1. Sept. 27, 2007 1 Apparent motions: Planets, Kepler’s Laws & Orbits Review celestial coordinate system: RA, DEC RA,DEC of Sun, Moon, and … planets? The great observer, Tycho, and analyst, Kepler Sidereal vs. synodic periods of planets: Kepler’s 3 rd Law Ellipses and Kepler’s 1 st and 2 nd Laws Grand overview: orbits

2. Sept. 27, 2007 2 Celestial coordinate system: RA, DEC Stars (and galaxies) “fixed” on celestial sphere, so give them a longitude (RA) and latitude (DEC) coord. We need to locate Sun, Moon, stars, galaxies on maps of the sky (“finding charts” as in EL1…) RA = longitude coord., units of time (or degrees) with 0 in constellation Aries DEC= latitude coord., with zero on Earth’s equator

3. Sept. 27, 2007 3 How about RA,DEC for Sun and Moon? Both are changing (continuously) since we view them from a rotating, orbiting Earth and Moon is itself orbiting Earth. RA,DEC are geocentric coords. Stars have fixed RA,DEC (ignoring precession…) since Earth’s spin axis fixed in 3D space (gyroscope) DL1 sundial observation: changing DEC of Sun; DL3 will also show changes in RA of Sun What about the planets – e.g. Uranus (EL1)?

4. Sept. 27, 2007 4 March of the Planets… Have you seen (last night) Uranus vs. the stars? It’s moving… Which way? Retro, moving W vs. the stars... You will (final week of EL1) “fast-forward” Uranus on computer and see it reverse: go East vs. stars. Why? Earth is overtaking Uranus (or Mars; or outer planets) ea. year Mars doing its Retro loop (Uranus does similarly…)

5. Sept. 27, 2007 5 How often does this happen? Approximately each Earth year, but not exactly… rather, with synodic period, S. Consider Jupiter: For Jupiter, Tycho observed S = 1.09y Kepler postulated this is explained by Jupiter orbiting Sun (like Earth; Copernican model) with period P (relative to fixed stars) vs. Earth orbiting with period E Then Earth vs. Jupiter line up (conjunction) with frequency, F (no. of conjunctions per Earth year) of Fs = Fe – Fp, where Fs = synodic, or conjunction, freq. and Fe and Fp are the true (vs. fixed stars) orbital freq. (=orbits/yr). And since Period = 1/Frequency, we have 1/S = 1/E – 1/P, as in your textbook

6. Sept. 27, 2007 6 So what does this mean? Tycho used parallax to deduce approx. distances for say Mars vs. Jupiter: Jupiter is more than twice distant The synodic period of superior conjunctions of Jupiter is shorter (399d) than for Mars (780d), so the sidereal period of Jupiter is longer since 1/P = 1/E – 1/S So more distant planets have longer periods: Kepler deduced his Third Law: P 2 = a 3, where a=distance from Sun in AU and P = sidereal period in years

7. Sept. 27, 2007 7 To complete his 1 st and 2 nd Laws Kepler’s First Law: Planets move on ellipses, not perfect circles (which are ellipses with e=0). How did Kepler deduce this? By requiring a good fit to the extensive data accumulated by Tycho: circles did not fit! (particularly for Mercury…) And how did planets have to move on ellipses to match the positions vs. time data of Tycho? In accordance with Kepler’s 2 nd Law: Fastest when closest to Sun, and sweeping out =area in =time