astronomical definitions and calculations

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ASTRONOMICAL DEFINITIONS OF GRAHAS AND THE ZODIAC

1.1. The Earths Equator (Vishvarekha)

This is an imaginary line running around the earth in the exact middle between the southand north poles. This divides the Earth into a northern and southern hemisphere. Thedifference between the two is especially visible in the changes of the seasons (determined

by the yearly motion of the Sun). In June for example we have summer in the northernhemisphere but simultaneously winter in the southern hemisphere. Therefore the locationof the nativity (place of birth) will be a determinant factor in the astronomical calculationsthat we carry out. Therefore it is necessary to be able to determine the location by certainmeasurements. To ascertain a point on the earth globe, we will need two coordinates: thelatitude and the longitude of the place.

1.2. The Latitude (Akshamsa)

This is the angular distance of the place from the Equator towards the North or South. It is

measured in degrees, minutes and seconds of arc. The equator is the 0point, and thepoles are at 90 to the south and the north. The southern or northern latitude of thenativity will determine the time of sunrise and sunset and the duration of the day andnight, which have an important role in a number of calculations in Jyotish.

1.3. The Longitude (Rekhamsa)

The longitude is the vertical measurement of degrees. The earth can be divided into 360

longitudinal meridians, each of the extent of 1. Now the choice of the beginning point, or

0 is not determined astronomically. In the ancient India the 0meridian was the oneintersecting the ancient town of Ujjain, where one of the Jyotirlingas (Lord Shivasmanifestation in a glowing stone) is situated. This Jyotirlinga is called Mahakaleshvara, andas astrology is the science of the measurement of the quantity and quality of time (Kala),

this was naturally taken as 0. In modern times the latitude is better known as the angular

distance from Greenwich, where the officially accepted 0meridian runs. Thus a place mayhave either eastern or western longitude from Greenwich and either southern or northern

latitude from the Equator. For example New York lies at 74West of Greenwich and at 4043 north of the equator. This is usually indicated thus: 74W00, 40N43. Paris is located at2E20 and 48N52. The longitude will influence which planets will be above the horizon, andwhich ones will be under the horizon. For example while theres noon in New York, therewill be night in Delhi. So in one chart the Sun is above the horizon, while in another its

under it, although the natives were born at the same time cosmically. So the latitudedetermines, where the Lagna (ascendant) will be, i.e. which sign or nakshatra will be risingon the eastern horizon at the time of birth.

2. THE DIVISION OF THE SKY GLOBE

We can look at the sky above us as a globe around the Earth. Thus for determiningpositions in the sky we will again need two coordinates.

2.1. The Celestial Equator (Nadivritta)

The celestial equator is the extension of the Earths equator in the skies, and it divides thesky globe into two halves.

2.2. The Declination (Kranti)

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This will be the angular distance of a heavenly body from the celestial equator. It will beeither negative if the planet is above the northern hemisphere, or positive, in case theplanet is above the southern hemisphere. The declination is also called Ayana. Thus theSuns yearly movement is divided into two parts, called Uttarayana and Dakshinayana. TheSun reaches the southest point of its trajectory at the time of the winter solstice (Dec. 23)and from there it begins travelling north, thus its declination gradually decreases. Itcrosses the equator at the time of the vernal equinox (March 21) when on the whole Earth

the duration of day and night is equal. Then it proceeds towards the northern hemisphereup until the point of summer solstice when the Sun is above the northest point of the Earthand we have the longest day in the northern hemisphere and the shortest night. After thatthe declination begins increasing from the lowest negative degree, and coming to the pointof autumn equinox. At this time the declination of the Sun equals 0 again, and it keepsincreasing positively till the point of winter solstice again.

2.3. The Ecliptic (Ravimarga)

The ecliptic is the Suns above described path, which forms a curved line, which once ayear touches the Tropic of Cancer (during summer solstice) and also once the Tropic of

Capricorn (during winter solstice), and crosses the equator twice a year at the time of theequinoxes.

