394_Physics ProblemsTechnical Physics

394_Physics ProblemsTechnical Physics - 396 P13.41...

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396 Universal Gravitation P13.41 The rocket is in a potential well at Ganymede’s surface with energy U Gm m r m Um 1 12 11 2 23 6 1 6 2 667 10 1495 10 264 10 378 10 =− ×⋅ × × × .. . . Nm kg kg m ms 2 2 22 ej The potential well from Jupiter at the distance of Ganymede is U Gm m r m 2 11 2 27 9 2 8 2 6 67 10 1 90 10 1071 10 118 10 × × × . . kg m 2 2 To escape from both requires 1 2 3 78 10 2 1 22 10 15 6 2 26 8 2 8 mv m v esc esc k m s =+ × + × × = P13.42 We interpret “lunar escape speed” to be the escape speed from the surface of a stationary moon alone in the Universe: 1 2 2 2 2 mv GM m R v GM R v GM R m m m m m m esc 2 esc launch = = = Now for the flight from moon to Earth KU mv GmM R GmM r mv GmM r GmM R GM R GM R GM r v GM r GM R if m m Em m E E m m m m m E E += + −−= −− a f a f 1 2 1 2 4 1 2 2 2 launch 2 el impact 2 el impact 2 vG M R M r M R M r G G m
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