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391_Physics ProblemsTechnical Physics

# 391_Physics ProblemsTechnical Physics - Chapter 13 Section...

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Chapter 13 393 Section 13.7 Energy Considerations in Planetary and Satellite Motion P13.33 1 2 1 1 1 2 2 2 mv GM m r r mv i E f i f + F H G I K J = 1 2 0 1 1 2 2 2 v GM R v i E E f + F H G I K J = or v v GM R f E E 2 1 2 2 = and v v GM R f E E = F H G I K J 1 2 1 2 2 v f = × × L N M O Q P = × 2 00 10 1 25 10 1 66 10 4 2 8 1 2 4 . . . e j m s P13.34 (a) v M G R E solar escape Sun Sun km s = = 2 42 1 . (b) Let r R x E S = represent variable distance from the Sun, with x in astronomical units. v M G R x x E S = = 2 42 1 Sun . If v = 125 000 km 3 600 s , then x = = × 1 47 2 20 10 11 . . A.U. m (at or beyond the orbit of Mars, 125 000 km/h is sufficient for escape). P13.35 To obtain the orbital velocity, we use F mMG R mv R = = 2 2 or v MG R = We can obtain the escape velocity from 1 2 mv mMG R esc 2 = or v MG R v esc = = 2 2 P13.36 v R h GM R h i E E E 2 2 + = + b g K mv GM m R h i i E E = = + F H G I K J = × × × + × L N M M O Q P P = × 1 2 1 2 1 2 6 67 10 5 98 10 500 6 37 10 0 500 10 1 45 10 2 11 24 6 6 10 . . . . . N m kg kg kg m m J 2 2 e je j b g e j e j The change in gravitational potential energy of the satellite-Earth system is
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