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393_Physics ProblemsTechnical Physics

# 393_Physics ProblemsTechnical Physics - Chapter 13 P13.38...

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Chapter 13 395 P13.38 The gravitational force supplies the needed centripetal acceleration. Thus, GM m R h mv R h E E E + = + b g b g 2 2 or v GM R h E E 2 = + (a) T r v R h E GM R h E E = = + + 2 2 π π b g b g T R h GM E E = + 2 3 π b g (b) v GM R h E E = + (c) Minimum energy input is E K U K U f gf i gi min = + e j e j . It is simplest to launch the satellite from a location on the equator, and launch it toward the east. This choice has the object starting with energy K mv i i = 1 2 2 with v R R i E E = = 2 1 00 2 86 400 π π . day s and U GM m R gi E E = − . Thus, E m GM R h GM m R h m R GM m R E E E E E E E min = + F H G I K J + L N M M O Q P P + 1 2 1 2 4 86 400 2 2 2 π s b g or E GM m R h R R h R m E E E E E min = + + L N M M O Q P P 2 2 2 86 400 2 2 2 b g b g π s P13.39 E GMm r tot = − 2 E GMm r r E i f = F H G I K J = × × + + F H G I K J = × = 2 1 1 6 67 10 5 98 10 2 10 1 6 370 100 1 6 370 200 4 69 10 469 11 24 3 8 . . . e je j kg 10 m J MJ 3 P13.40
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