2.4. The Celestial Latitude (Kshepa)

This is the angular distance of a planet from the ecliptic (the Suns path). It is negative ifthe planet is to the north from the ecliptic and is positive if it is to the south from it.

3. THE CIRCLE OF THE ZODIAC

3.1. The Zodiac (Bhacakra)

This is a broad band in the sky extending 9 degrees on either side of the ecliptic andcomprised of different constellations (nakshatras). The planets never get very far awayfrom the ecliptic, therefore they are always within this belt. As the circle has no beginning,again, as in the case of the terrestrial longitudes, we should select an arbitrary point in theskies as the beginning of the zodiac, which will be determined by the placement of certainstars (nakshatras), since Parashara gave the definition that only the grahas move, and therest of the bodies is fixed. The zodiac consists of 360 degrees of arc (rekhas). Each degreehas 60 minutes (kala) and each minute has 60 seconds (vikala). Thus the full extent of thezodiac may also be expressed as 21 600 minutes or 129 600 seconds of arc. There are

further submeasurements like para, paratpara and tatpara.

3.2. The 0 of the Zodiac

This point is determined on the basis of the placement of the star which is known as Zeta

Piscium in the west. This is taken as the 0of Aries, and the beginning of AshwiniNakshatra also. However, this star is no longer visible as much, as it was in Parasharas

times, therefore we can determine the exact middle of the zodiac (180 ) by the position of

the star Spica. This will also indicate the 0of Libra, and the exact middle of ChitraNakshatra.

3.3. The Tropical ( Sayana) and Sidereal ( Nirayana) Zodiac

The above statements reveal that the zodiac used in Vedic astrology is linked with thestars, and is immovable in comparison to them. On the other hand, observation confirmsthat the Suns yearly cycle on the Ecliptic does not fully coincide with its making a

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complete circle relative to the stars, but the former is a bit shorter. This in other wordsmeans that the Sun at the time of the vernal equinox will not come back to the same pointof the sidereal zodiac, but a little less than that. This is called precession. The tropicalzodiac is fixed to the Suns movement through the ecliptic, and thus its called themovable (sayana) zodiac.

3.4. The Precession (Ayanamsha)

As the two zodiacs are rotating compared to each other, theres a certain cycle to it, whichis 25 870 solar years long. Then there is a certain date of coincidence, when the 0 degreesof both zodiacs exactly coincide. Although authorities differ on this, the most widelyaccepted opinion is that the last coincidence was at the vernal equinoxe in 285 AD. Thereare also different opinions regarding the yearly value of precession. Varaha Mihira statesthat its approximately 50 1/3 vikalas or seconds of arc. Of course the precession has anegative value, so the vernal equinox is pushed back to Pisces, then Aquarius etc. over theyears. Also the value of the ayanamsha is not linear but cyclical, as it describes the changeof the position of the ecliptic towards the celestial equator.

3.5. The Ayanamsha Value

Out of the number of suggested precessional values, the Lahiri or Chitra PakshaAyanamsha stands out as the most accurate, although testing with divisional chartsindicates that even this may be inaccurate for a couple of seconds of arc. But until a moreexact Ayanamsha value is suggested, this is recommended for calculations. LahiriAyanamsha is verified on the basis of the placement of the above mentioned star Spica,which forms the exact middle of the Chitra Nakshatra. According to this system, the

Ayanamsha value at the present time is 235240". This means that the Sun will this much

fall behind the 0of Aries of the sidereal zodiac at the time of the vernal equinox. So it will

be somewhere around 6 degrees of Pisces.

