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2.9: S10. A Newtonian Homogeneous Expanding Universe - SOLUTIONS

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Exercise 10.1.1

Answer

Since x(t)=a(t)xc with xc a constant, we have v=dx(t)/dt=˙axc=(˙a/a)x which is Hubble's law with the proportionality between velocity and distance given by ˙a/a. For the second part, note that =ˆx/x+ˆy/y+ˆz/z and v=(˙a/a)(xˆx+yˆy+zˆz) so v=(˙a/a)×(1+1+1)=3(˙a/a). (Here we've used e.g. ˆx as the unit vector in the x direction.) 


This page titled 2.9: S10. A Newtonian Homogeneous Expanding Universe - SOLUTIONS is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Lloyd Knox.

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