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Finding the total gravitational potential energy of a gas cloud

  1. Apr 30, 2010 #1
    An interstellar gas cloud can be roughly described as spherical with a uniform density. Its radius is R and its total mass M.
    By considering the gravitational potential energy of a thin spherical shell, show that the total potential energy of the cloud is given by:
    Egrav=-[tex]\frac{3}{5}[/tex]*[tex]\frac{GM^2}{R}[/tex]​


    Ok, so I believe that I need to find the gravitational force acting on this shell, which I have found to be
    F=4[tex]\pi[/tex]GM(r)[tex]\rho[/tex](r)[tex]\delta[/tex]r​
    and I must integrate this to find energy of the shell, and then integrate over the mass to find the total energy, but I am failing to get the desired result.
     
  2. jcsd
  3. Apr 30, 2010 #2
    Think of it more as if you had a shell with mass dM. And you brought it in from infinity to a solid sphere of mass M.

    So write out the differential change in potential energy to bring a shell of mass dM from infinity to 'r'.

    This is what you will want to integrate.
     
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