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Homework Help: Puzzling problem (using virial theorem)

  1. Jun 19, 2011 #1
    Consider a star of Radius R and mass M, with a pressure gradient given by

    [itex]\frac{dP}{dr}[/itex] = [itex]\frac{4\pi}{3}[/itex]G[itex]\rho[/itex]2r exp(-[itex]\frac{rr}{\lambda\lambda}[/itex])

    where [itex]\rho[/itex] is the central density. calculate the gravitational energy, using the Virial theorem. Show that in the limit [itex]\lambda[/itex] « R this energy is given by

    E = [itex]\frac{RGMM}{3R\lambda}[/itex]

    for tecnical reasons:
    MM = M2
    rr = r2
    [itex]\lambda\lambda[/itex] = [itex]\lambda[/itex]2
    Last edited: Jun 19, 2011
  2. jcsd
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