problem12_74

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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12.74: Using conservation of energy, or , 2 1 2 1 p M S 2 p M a M S 2 a M r m GM v m r m GM v m - = - s. m 10 650 . 2 1 1 2 4 p a S 2 a p × = - - = r r GM v v The subscripts a and p denote aphelion and perihelion. To use conservation of angular momentum, note that at the extremes of distance (periheleion and aphelion), Mars’ velocity vector must be perpendicular to its radius
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Unformatted text preview: vector, and so the magnitude of the angular momentum is mrv L = . Since L is constant, the product rv must be a constant, and so s, m 10 650 . 2 m) 10 067 . 2 ( m) 10 492 . 2 ( s) m 10 198 . 2 ( 4 11 11 4 p a a p × = × × × = = r r v v a confirmation of Kepler’s Laws....
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