1297_Physics ProblemsTechnical Physics

1297_Physics - 638*P46.47 Particle Physics and Cosmology(a Consider a sphere around us of radius R large compared to the size of galaxy clusters If

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638 Particle Physics and Cosmology *P46.47 (a) Consider a sphere around us of radius R large compared to the size of galaxy clusters. If the matter M inside the sphere has the critical density, then a galaxy of mass m at the surface of the sphere is moving just at escape speed v according to KU g += 0 1 2 0 2 mv GMm R −= . The energy of the galaxy-sphere system is conserved, so this equation is true throughout the history of the Universe after the Big Bang, where v dR dt = . Then dR dt GM R F H G I K J = 2 2 dR RG M = 12 2 / RdR GM RT 00 2 zz = R GM t R T 32 0 0 2 / = 2 3 2 M T / = T R GM R GM R == 2 3 2 2 3 2 . From above, 2 GM R v = so T R v = 2 3 . Now Hubble’s law says vH R = . So T R HR H 2 3 2 3 . (b) T = ×⋅ × F H G I K J = 2 317 10 31 0 1 118 10 118 3 8 10 msly ms ly yr yr billion years ej .. *P46.48 In our frame of reference, Hubble’s law is exemplified by vR 11 = H and 22 = H . From these we may form the equations
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This note was uploaded on 12/15/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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