PHY134 Introductory Astronomy The Celestial Sphere

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

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

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

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.

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” 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 Athens – with coordinates. Time moving

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

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

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

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

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)?

…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

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

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