396_Physics ProblemsTechnical Physics

396_Physics ProblemsTechnical Physics - 398 *P13.45...

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398 Universal Gravitation *P13.45 (a) The major axis of the orbit is 2 50 5 a = . AU so a = 25 25 . A U Further, in Figure 13.5, ac += 50 AU so c = 24 75 A U Then e c a == = 24 75 25 25 0980 . . . (b) In TK a s 23 = for objects in solar orbit, the Earth gives us 11 2 3 yr AU bg af = K s K s = 1 1 2 3 yr AU bg a f Then T 2 2 3 3 1 1 25 25 = yr AU AU a f af . T = 127 yr (c) U GMm r =− ×⋅ × × × × 667 10 1991 10 12 10 50 1 496 10 213 10 11 30 10 11 17 .. . . . N m kg kg kg m J 22 ej e j e j *P13.46 (a) For the satellite Fm a = GmM r mv r E 2 0 2 = v GM r E 0 12 = F H G I K J (b) Conservation of momentum in the forward direction for the exploding satellite: mv mv mv mv m vv GM r if i i E ∑∑ = =+ F H G I K J ch 54 0 5 4 5 4 0 0 (c) With velocity perpendicular to radius, the orbiting fragment is at perigee. Its apogee distance and speed are related to r and v i by 4 4 mrv mr v f = and 1 2 4 4 1 2 4 4 mv GM m r mv GM m r i E f E f −= . Substituting
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