388_Physics ProblemsTechnical Physics

388_Physics ProblemsTechnical Physics - 390*P13.22...

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390 Universal Gravitation *P13.22 For the Earth, Fm a = : GM m r mv r m r r T s 2 2 2 2 == F H G I K J π . Then GM T r s 22 3 4 = . Also the angular momentum Lm v rm r T r 2 is a constant for the Earth. We eliminate r LT m = 2 between the equations: GM T LT m s 32 4 2 = F H G I K J GM T L m s 12 2 4 2 = F H G I K J . Now the rate of change is described by GM T dT dt G dM dt T s s 1 2 10 F H G I K J + F H G I K J = dT dt dM dt T M T T s s =− F H G I K J 2 ∆∆ Tt dM dt T M T s s ≈− F H G I K J × F H G I K J −× × F H G I K J 25 0 0 0 316 10 364 10 2 1 182 10 7 9 2 yr s 1 yr kg s yr 1.991 10 kg s 30 . . . ej Section 13.5 The Gravitational Field P13.23 gij i j =++ ° + Gm l Gm l Gm l 2 2 45 0 45 0 ±± cos . ± sin . ± so gi j =+ F H G I K J + GM l 2 1 1 or g F H G I K J Gm l 2 2 1 2 toward the opposite corner y m O m x m l l FIG. P13.23 P13.24 (a) F GMm r ×⋅ × ×+ 2 11 30 3 4 2 17 6 6 71 0 1 0 0 1 9 91 0 1 0 100 10 500 131 10 .. . N m kg kg kg
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