1. PHY134 Introductory Astronomy
The Celestial Sphere

2. 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
Lat/Long Demo

3. 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
Celestial Sphere coords demo

4. 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

5. Angles and Distances How large is Celestial Sphere?
Every point on Earth can be taken to be in center to within accuracy of measurement
AB arc is red
AB is green
In our e.g. AB can be two points on Earth, O a star. Lines should be parallel, a~0.

6. Numbers and Units You may see the formula AB = (a/206265”) R
I had AB = (α/57.3°) R
Who’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” ° = ”
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
Athens – with coordinates. Time moving

7. 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)
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!
Alt/Az Demonstrator

8. 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
Rotating Sky Demonstrator

9. 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°
Athens, looking South, both coordinates.
Find Alpheratz, watch it move an hour at a time

10. 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

11. 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)?

12. …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
Sidereal and Solar Time Demonstrator

13. 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

14. 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