probset2 - COSMOLOGY Problem Set 2 April 7, 2010 Problem 1...

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Unformatted text preview: COSMOLOGY Problem Set 2 April 7, 2010 Problem 1 : Collapse of a Uniform Sphere This is really a problem in Newtonian mechanics. Consider a uniform (homoge- neous) sphere of mass M whose initial radius (at t = 0) is R . The sphere is released from rest at t = 0, collapsing under its own gravity. a) In terms of M and R , find the time, t coll , for the sphere to collapse to R = 0. [10] b) Suppose the same uniform sphere of mass M were released from R = R . Find the ratio of the new collapse time t coll to t coll (from part a). [5] c) In the limit R R , where R = R ( t ) is the radius of the collapsing sphere ( t > t ), find how rapidly the collapse is accelerating; i.e., find the de celeration parameter q . (Recall that q 1 H 2 [ 1 R ( d 2 R dt 2 )].) [5] Problem 2 : Power-Law Expanding Universe There is an interesting class of cosmological models for which the 3-space curvature may be neglected ( k = 0) and the time-evolution of the scale factor is a power law ( a...
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This note was uploaded on 07/28/2011 for the course PHY 880.20 taught by Professor Steigman during the Spring '10 term at Ohio State.

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probset2 - COSMOLOGY Problem Set 2 April 7, 2010 Problem 1...

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