4. THE DIVISIONS OF THE ZODIAC

4.1. The Nakshatra Chakra

As we have mentioned earlier, the basis of the division of the zodiac is the placement ofdifferent constellations in it. The constellations are divided into areas in the sky, each of

which covers 1320 of the whole zodiac. Thus there are 27 nakshatras beginning fromAshwini and ending with Revati. There is also a 28th nakshatra called Abhijit. This is anintercalary Nakshatra, i.e. it does not have any own extension, rather it occupies the last

quarter of the Uttarashadha Nakshatra and the first 1/15th part of the Shravana Nakshatra,i.e. it extends from 27640 to 28053 1/3 of the zodiac. The division ofNakshatras isbased on the Moon, which makes a complete cycle in the zodiac within one month. TheMoon spends approximately one day in each Nakshatra. Every Nakshatra may be further

divided into four quarters (Padas) 320 each. Thus the zodiac will have 108 NakshatraPadas, which are also called Navamshas (1/9th of a sign).

4.2. The Rasi Chakra

There other main method for the division of the zodiac is based on the Sun. The Sun

travels through the zodiac within one year, and during this he meets the Moon 12 times.Thus there will be 12 months within one year. Therefore we could divide the zodiac into 12Rasis or signs, in which the Sun will spend one month each. These signs will have an

extent of 30 .

4.3. The Divisional charts (Amsas or Vargas)

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The signs of the zodiac may be further divided into subparts. Maharishi Parashara andother Jyotish authors have specifically mentioned the following subdivisions of the signs:Hora (D-2), Drekkana (D-3), Caturthamsa (D-4), Panchamsa (D-5), Sashthamsa (D-6),Saptamsa (D-7), Ashtamsa (D-8), Navamsa (D-9), Dasamsa (D-10), Rudramsa (D-11),Dwadasamsa (D-12), Shodasamsa (D-16) Vimsamsa (D-20), Siddhamsa (D-24),Nakshatramsa (D-27), Trimsamsa (D-30), Khavedamsa (D-40), Akshavedamsa (D-45),Shashtyamsa (D-60), Ashtottaramsa (D-108), Dwadasamsa-Dwadasamsa (D-144) and

Nadiamsa (D-150). The most important divisional chart is however the Navamsha, as it isbased both on the division of the Sun and the Moon.

4.4. The Celestial Longitude (Sphuta)

The position of the planets in the zodiac is expressed through the celestial longitude, whichis counted from the beginning of Aries. Sometimes the degree of the planet within a sign isindicated, or also its position in the Nakshatra Padas and the divisional charts.

ASTRONOMICAL CALCULATIONS IN JYOTISH

4.1. The Time of Birth

Astrology is the science that examines the quality of time, while astrology is the sciencethat calculates the quantity of passing time. For purposes of an astrological reading weutilize certain tools of astronomy, with the help of which we are able to calculate theposition of planets and other significant points of the chart at the time of birth, etc.

After all, in Jyotish we are always interested in the position of the planetst at the time of acertain event. This is true for all branches of Jyotish. In natal astrology (Jataka) we areinterested where the planets were transiting at the time of the natives birth, as this is themost determinant time point in his life. In horary astrology (Prashna) we are interested inthe transit of the planets at the time of the natives putting his question to the astrologer.In Dasa analysis we are interested in the transit of planets at the time of dasa-pravesa(setting in of a period). In Tajaka astrology we are interested in the transit fo the planets atthe time of the natives birth day. In Gochara (transit analysis) we are interested in thetransit of the planets at the time of a certain event. This is also the point of interest inelectional astrology (Muhurtha).

Therefore the astrologer should be able to ascertain the position of the planets within thezodiac at a certain given point in time. Lets take as an example the time of birth forRabindranath Tagore (May 7, 1861, 4.02 am LMT, Kolkata). The exact time of birth isusually taken as the time when the umbilical chord is cut, although there are some otheropinions as well, but at this time the body of the child is completely separated from thebody of the mother.

4.2. Local and Zonal Time

Time is a phenomenon which is inseparable from space. Therefore besides ascertaining thetime of birth, we also need to know its location, because at the same point in time (if it isindependent of location, it is called Universal Time) the planets and the ascendant are

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situated differently above different parts of the globe, although their mutual disposition isthe same.

