2. Knowing the Heavens• Ancient naked-eye astronomy• Eighty-eight constellations• The sky’s ever-changing appearance• The celestial sphere• Celestial coordinates• Seasons: Earth’s axial tilt• Precession of Earth’s rotational axis• Position & time in astronomy• Observations & the modern calendar

Ancient Naked-Eye Astronomy• Cultural context

– Most people lived in rural areas near few people– Most people were too poor to afford fuel for light– Most people had lots of time to observe the sky

• People were extremely familiar with diurnal sky motion

• People were extremely familiar with lunar phases

• People were extremely familiar with planetary motion

– People used their imagination• Constellation arrangements & names• Astrology and its presumed impact on human affairs

• Scientific context– People devised accurate measurement equipment– People tried to predict future events

• Conjunctions of planets with each other & with stars• Eclipses of the Sun & Moon

Ancient Positional Astronomy• Definition

– Study of the location in the sky of celestial objects• Sky location is inextricably tied to observation time

• Examples– Moon’s position Monthly cycles– Sun’s position Annual cycles– Planets’ positions Synodic period cycles

• Instruments– Stonehenge England– Chichén Itzá Yucatan Peninsula– Casa Grande Arizona

Stonehenge: Wiltshire, England

http://www.seeyourinterest.com/2013/05/stonehenge-wiltshire-england/

Chichén Itzá, Yucatan, Mexico

http://www.journeymart.com/holidays-ideas/festivals/chichenitza-equinox-mexico.aspx

Casa Grande National Monument

http://www.theroamingboomers.com/wp-content/uploads/2010/07/Casa-Grande-Ruins-National-Monument.jpg

Eighty-Eight Constellations• Constellations

– Names given to irregular areas of the night sky• Based on recognized patterns• Similar to cloud patterns

– Constellation sizes vary tremendously• Ursa Major is a very large constellation• The Southern Cross is a very small constellation

– Stars in constellations are usually far apart• Analogous to aligned nearby trees & distant mountains

• Asterisms– Easily recognized parts of constellations

• Big Dipper• Pleiades• Orion• Trapezium

The Pleiades Asterism

http://en.es-static.us/upl/2009/07/Pleiades_1000.jpg

Modern Orion Representation

Ancient Orion Representation

Sky’s Ever-Changing Appearance• Diurnal motion The daily motion of the

stars– Caused by the Earth’s very regular axial rotation– Observational evidence

• The motion of the Sun across the sky every day• The motion of the stars across the sky every night

• Monthly– Moon One cycle per “moonth”

• Annual motion The yearly motion of the Sun– Caused by Earth’s slightly irregular orbital revolution– Observational evidence

• The annual cycle of changing Sun elevation at noon• The annual cycle of changing constellations at midnight

• Irregular motion– Planets One cycle persynodic year

Stars Through the Night

The night sky over Kitt Peak Observatory west of Tucson, Arizona

Circumpolar Stars Through a Night

The South celestial pole over Siding Spring Mountain, Australia

The Celestial Sphere• Unassisted human vision

– Earth appears to be at the center of a huge sphere• Diurnal motion requires at least one celestial sphere• Annual motion requires at least one additional sphere• Irregular motion requires at least two additional spheres

– Many celestial bodies are beyond closest sphere• These spheres must be made of transparent crystal

– No compelling evidence for any other model• Assisted human vision

– The Moon• Obvious mountains & craters

– The planets• Jupiter has four large moons• Saturn has rings• Venus has phases like the Moon

A Model of the Celestial Sphere

Celestial Coordinates• Foundations

– Two natural points: The celestial poles– One natural surface: The celestial equator

• Characteristics– Spherical coordinate system

• Coordinate lines always intersect at right angles– North-to-South direction Declination

• Units: Angle – 8°12’06”

• Positive: Point is north of the celestial equator

• Negative: Point is south of the celestial equator

– East-to-West direction Right ascension• Units: Time 5h 14m

32.2s

• Positive: Point is east of the vernal equinox• Negative: Point is west of the vernal equinox

Celestial Sphere Coordinates

Earth’s Axial Tilt Causes Seasons• Facts

– The Earth is a massive spinning top• The axis points in nearly the same direction in space• Precession seen as a very slow wobbling of Earth’s axis

