 10 1 4 7

11 Bhag 12/13/20 11 2 5 8 11 2 5 8 1l 2 5 8

12 Aryama 13/20/00 12 3 6 9 12 3 6 9 12 3 6 9

13 Ark a 14/26/40 1 4 7 10 1 4 7 10 1 4 7 10

14 Tvasta 15/33/20 2 5 8 11 2 5 8 11 2 5 8 11

15 Vayu 16/40/00 3 6 9 12 3 6 9 12 3 6 9 12

16 Shakragni 17/46/20 4 7 10 1 4 7 10 1 4 7 10 1

17 Mitra 18153/20 5 8 11 2 5 8 11 2 5 8 11 2

18 Vasava 20/0/00 6 9 12 3 6 9 12 3 6 9 12 3

19 Nirriti 21/6/40 7 10 1 4 7 10 1 4 7 10 r 4

20 Udaka 22/13/20 8 11 2 5 8 11 2 5 8 11 2 5

21 ~ 23/20/00 9 12 3 6 9 12 3 6 9 12 3 6

22 Govinda 24/26/40 10 1 4 7 10 1 4 7 10 1 4 7

23 Vasu ' 25/33/20 11 2 5 8 11 2 5 8 11 2 5 8

24 Varun 26/40/00 12 3 6 9 12 3 6 9 12 3 6 9

25 Ajpat 27/46/40 1 4 7 10 1 4 7 .10 1 4 7 10

26 Ahirbundy 28153/20 2 5 8 11 2 5 8 11 2 5 8 11

27 Poosha 30/0/00 3 6 9 12 3 6 9 12 3 6 9 12 .


Khavedamsa Chart (D/40) Sl. ~n up to 1 2 3 4 5 6 7 8 9 10 11 12 No d . '

1 Vishnu 0/45 1 7 1 7 1 7 1 7 1 7 1 7

2 Chandra 1/30 2 8 2 8 2 8 2 8 2 8 2 8

3 Maricha 2/15 3 9 3 9 3 9 3 9 3 9 3 9

4 Tvasta 3/00 4 10 4 10 4 10 4 10 4 10 4 10 5 Dhata 3/45 5 11 5 11 5 11 5 11 5 11 5 11

6 Shiva 4/30 6 12 6 12 6 12 6 12 6 12 6 12 7 Ravi 5/15 7 1 7 1 7 1 7 1 7 1 7 1 8 Yam a G/00 8 2 8 2 8 2 8 2 8 2 8 2 9 Yakshesh 6/45 9 3 9 3 9 3. 9 3 9 3 9 3

