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Total Energy in Newtonian Cosmology

  1. Sep 19, 2012 #1
    1. The problem statement, all variables and given/known data
    "Consider a perfectly homogeneous and isotropic universe filled with dust of uniform density ρ(t).
    Let universe expand, dust is carried radially outward from origin.
    Conservation of total energy E. E = K(t) + U(t)
    K(t) = (1/2)*mv^2(t) and U(t) = -GMm/r(t)
    where M = 4/3*∏r^3(t)ρ(t).
    Let E = -1/2*mkc^2s^2 with k a constant and s labelling a shell"


    2. Relevant equations
    I am at loss as to where that last line came from.


    3. The attempt at a solution
    From the information given it is easy to show that v^2 - 8/3*∏Gρr^2 = -kc^2s^2 and therefore determine what values of k allow a bounded or unbounded universe but I just don't get that last conclusion in the introduction.
     
  2. jcsd
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