p45_037 - v 2 /r , where v is the speed of Earth, GMm/r 2 =...

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37. (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 = ³ r R ´ 3 M S = µ 1 . 50 × 10 11 m 5 . 90 × 10 12 m 3 (1 . 99 × 10 30 kg) = 3 . 27 × 10 25 kg . 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 2 = mv 2 /r and v = r GM r = s (6 . 67 10 11 m 3 / s 2 kg)(3 . 27 10 25 kg) 1 . 50 10 11 m = 1 . 21 10 2 m / s . (b) The period of revolution is T = 2 r v = 2 (1 . 50 10 11 m) 1 . 21 10 2 m / s = 7 . 82 10 9 s = 248 y ....
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