10 Gandharva 7/30 10 4 10 4 10 4 10 4 10 4 10 4

11 Kala 8/15 11 5 11 5 11 5 11 5 11 5 11 5

12 Varuna 9!00 12 6 12 6 12 6 12 6 12 6. 12 6 13 Vishnu 9/45 1 7 1 7 1 7 1 7 1 7 1 7

14 Chandra 10/30 2 8 2 8 2 8 2 8 2 8 2 8 15 Maricha 11!15 3 9 3 9 3 9 3 9 3 9 3 9

16 Tvasta 12/00 4 10 4 10 4 10 4 10 4 10 4 10 17 Dhata 12/45 5 11 5 11 5 11 5 11 5 11 5 11

18 Shiva 13/30 6 12 6 12 6 12 6 12 6 12 6 12

19 Ravi 14/15 7 1 7 1 7 1 7 1 7 1 7 1 20 Yama 15/0 8 2 8 2 8 2 8 2 8 2 8 2

21 Yakshesh 15/45 9 3 9 3 9 3 9 3 9 3 9 3

22 Gandharva 16/30 10 4 10 4 10 4 10 4 10 4 10 4

23 Kala 17/15 11 5 11 5 11 5 11 5 11 5 11 5

24 Varuna 18/0 12 6 12 6 12 6 12 6 12 6 12 6

25 Vishnu 18/45 1 7 1 7 1 7 1 7 1 7 1 7 26 Chandra 19/30 2 8 2 8 2 8 2 8 2 8 2 8

27 Marich a 20/15 3 9 3 9 3 9 3 9 3 9 3 9

28 Tvasta 21/0 4 10 4 10 4 10 4 10 4 10 4 10

29 Dhata 21/45 5 11 5 11 5 11 5 11 5 11 5 11

30 Shlva 22/30 6 12 6 12 6 12 6 12 6; 12 6 12

31 Ravi 23/15 7 1 7 1 7 1 7 1 7 1 7 1

32 Yama 24/0 8 2 8 2 8 2 8 2 8 2 8 2

33 Yakshesha 24/45 9 3 9 3 9 3 9 3 9 3 9 3 34 Gandharva 25/30 10 4 10 4 10 4 10 4 10 4 10 4

35 Kala 26/15 11 5 11 5 11 5 11 5 11 5 11 5 36 Varuna 27/0 12 6 12 6 12 6 12 6 12 6 12 6

37 Vishnu 27/45 1 7 1 7 1 7 1 7 1 7 1 7

38 Chandra 28/30 2 8 2 8 2 8 2 8 2 8 2 8

39 Marich a 29/15 3 9 3 9 3 9 3 9 3 9 3 9

40 Tvasta 30/0 4 10 4 10 4 10 4 10 4 10 4 10


Sl. No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

Akshavedamsha Chart or

Panch-chatvarishamsa (D/45) Moveable sign's

lord is Brahma,fixed sign's lord is Shankar and dual sign's Lord is Vishnu

Degrees 1 2 3 4 5 6 7 8 9 10 0 '

