lec07 - Lecture 7 Planetary Motion Lecture 7 Purdue...

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Unformatted text preview: Lecture 7 Planetary Motion Lecture 7 Purdue University, Astronomy 364 1 General Solutions Lecture 7 Purdue University, Astronomy 364 2 F = − G Mm r 2 ˆ r = m d v dt r = L GMm 2 (1 + e cos θ ) < e < 1 e > 1 e = 1 e = conic section Kepler’s 1 st Law Lecture 7 Purdue University, Astronomy 364 3 Close orbits: ellipses or circles a 2 = b 2 + c 2 = b 2 + ( ae ) 2 ⇒ e = 1 − b 2 / a 2 ( ) 1/2 r = a (1 − e 2 ) 1 + e cos θ L 2 m 2 = GMa (1 − e 2 ) ⇒ r 2 v t 2 = GMa (1 − e 2 ) Velocities Lecture 7 Purdue University, Astronomy 364 4 At perihelion and aphelion, the velocity of a planet is entirely tangential. At perihelion, r = a-c = a (1-e) a 2 (1 − e ) 2 v pe 2 = GMa (1 − e 2 ) ⇒ v pe = GM a 1 + e 1 − e ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1/2 At aphelion, r = a+c = a (1+e) a 2 (1 + e ) 2 v ap 2 = GMa (1 − e 2 ) ⇒ v ap = GM a 1 − e 1 + e ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1/2 Kepler’s 3 rd Law Lecture 7 Purdue University, Astronomy 364 5 The rate at which the area swept out by the planet-Sun line is...
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This note was uploaded on 04/23/2011 for the course ASTR 364 taught by Professor Cui,weik. during the Spring '11 term at Purdue.

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lec07 - Lecture 7 Planetary Motion Lecture 7 Purdue...

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