638 Particle Physics and Cosmology*P46.47(a)Consider a sphere around us of radius Rlarge compared to the size of galaxy clusters. If thematter Minside the sphere has the critical density, then a galaxy of massmat the surface ofthe sphere is moving just at escape speed vaccording toKUg+=01202mvGMmR−=.The energy of the galaxy-sphere system is conserved, so this equation is true throughout thehistory of the Universe after the Big Bang, where vdRdt=. ThendRdtGMRFHGIKJ=22dRRGM=−122/RdRGMRT002zz=RGM tRT32002/=232MT/=TRGMRGM R==232232.From above,2GMRv=soTRv=23.Now Hubble’s law saysvHR=.SoTRHRH2323.(b)T=×⋅×FHGIKJ=×=−2317 103101118 101183810mslymsly yryrbillion yearsej..*P46.48In our frame of reference, Hubble’s law is exemplified by vR11=Hand 22=H. From these wemay 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 .