0/40 1 5 9 1 5 9 1 5 9 1

1/20 2 6 10 2 6 10 2 6 10 2

2/0 3 7 11 3 7 11 3 7 11 3

2/40 4 8 12 4 8 12 4 8 12 4

3/20 5 9 1 5 9 1 5 9 1 5

4/0 6 10 2 6 10 2 6 10 2 6

4/40 7 11 3 7 11 3 7 11 3 7

5/20 8 12 4 8 12 4 8 12 4 8

6/0 9 1 5 9 1 5 9 1 5 9

6/40 10 2 6 10 2 6 10 2 6 10

7/20 11 3 7 '11 3 7 11 3 7 11

8!0 12 4 8 12 4 8 12 4 8 12

8/40 1 5 9 1 5 9 1 5 9 1

9/20 2 6 10 2 6 10 2 6 10 2

10/0 3 7 11 3 7 11 3 7 11 3 -

10/40 4 8 12 4 8 12 4 8 12 4

11/20 5 9 1 5 9 1 5 9 1 5

12/0 6 10 2 6 10 2 6 10 2 6

12/40 7 11 I 3 7 11 3 7 11 3 7

11 12

5 9

6 10

7 11

8 12

9 1

10 2

11 3

12 4

1 5

2 6

3 7

4 8

5 9

6 10

7 11

8 12

9 1

10 2

11 3


20 13120 8 12 4 8 12 4 8 12 4 8 12 4

21 4/0 9 1 5 9 1 5 9 1 5 9 1 5

22 14/40 10 2 6 10 2 6 10 2 6 10 2 6

23 15/20 11 3 7 11 3 7 11 3 7 11 3 7

24 16/0 12 4 8 12 4 8 12 4 8 12 4 8

25 16/40 1 5 9 1 5 9 1 5 9 1 5 9

26 17/20 2 6 10 2 6 10 2 6 10 2 6 10

27 18/0 3 7 11 3 7 11 3 7 11 3 7 11

28 18/40 4 8 12 4 8 12 4 8 12 4 8 12

29 19120 5 9 1 5 9 1 5 9 1 5 9 1

30 20/0 6 10 2 6 10 2 6 10 2 6 10 2

31 20/40 7 11 3 7 11 3 7 11 3 7 11 3

32 21120 8 12 4 8 12 4 g 12 4 8 12 4

33 22/0 9 1 5 9 1 5 9 1 5 9 1 5

34 22/40 10 2 6 10 2 6 10 2 6 10 2 6

35 23120 11 3 7 11 3 7 11 3 7 11 3 7

36 24/0 12 4 8 12 4 8 12 4 8 12 4 8

37 24140 1 5 9 1 5 9 1 5 9 1 5 9

38 25120 2 6 10 2 6 10 2 6 10 2 6 10

39 26/0 3 7 11 3 7 11 3 7 11 3 7 11

40 26/40 4 8 12 4 8 12 4 8 12 4 8 12

41 27120 5 9 1 5 9 1 5 9 1 5 9 1

42 28/0 I 6 10 2 6 10 2 6 10 2 6 10 2

43 28/40 7 11 3 7 11 3 7 11 3 7 11 3

44 29120 8 12 4 8 12 4 8 12 4. ~· 12 4 '.

45 30/0 9 1 5 9 1 5 9 1 5 9 1. 5 .


Shashthiamsa Chart (D/60)

St. Degrees 1 2 3 4 5 6 7 8 9 10 11 12 No. . '

1 0/30 1 2 3 4 5 6 7 8 9 10 11 12

2 1/0 2 3 4 5 6 7 8 9 10 11 12 1

3 1/30 3 4 5 6 7 8 9 10 11 12 1 2

4 2/0 4 5 6 7 8 9 10 11 l~ 1 2 3

5 2/30 5 6 7 8 9 10 11 12 1 2 3 4

6 3/0 6 7 8 9 10 11 12 1 2 3 4 5

7 3/30 7 8 9 10 11 12 1 2 3 4 5 6

8 4/0 8 9 10 11 12 1 2 3 4 5 6 7

9 4/30 9 10 11 12 1 2 3 4 5 6 7 8 . 10 5/0 10 11 12 1 2 3 4 5 6 7 8 9

11 5/30 11 12 1 2 3 4 5 6 7 8 9 10

12 6/0 12 1 2 3 4 5 6 7 8 9 10 11

13 6/30 1 2 3 4 5 6 7 8 9 10 11 12

14 7/0 2 3 4 5 6 7 8 9 10 i1 12 1

15 7/30 3 4 5 6 7 8 9 10 11 12 1 2

16 8/0 4 5 6 7 8 9 10 11 12 1 2 3

17 8/30 5 6 7 8 9 10 11 12 1 2 3 4

18 9/0 6 7 8 9 10 11 12 1 2 3 4 5

19 9/30 7 8 9 10 11 12 1 2 3 4 5 6

20 10/0 8 9 10 11 12 1 2 3 4 5 6 7

21 10/30 9 10 11 12 1 2 3 4 5 6 7 8

22 11/0 10 11 12 1 2 3 4 5 6 7 8 9

23 11/30 11 12 .1 2 3 4 5 6 7 8 9 10

24 12/0 12 1 2 3 4 5 6 7 8 9 10 11

25 12/30 1 2 3 4 5 6 7 8 9 10 11 12

26 13/0 2 3 4 5 6 7 8 9 10 11 12. 1

27 .·13/30 3 4 5 6 7 8 9 10 11 12 1 2

28 14/0 4 5 6 7 8 9 10 11 12 1 2 3

29 14/30 5 6 7 8 9 10 11 12 1 2 3 4

Elements of Astronomy and Astrological Calculations 261 "

