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# ch44_p33 - v 2 r where v is the speed of Earth GMm r mv r 2...

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33. (a) The mass M within Earth’s orbit is used to calculate the gravitational force on Earth. If r is the radius of the orbit, R is the radius of the new Sun, and M S is the mass of the Sun, then M r R M s = F H G I K J = × × F H G I K J × = × 3 11 12 3 30 25 150 10 590 10 199 10 327 10 . . . . . m m kg kg c h The gravitational force on Earth is given by GMm r 2 , where m is the mass of Earth and G is the universal gravitational constant. Since the centripetal acceleration is given by
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Unformatted text preview: v 2 / r , where v is the speed of Earth, GMm r mv r 2 2 = and v GM r = = × ⋅ × × = × − 6 67 10 327 10 150 10 121 10 11 2 25 11 2 . . . . . m s kg kg m m s 3 c hc h (b) The ratio is 2 4 1.21 10 m s 0.00406. 2.98 10 m s × = × (c) The period of revolution is T r v = = × × = × = 2 2 150 10 121 10 7 82 10 248 11 2 9 π π . . . . m m s s y c h...
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