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PHY134Introductory Astronomy

The Celestial Sphere

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The Celestial Sphere• Pattern of stars unchanging: can imagine them fixed on a

sphere surrounding Earth• Celestial Sphere is large and rigid• Celestial Sphere rotates daily about axis through poles from

East to West• Equivalently, Earth rotates from West to East inside stationary

Celestial Sphere• Stars occupy fixed positions on Celestial Sphere: use Celestial

coordinates to specify this with mathematical precision

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Coordinates on Earth• Locations on Earth usefully labeled by– Latitude: angular distance from equator - natural– Longitude: angular distance from prime meridian

• Location determines half of sky visible– Latitude: permanently– Longitude: instantaneously

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Celestial Coordinates• Use same coordinate

system on Celestial Sphere– Celestial Poles are directly

above terrestrial poles– Celestial Equator is directly

above terrestrial equator– Celestial Latitude is called

Declination

• As on Earth, choice of prime meridian is random.– Celestial Longitude

measured East is called Right Ascension

– Measured in hours according to rotation

360° = 24h or 15° = 1h

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Angles and Distances• How large is Celestial Sphere?• Every point on Earth can be taken

to be in center to within accuracy of measurement

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Numbers and Units

• You may see the formula AB = ( /a 206265”) RI had AB = (α/57.3°) RWho’s wrong?

• Neither. For convenience, small angles are often measured in units other than degrees. In particular, we use arcminutes and arcseconds

1o = 60’ = 3600” 57.3° = 206265”• In Physics numbers are ratios and must remember units! For

example, in above can use any units for AB and R so long as we use the same units for both

Local Coordinates• To find a star, need to

know what direction to look. Use– Altitude: angle above

horizon– Zenith Angle: angle from

Zenith 90°-Altitude– Azimuth: angle from

North (clockwise)

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• To an observer on Earth sky appears to rotate about celestial pole

• Pole appears North (South) at an altitude equal to Latitude

Azimuth = 0° (180°)Altitude = Latitude

• Can use stars to navigate!

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What We Can See• As sky rotates about celestial pole stars near

North (South) pole never set (circumpolar)• Stars near South (North) celestial pole never

visible• Stars near celestial equator rise, move West

across sky, and set

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Sidereal Time• Zenith at Decl = Latitude

RA = Sidereal Time• Sidereal Time is celestial meridian coinciding with local

meridian• Changes with time: 24 sidereal hours = One full rotation of

Earth• Can use stars to measure time! In one (sidereal) hour

Celestial sphere shifts by one hour of RA• Changes with longitude at 1h/15°

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Summary: Finding A Star• Star is highest at meridian crossing when sidereal time is its

RA• At this time Zenith angle is |Decl-Latitude|• Altitude is 90° - Zenith angle• Azimuth is 0° if Decl > Latitude

180° if Decl < Latitude• To find star earlier/later, rotate East/West by 15°/h• Need to know how to tell sidereal time

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The Sun Also Rises (and Sets)…• The Sun, like anything off Earth, is somewhere on

Celestial Sphere• When sidereal time near RA of Sun it is daytime• Stars near Sun not visible• Where is the Sun?• How is sidereal time (ST) related to local time (LT)?

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…But Slower• As it spins once a day, Earth also orbits Sun once a year in the

same sense• Seen from Earth, Sun orbits once a year, so not fixed on Celestial

Sphere• Sun moves along Celestial sphere from West to East (increasing

RA) completing full revolution in a year• Visible (night) part of sky changes over the year• This means Sun moves across sky from East to West slightly

slower than stars – one less revolution per year

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Clocks• This means time from noon to noon is a bit (1/365

of a day or about 4min) longer than time it takes Earth to turn 360°

• A (mean) solar day is longer than a sidereal day• Our clocks (LT) keep solar time so run slower than

sidereal clock (ST)24 sidereal hours = 23h 56m 4s

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Finding Sidereal Time• By convention ST ≅ LT on September 21• D days later (earlier)

ST ≅ LT +/- D×4m• This is approximate. In any event ignores time

zones and Daylight Savings Time• On December/March/June 21

ST ≅ LT + 6/12/18 h