30 15/0 6 7 8 9 10 11 12 1 2 3 4 5

31 15/30 7 8 9 10 11 12 1 2 3 4 5 6

32 16/0 . 8 9 10 11 12 1 2 3 4 5 6 7

33 16/30 9 10 11 12 1 2 3 4 5 6 7 8

34 17/0 10 11 i2 1 2 3 4 5 6 7 8 9

35 17/30 11 12 1 2 3 4 5 6 7 8 9 10

36 1810 12 1 2 3 4 5 6 7 8 9 10 11

37 18/30 1 2 3 4 5 6 7 8 9 10 11 12

38 19/0 2 3 4 5 6 7 8 9 10 11 12 1

39 19/30 3 4 5 6 7 8 9 10 11 12 1 2

40 20/0 4 5 6 7 8 9 10 11 12 1 2 3

41 20/30 5 6 7 8 9 10 !1 12 1 2 3 4

42 21/0 6 7 8· 9 10 11 12 1 2 3 4 5

43 21/30 7 8 9 10 11 12 1 2 3 4 ,5 6

44 22/0 8 9 10 11 12 1 2 3 4 5 6 7

45 22/30 9 10 11 12 1 2 3 4 5 6 7 8

46 23/0 10 11 12 1 2 3 4 5 6. 7 8 9

47 23/30 11 12 1 2 3 4 5 6 7 8 9 10

48 24/0 12 1 2 3 4 5 6 7 8 9 10 11

49 24/30 1 2 3 4 5 6 7 8 9 10 11 12

50 25/0 2 "3 4 5 6 7 8 9 10 11 12 1

51 25/3C 3. 4 5 6 7 8 9 10 11 12 1 2

52 26/0 4 5 6 7 8 9 10 11 12 1 2 3

53 26/30 5 6 7 8 9 10 11 12 1 2 3 4.

54 27/0 6 7 8 9 10 11 12 1 2 3 4 5

55 27/30 7 8 9 10 11 12 1 2 3 4 5 6

56 28/0 . 8 9 10 11 12 1 2 3 4 5 6 7

57 28/30 9 10 11 12 1 2 3 4 5 6 7 8

58 29/0 10 11 12 . 1 2 3 4 5 6 7 .8 9

59 29/30 11 12 1 2 3 4 5 6 7 8 9 10

60 30/0 12 1 2 3 4 5. 6 7 8 9 10 11 .


Appendix-Ill

Sl. Indian Name of Nlrayana Magnl- Distance No. name of Star langitud• tude In light