Local time is calculated according to the movements of the Sun. The Sun needs exactlyone day to make a circle around the globe of the earth (at least apparently, if we look at itfrom the point of view of the earth), and this means that there will be a certain point intime every day when the Sun will exactly cross the longitudinal meridian of a certain

nativity. This time is called local noon. The time interval between two points of local noonis exactly one day, which is divided into 60 ghatikas in Jyotish. One ghatika thus equals 24minutes of the western calendar. So astronomically tha time of an event may be identifiedby saying how much time have passed since local noon at that meridian. Since the Earth isdivided into 360 longitudinal meridians, the Sun traverses over one degree within 1/6th of aghatika, which is four minutes. Therefore local times at different longitudes are different byfour minutes each.

Tagore was born in Kolkata, which is at 88 degrees 22 minutes of arc to the east ofGreenwich. Lets say if we take a city which lies at 80 degrees 22 min east, local noon willoccur 8*4=32 minutes later than in Kolkata, because the Sun travels from east to west.

This measurement of time, although very exact astronomically, may create problems whenmore distant places develop communication with each other. Thus with the setting in ofthe telecommunication era, in the beginning of the XX. cetury it was decided that thecountries of the world would be divided into time zones, within which the time would beidentical. This means that most of the smaller countries are situated within one time zone,and therefore the zonal time is identical in the whole country.

The zonal time is actually the local time of a certain meridian within the zone, which isextended to the whole of it. For example in the whole of England, and part of WesternEurope the zonal time is identical with the local time in Greenwich, which is assigned to be

at the zero degree longitudinal meridian. The local time at 15

east from Greenwich is 1 hrsmore than there, because the Sun crosses that place earlier. So in modern times thewatches usually go by the zonal time, and therefore we also need to know the time zone ofthe nativity, plus in some countries one or two hours are added as summer time. Afterascertaining which point in local time (or universal time) corresponds to the reported birthtime, we may proceed to the calculation of the position of the planets. Local time isusually indicated as LMT (Local Mean Time). Other time zones also have theirabbreviations, like GMT (Greenwich Mean Time), CET (Central European Time), IST (IndianStandard Time) etc.

4.3. Divisions of Time

An interesting question is how did the ancients measure the passing of time? As we havestated, the relationship between time and space is inseparable, therefore they havemeasured it with the help of the motion of the planets, especially the Sun. There are stillseveral Sun-dials existing in different parts of India, exact up to the second. This methodhowever is limited to the time when the Sun is up and visible in the skies. Undoubtedly,many people are born during the night, so we also need to have a way to measure timewhen the Sun is not visible. This is where the word "ghati" comes from. It means anearthen pot of a certain size with a spout of a certain diameter. When the pot was filledwith water, it took exactly 24 minutes for the water to flow out of it. One ghati is alsodivided into 60 vighatis, and one vighati into 60 palas.

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4.4. Determining Planetary Positions

After finding out the time and place, the next task is to detemine the position of theplanets. Ths can be done in several ways:

By applying certain astronomical equations.

By making astronomical observations.

By using an ephemeris (Panchanga) with precalculated planetary positions.

It is said that in the Rig Veda one can find certain mantras, which translate intoastronomical equations, with the help of which, the planetary positions for any moment intime may be calculated. However these rules are quite obscure nowadays.

Astronomical observations are made regularly in different parts of the globe, and thoseinformations serve as a basis for calculating the ephemeris positions for the planets. Thesetables of ephemeris are available both in India and the West. If it is a western astrology

ephemeris, you need to know the exact ayanamsha value, with which the tropical zodiac isshifted from the sidereal one.

The ephemeris usually gives the exact positions of the planets for certain points of time(daily, weekly, monthly etc.) which means that in the majority of the cases we need toknow how far is the point of birth from the closest time indicated in the ephemeris, andafter calculating the difference, we should also calculate how much do the different planetsmove within this time.