• Cause– Earth’s rotational axis is tilted to its orbital plane

• ~ 23.5° Sun angle varies ~ 47° summer to winter

• Result: Sun intensity varies ~ 30% summer to winter

• Patterns– Opposite in northern & southern hemispheres– Repeated every year

• Summer Sun high at noon & days longest of the year

• Winter Sun low at noon & days shortest of the year

Changes in Sunlight Intensity

Earth’s Axial Tilt: Constant In Space

Hallmarks on the Celestial Sphere• The ecliptic One circle around the sky

– The apparent path of the Sun through the sky– The projection of the Earth’s orbit onto the sky

• The equinoxes Two points on the ecliptic– Derivation: Equal night & day hours– Intersection points of ecliptic & celestial equator

• Vernal equinox: First day of northern springMarch equinox

• Autumnal equinox: First day of southern springSeptember equinox

• The solstices Two points on the ecliptic– Derivation: North–south Sun motion ceases– Points halfway between the two equinoxes

• Summer solstice: First day of northern summer

• Winter solstice: First day of southern summer

A Model of Solstices & Equinoxes

The Tropics & Circles• The celestial tropics

– The farthest pole-ward the Sun is directly overhead• Tropic of Cancer ~ 23.5° North of the celestial

equator• Tropic of Capricorn ~ 23.5° South of the

celestial equator

• The celestial circles– The farthest equator-ward daylight lasts 24 hours

• Arctic circle ~ 23.5° South of North celestialpole

~ 66.5° North of celestial equator• Antarctic circle ~ 23.5° North of South celestial

pole

~ 66.5° South of celestial equator

Earth at Northern Winter Solstice

This is also known as the Southern Summer Solstice

Earth at Southern Winter Solstice

This is also known as the Northern Summer Solstice

Earth’s Rotational Axis Precession• All spinning tops

– Abundant angular momentum– Unbalanced forces cause rotation axis to

wobble• Directly proportional to angular momentum• Circular motion of the axis projected into space

• Earth as a spinning top– RPMs are low but mass is high– Sun & Moon cause rotation axis to

wobble• Circular motion of the axis projected into space

– ~ 26,000 years for one complete precessioncycle

• Changing orientation of the celestial equator– Precession of the equinoxes– ~ 26,000 years for one complete first-day-of-

season cycle

Precession: Earth A Spinning Top

Ever-Changing Celestial North Pole

Position & Time in Astronomy• Apparent solar time

– Time based on the Sun’s position in the sky• Earth’s orbital revolution varies due to its elliptical orbit

– Earth orbits the Sun slowest when distance is greatest– Earth orbits the Sun fastest when distance is least

• Earth’s axial rotation does not vary– Local solar noon occurs at Sun’s meridian transit

• The Sun is at its highest point in the sky• This is the basis for sundial time

• Mean solar time– Apparent solar time averaged over an entire year

• This does not vary• This is the basis for clock time

The Prime Meridian at Greenwich

Earth’s Variable Orbital Speed

Angelic Sundial: Chartres, France

Sidereal & Synodic Time• Definitions

– Sidereal time“siderus” = “star”• Time based on relationship to the stars

– Synodic time“synod” = “meeting”• Time based on relationship to the Sun

• Causes– Earth rotates one time relative to the stars

• 360° of rotation Sidereal day• Astronomers use sidereal time Telescope

time– Earth revolves one degree around the Sun

• ~ 361° of rotation Synodic day• Everyone else uses synodic time Clock time

Visualizing Sidereal Time

Observations & the Modern Calendar• Observations

– 1.0000 sidereal year = 365.2564 mean solar days– Julian calendar Leap years every four

years• Complicated because of precession of the equinoxes

– 1.0000 tropical year = 365.2422 mean solar days• Julian calendar in error by 11 min 14 sec per year

• The modern calendar– Gregorian calendar Pope Gregory XIII

intervenes• Concern about the progressive shift of the date of Easter• He arbitrarily dropped 10 days (October 5 to 14, 1582)• He modified the system of leap years

– Only century years divisible by 400 are leap years– The year 2000 was therefore a leap year– The year 2100 will not be a leap year

• Positional astronomy• Patterns in the sky

– Constellations– Asterisms

• Movements in the sky– Diurnal… Stars– Monthly… Moon– Annual… Sun– Irregular… Planets

• The celestial sphere– The celestial poles & equator– The celestial grid

• Right ascension [time]• Declination [angle]

– Earth’s axial tilt• The ecliptic• Vernal & autumnal equinoxes• Winter & summer solstices

• Tropics of Cancer & Capricorn• Arctic & Antarctic circles

• Precession of the equinoxes• Time in astronomy

– Apparent & mean solar time– Sidereal & synodic time

• The calendar and astronomy– Julian & Gregorian calendars

Important Concepts