Stars years

1 Ashwini ~ Arietis 10° 6 2.72 -2 Bharni ~ or 35 Arietis 24° 20 3.86 -3 Kritika Aleyone2 36° 8 2.96 -

4 Rohini IX Touri or Aloebaran 45" 55 0.8 68

5 Brahmarda (IX Aurogue) Capella 58" 0.1 46

6 Agni P Touri 58' 43 1.78

7 Mrigshira '- Orionis 59" 50 3.66

8 Dhruva Polaris 64' 42 2.1 680

9 Aardra CI Orionis 64° 53 0.8 652

10 Lubdhaka Sirius (IX Conis Majoris) so.· 13 (-) 1.41 8.7

11 Agastya Conopus (IX Camiae) 81" .06 -0.7 196

12 Punatvasu Pollux ~ Geninoram 89' 21 1.14 36

13 Pushya o Coneri 104' 51 3.94

14 Ashlesha EHydrae 108" 29 3.48

15 Kritu Dubhe (Ursae Majoris) 114" 20 1.95 75

16 Magha IX Leon is (Regulus) 125' 58 1.34 425

17 Poorva Phalguni 8Leonis 137" 27 2.58

18 Uttara Phalguni ll Leonis (Denebola) 147" 45 2.23

19 Hasta o Corvi 169' 35 2.95

20 Chitra Spica (u virginis) 179" 59 1.21 260

21 Swati Arcturus (IX Boots) 180" 22 -0.04 36

22 Vishakha a or k l.ibrae 201" 13 2.90 330

23 Anucadha o Scorpii 218" 42 2.32

24 Jyeshtha ex Scorpii (Anteres) 225' 54 1.2 423

25 Mula V or 34 Scorpii 240" 43 1.63

26 P. Ashadha o Saggettarii 250' 43 2.70

27 U. Ashadha 8 Saggettaric 258' 31 2.14

28 Ab.hijit B Lyrae 261" 27 0.03- 26

29 Sravana r< Aquilae Aaltair 277" 55 0.8 16.6

30 Ghanishta aDelphini 293' 51 3.72

31 Shatbhishak ). Aquarii 317' 43 3.74

32 P. Bhadra Markab (IX Regasi) 329" 37 2.57

33 U. Bhadra y Pegasi 345' 17 2.87

34 Revati ; Piscium 356.01 5.24


Appendix - IV Table of Planetary distances and movement.

Col. 1 2 3 4 5 6 7 8 9 10 Mean distance

from sun Name in in Sid. synodic Equa- Rlriodof Orbital Eccenw lndi- Mean

of lacs of lacs of period period torial rotation incli· tricity nation orbital planet mles KM. in earth diameter Days nation f the ort bfEqu- velo-

days inK.M. on ecli- atorto ci1y ptic orbit 1\M&c

Mer 360 580 87.969 115.88 4.878 58.65 7".00 0.2056 oo 47.89

Ven 672 1082 224.701 583.92 12,100 243.01 3°.39 0.0066 (-)2' 35.03

Earth 930 1498 365.256 - 12,756 23h56m4s - tl.0167 23"27' 29.79

Mar.; 1.415 2279 686.980 779.94 6794 24 '.II 23 1'.85 0.0934 23°59' 24.13

Jup 4.833 7.783 11.862 398.88 142,796 9 50 30 1°30 0.0485 3°5' 13.06

Sat 8.861 14.270 29.4577 378.09 1,20.000 10 39 0 2".49 0.0556 29' 9.64

Ura. 17.830 28696 84.0139 369.66 52.290 17 12 0 'J'.77 0.0472 98° 6.81

Nep 27.930 44.966 164.793 367.49 48.600 17 50 0 1°.77 0.0086 28048' 5.43 Days

Pluto 37.000 59.000 247.7 366.73 2,300 6.3874 17°.2 0.250 - 4.74 Sun - - - - 8,65.000 25.4 - - - 135

Miles Mdes

Moon Mil~ K.M. Days K.M. K.M.

,23QOOO 3,84,402 27.321 29.53 3.476 27.3 5°.25 0.054 1.02

Col. 11 12 13 14 15 16 17 18 Name Numbe Acce- Valoume Density Mass Exape Maximum Albedo

of of laratior Earth Water Earth velocity Magni-Planet Moons due to = 1 = 1 =1 K.M.Per tude

gravity sec.

Mer - 3.78 0.055 5.42 0.0558 4.3 (-) 1.9- 0.06

Ven - 8.60 0.86 5.25 0.815 10.3 (-) 4.4 0.76

Earth 1 9.78 1 5.52 1 11.2 - 0.36

Mars 2 3.77 0.15 3.94 0.1074 5.0 (-) 2.8 0.16

Jup 16 22.88 1310 1.314 317.893 59.5 (-) 2.6 0.43

Sat 21 9.05 744 0.69 95.147 35.6 (-) 0.3 0.61

Ura. 15 7.77 67 1.19 14.54 21.22 3.6 0.35

Nep 8 11.00 57 1.71 17.23 23.6 7.7 0.35

Pluto 1 4.3 - 0.06 0.0017 5.3 14.0 0.47

S~n - - 13,00.(XXl 1.4 3,30,000 384 - -Moon - 1.62 - 3.34 1/81 1.5 (-) 12.7 7%

(Column 17) Magnitude : The greater is the magnitude, lesser is the brightness. Minus magnitt..::le planets are more bright than the positive figure.

Albedo is the reflecting power ratio of the planet with the light falls on it by an external source.