All of the above methods are combined in the different Jyotish software available, whichusually give exact planetary position for any specified time. Therefore nowadays this is themost popular tool used for astronomical calculations.

4.5. Movements of the planets

Vedic astrology deals with seven grahas, i.e. Sun, Moon, Mars, Mercury, Jupiter, Venus,Saturn. Besides that the lunar nodes, i.e. Rahu and Ketu also ocuppy an important role.They are called shadowy planets, or chaya-grahas. The trans-Saturnian planets are nottaken into consideration when erecting a Vedic chart. This is not because the ancients

were unfamiliar with the rest of the planets, but rather because these seven visible planetsand the lunar nodes represent the whole spectrum of energies, similarly to the sevencolors of the rainbow, plus ultraviolet and infrared, which would represent all the colors ofthe spectrum. Therefore adding new heavenly bodies will not enhance the system ofpredictions extrapolated by the ancient Maharishis. However in Jyotish another set ofplanets appears, which is called upagrahas. These secondary planets will be explained in alater issue.

The planets move within the belt of the zodiac with a different average of speed. The twoluminaries, i.e. the Sun and the Moon have steady and direct motion, which means fromAries to Taurus to Gemini, etc. Therefore when any planets move in the opposite direction

to the luminaries, that motion is called vakra, or retrograde. The luminaries move with thesame angular speed at all times. For the Sun it takes one year to complete a circle, whilefor the Moon its one month. As the Lagna (ascendant, which actually signifies the Earth)completes one circle of the zodiac within one day, these three will from the tripod of life

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(Lagna-body; Moon-mind; Sun-soul) and determine by their movements the three basicunits of time (a day, a month and a year)

On the other hand, the lunar nodes, Rahu and Ketu always move in retrograde direction, also with aregular angular speed. The nodes need 18 2/3 years to complete one circle of the zodiac and theystay one and a half year in every sign. The luminaries are said to be the two eyes of Lord Vishnu withwhich He maintains and oversees His creation, always upholding dharma and leading people on the

path of righteousness. The nodes, however are the separated body and head of a demon called Rahu,who rebelled against dharma. Thus the nodes will represent karmic reactions which are the result ofnot following dharma and performing sinful activities. Therefore they are always against progress,although Ketu may be considered a benefic towards dharma, because after all the role of karma isalso to teach us where we went wrong, thus encouraging detachment from sinful life.

The rest of the planets, i.e. Mars, Mercury, Jupiter, Venus and Saturn most of the time move in thedirect way, but at times they fall into a retrograde cycle. Their movement is not regular, whichmeans that at different angular distances from the Moon they move at a different speed. Thisresembles human beings, who most of the time try to follow dharma, although their endeavour is notsteady, but at times they fall under the influence of adharma, and thus they perform sinful activities

and block their own advancements. Thus while the luminaries represent deva-gana or godly beings,Rahu and Ketu represent rakshasa-gana or demons, the rest of the planets will represent manushya-gana or human beings.

Mercury and Venus are inner planets, i.e. they revolve around the Sun and pass between the Sun andEarth. Thus they revolve around the zodiac in the company of the Sun, and therefore the greatest

angular distance of Mercury from the Sun is 27, while for Venus the same is 47 .

The following table represents the average daily angular motion of the planets, theapproximate time they spend in one sign and the approximate time they need to completea full circle in the zodiac. The symbols in the brackets indicate the direction of theirmovement.

