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Unformatted text preview: 1 Lecture 22 • Kepler’s three laws • Application: Detection of exoplanets 2 Johannes Kepler used observations made by Tycho Brahe to “discover” three laws of planetary motion. http://en.wikipedia.org/wiki/Johannes_Kepler 3 Kepler’s 1 st Law: The orbits of the planets are ellipses with the Sun at one focus. F F d’ d a Semimajor axis b Semiminor axis a d d 2 = ′ + 1 2 2 2 2 = + b y a x 4 The Sun is at one focus of the ellipse. There is nothing at the other focus. The eccentricity of an ellipse is axis major of length foci e between th distance = e Note: A circle has an eccentricity of zero. 5 Kepler’s 2 nd Law: A line that connects the planet to the Sun sweeps out equal areas in equal times. t 2 t 1 d θ rd θ r r m L m mr r dt dA dt dt d r rrd dA 2 2 2 1 2 1 2 1 2 2 2 = = = = = ϖ ϖ θ θ 6 dA/dt is the areal velocity . Is this constant? r F F r τ ˆ 2 r GmM = × = Since gravity is a central force, the torque is always zero....
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This note was uploaded on 07/04/2011 for the course PHYS 121 taught by Professor Staff during the Spring '11 term at ASU.
 Spring '11
 Staff
 Orbits

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