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1296_Physics ProblemsTechnical Physics

# 1296_Physics ProblemsTechnical Physics - Chapter 46 P46.44...

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Chapter 46 637 P46.44 The density of the Universe is ρ ρ π = = F H G I K J 1 20 1 20 3 8 2 . . c H G . Consider a remote galaxy at distance r . The mass interior to the sphere below it is M r H G r H r G = F H G I K J = F H G I K J F H G I K J = ρ π π π 4 3 1 20 3 8 4 3 0 600 3 2 3 2 3 . . both now and in the future when it has slowed to rest from its current speed v H r = . The energy of this galaxy-sphere system is constant as the galaxy moves to apogee distance R : 1 2 0 2 mv GmM r GmM R = so 1 2 0 600 0 0 600 2 2 2 3 2 3 mH r Gm r H r G Gm R H r G F H G I K J = F H G I K J . . = − 0 100 0 600 . . r R so R r = 6 00 . . The Universe will expand by a factor of 6 00 . from its current dimensions. P46.45 (a) k T m c p B 2 2 so T m c k p = × × F H G I K J 2 2 938 3 1 38 10 1 60 10 10 2 23 13 13 B MeV J K J 1 MeV K . . . ~ a f e j (b) k T
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