Planet Av. DailyMotion

Time spent in asign

Duration of a cycle

Sun (D) 059 1 month 1 year

Moon (D) 1310 2 1/4 days 1 month

Mars ( ) 031 1 1/2 months 18 months

Mercury ( ) 45 27 days 1 year

Jupiter ( ) 05 1 year 12 years

Venus ( ) 136 28 days 1 year

Saturn ( ) 02 2 1/2 years 29 years

Rahu (R) 03 1 1/2 years 18 2/3 years

Ketu (R) 03 1 1/2 years 18 2/3 years

4.6. Retrograde planets

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As we have said, retrograde motion indicates the destructive and obstructive forces ofkarma. Therefore, if any planets are retrograde in the chart, we may expect that a strongdesire is connected to that planet. The planets power increases when it is retrograde orstationary (state of planet just before and after retrogression), but the results get delayed,become disturbed. After ascertaining what role does the given planet play in the chart, wemay understand that the native has some unresolved problems or unfulfilled duties in thatarea, coming from previous life. Every planet gets retrograde when it is at a certain degree

from the Sun. Before retrogression occurs, the planet gets stationary for a certain period oftime. At this time the planet gives a very strong and steady effect. The same thing occurswhen the planet ends its retrograde cycle. The following table shows the degrees anddurations of retrograde and stationary motions:

Angular Distance from Sun

Mars 228 132 3 80

Mercury 14-20 17-20 1 24

Jupiter 245 115 5 120

Venus 29 26 2 42

Saturn 251 109 5 140

4.7. Combustion

Combustion occurs when the planets get too close to the Sun. The Sun is the strongestplanet and its rays burn up the rays of the other planets. However the lunar nodes do not

get combust, but rather they will eclipse the Sun and the Moon if they get closer than 5 tothe luminaries. If at the same time the Sun and the Moon are conjunct or in opposition (i.e.at the time of new Moon or full Moon), then the nodes eclipse both the luminaries. At thetime of new moon even a visible solar eclipse could occur, as well as at the time of fullmoon a visible lunar eclipse. Birth during eclipses is considered to be inauspicious, andproper remedial measures should be undertaken. At the same time, when the Moon gets

closer than 12 to the Sun, especially on the last day of decreasing Moon, krishna-

caturdasi, it also becomes very inauspicious, and remedial measures should be performed.

The rest of the planets become combust when they get closer to the Sun than a certainorb. When they are exactly conjunct with the Sun, then the Sun completely burns up theirrays, and thus they are unable to function. In this case the areas lorded and influenced bythe combust planet become inactive. Thye will bear very meager results, and the nativewill experience strong oppression from some superior force in certain areas of his life. Thedegree of combustion depends on the proximity of the combust planet. However we shouldnote that the planets will get combust only when they approach the Sun during directmotion, because in this case they pass behind the Sun, while during retrograde motionthey pass in front of the Sun. Thus the phenomenon of combustion does not occur, rather

the planet gains more strength from the Sun. The only exception is Venus, which revolvesin the opposite direction, thus it will get combust while retrograde, and will not get so whiledirect.

The degrees of combustion for the different planets are the following:

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Planet Degree of combustion

Mars 17

Mercury 13

Jupiter 11

Retr. Venus 8

Saturn 15

4.8. Planetary war

Planetary war (graha yuddha) occurs when two planets come closer than one degree toeach other in longitude. We should note that only the five above mentioned planets may

get into a graha yuddha. The Sun will burn off any planets getting close to him. The Moonis very friendly, so she will avoid fight. The nodes are so subtle that they cannot be caught.However, they tend to eclipse and thus negatively influence any planet with which theyget into close conjunction.

Of the two planets, the following will win the war:

One which passes to the north of the other (which has higher latitude),

One which has a more favourable appearance, brightness and steadiness,

One which has bigger size,

One which is direct and more distant from the Sun,

One which has more strength from other sources.

The effect of planetary war is significantly different from that of combustion. Whileduring combustion the Sun suppresses the influence of the combust planet, at thetime of planetary war, the winning planet takes over the influences of the loser. Thisis like in a war the winner takes over the land, people, treasures, animals etc. of the

loser and exercises control over them. So the winner will act as the lord of thehouses lorded by the loser, and occupy its natural karakat was also.

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