Index

[[4] Char Khanda 96

Abdabala 192 Chaldean saros 154

Acquarius 107 Civil day 26

·Albedo 240 Coments 55

Altitude 19 Periodic 57

Annual Horoscope 227-231 Non-Periodic 57

Aphelion 24,39 Combustion of planets 154

Apogee 153 Moon 160

P.pparent solar day 26 Inner planets 160

Amsayu 174 Outer Planets 161

Aries 107 Conjunction 22,70

Ascendant 78 _Constellation 108, 142

Aspectual strength 210 [lQ] Asteriods 49 Astronomers 5

Dashas of Varshphal 233-236

Astronomical Unit 24 . Vimshotri Mudda

Autumnal equinox 43 Dasha 233

Axis 12 Yogini Mudda

Ayanbala 196 Dasha 235

Aynamsa 105 Palyayini Dasha 236

Azimuth 19 Dash Varga 125

m Declination 17, 198 Declination Circle 20

Bhava 120 Deimos 49

Bhavabala 221 Density 240

Black hole 168 Dhruvanka Table 228-229

Bode's law 39 Digbala 188

[[£] Diurnal Motion 26,158 Dreshkona bala 187

Cancer 107 Drik bala 210

Capricorn 107 Dwadash Vargiya Bala 243

Celstial rn Equator 15 longitude 16 Earth 12,41 latitude 17 Eccentricity 46,240 Meridian 18 Ecliptic 15 Pole 15 Eclipse 151 Sp~hre 15 Lunar 151

Central Meridian 14 Solar 152 Chesta bala 205 Annular 153

Index 265

Ellipse 10 (I.S.'I:.) 59 Ephemeries · 84 Inferior conjunction 21,69 Encke's comet 57 Inner planets 38 Equation of time 26 Ishtaphala 225 Equinox [[lJ] Autumnal 43

Vernal/ spring 43 Jupiter 50 Evening star 47 [[!)] m Kalabala 189 Formation of seasons 42 Kashta Phala 225 Full Moon 2,151 Kama 143 Fixed zodiac 105 Kendrabala 187

[QJ] Kepler's laws 38 Ketu 150

Galaxy 168 m Gemini 107 Ge-centric longitude 109 Leap year 138 Grahabala in Varshphal 237 Leo 107 Great Circle 11 Ubra 107 Greenwich Mean Time Light year 24 (G.M.T.) 28 Local Mean Time (L.M.T.) 28,

ffill 59 Longevity 170

Harsh Bala 238 Lunar day /Tithi 29,139 Hadda Bala Table 239 Lunar eclipse 151 Helley's comet 57 Lunar Month 30 Heliacal Lunar Adhika Masa 34

Rising 159 Luni-solar year 33 Setting 159

~ Helio-centric longitude 110 Horabala 194 Magnitude of planets 114 Horizon Circle 18 Mars 48 Horoscope 75 Mass-bala 19!_ Hour Angle 20 Metonic cycle 33 History of Mean solar day 26

Indian Astronomy 4 Mean Sun 26 Western Astronomy 6 Mercury 45

[[] Meteorites 58 Meteors 58

Indian Astronomy 4 Mil,kyway 168 Indian Astrologers 5 Minor planets 49 Indian Standard Time Moon 45

266 Index

Month 30 Perigee 153 Anomalistic 31 Perihelion 24,39 Adhika 34 Phases of Lunar 30. Moon 148 Missing 34 Inner Planets 113 Nodical 31 Outer Planets 114 Nakshtra 31 Phobos 48 Solar 31 Pindayu 170

