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PHY134 Introductory Astronomy

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

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PHY134 Introductory Astronomy

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  1. PHY134Introductory 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

  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

  4. Celestial Coordinates • Use same coordinate system onCelestial Sphere • Celestial Polesare directly above terrestrial poles • Celestial Equatoris directly above terrestrial equator • Celestial Latitudeis 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

  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 usearcminutesand 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 thesame units for both

  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!

  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

  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 longitudeat 1h/15°

  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 is0° 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 RAof Sun it is daytime • Starsnear 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

  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/June21 ST ≅ LT + 6/12/18h

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