Sept. 27, 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

Sept. 27, 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

Sept. 27, 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)?

Sept. 27, 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…)

Sept. 27, 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

Sept. 27, 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

Sept. 27, 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