Motional strength 205 Pisces 107 Morning star 47 Plane 10 Moveable zodiac 105 Planets 36 Muntha 233 Planetary aspects 210

llill Pluto 55 Pole of Ecliptic 103

Nadir 18 Pole 12 Nakshatra 108 Positional strength 179 Nakshatrayu 178 Precession of Equinox 102 Name of week days 29 Prime-Meridian 14 Naisargikayu 177 Prime-Vertical 19 Naisargik-bala 210 Pulsars 166 Nathonnath-bala 189 [@] Nebula 169 Neptune 54 Rahu 150 Neutron Star 166 Rashiman 95,97 New Moon 1 Red-giant 166 Newton's Law 115 Retrogression of Planets 110 Nodes 150 Right ascension 17 Nodical Month 31 Rising and setting 158 Nova 165 m Nutation 103

[[§1] Sagittarius 107 Samagama 155

Obliquity of Ecliptic 15,42 Sapt-Vargas 125 Occultation 155 Sapt-Vargiyabala 184 Opposition. 22,71 Satellites 36 Outer Planets 38 Saturn 51 m Sco_rpio 107 Paksha-bala 190 Seasons 42 Palbha 96 Shadbala 179 Panchanga 135 Shad-Vargas 125 Panchvargiva Bala 239 Shodash-Vargas 125 Parsec 25 Shooting stars 58 Penumbra 152 Sidereal

Index 267

Day 28,62 Sidereal Time 28,65 Hour 64 Standard Time 59 Period 69 Z.S.T. 59 Time 28,65 Tithi 29, 139 Year 32 Tribhaga-bala 191

Small Circle 11 Tri Pataki Chakra 247 Solar Eclipse 152, 153 Tropic of Cancer 13 Solar Mo~th 31 Tropic of Capricorn 13 Solar flares 41 mJl Solar system 36 Sphere 10 Uchchabala 183 Spring Equinox 43 Umbra152 Stars 36, 164 Units of

Birth 166 Time 23 Colour 165 Angles 107 Life-Time 167 Distances 24 Magnitude 165 Upgrahas 155 Mass 167 Uranus 53 Names 164 [[Y] Spectrum 166

Standard Meridian 14 Vara (Week Day) 137 Standard Time 59 ·vara-bala 194 Superior Conjunction 21,70 Venus 47 Summer Solstice 43 Vernal equinox 43 Sun 40 Verticals 18 Sun-rise 94 Vimshotri-dasa 116 Surya-siddhanta 4 Virgo 107 Sun-set 94 Volume 240 Super-Nova 166

~ Synodic-Period 69,71

[!]] Weekdays 29, 137 Winter Solstice 43

Taurus 107 White Dwarf 166 Terrestrial [[]]

Equator 12 longitude 14 Year Latitude 12 Anomalistic Year 32 Meridian 13 Calander Year 32

Time Lunpr Year 33 G.M.T. 28 Luni-solar Year 33 I.S.T. 59 Sidereal Year 32 L.M.T. 28,59 Tropical Year 32

268 Index

Year Lord Yoga Yudha-bala Yugmayugm-bala

~ Zenith

246 Zodiac 16, 105 145 Fixed/Nirayan/ 203 Side real 105 186 MoveabletSayami 105

Terrestrial 105 18 Zonal Standard Time 59

Bibliography 1. Elements of Astronomy by George W. Parker.

2. Spl).erical Astronomy by W. M. Smart.

3. A to Z Astronomy by Patrie Moore.

4. New Horizons in Astronomy by John C. Brandt.

5. Discovering Astronomy by Robert D. Champman.

6. The cambridge Atlas of Astronomy by Jean Andouze and Guy Isreal.

7. Surya Siddhanta by Mahabir Prasad Srivastava.

8. Bhartiya Joytish by Nemi Chand Shashtri.

9. A Manual of Hindu Astrology by B. V. Raman.

10. How to Judge a Horoscope by B. V. Raman.

11. Saur Parivar (Solar System) by Gorakh Pershad

12. Vrihat Parasar Hora Shashtra.

13. Sripatipaddhati by V. Subrahmanya Sastri.

14. Mathematical Astrology by Y. K. Bansal.

15. Ayurnirnaya by Mukul Daivagya 'Parvatiya' .

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