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Find gravitational potent. energy - isotropic distribution

  1. Nov 6, 2016 #1
    1. The problem statement, all variables and given/known data
    I am told that the gravitational force of a mass m located inside an isotropic distribution of spherical radius R and total mass M is given by
    Fg = -GmM(r)/r^2
    where r is the distance between m and the center of distribution and M (r) is the mass contained below the distance r (weight between 0 and r). Suppose the sphere is homogeneous of constant density
    ρ= M/((4πR^3)/3)
    I need to find the gravitational potential energy inside the distribution as a function of M, m, R, r and G

    2. Relevant equations


    3. The attempt at a solution
    So far I have found the gravitational potential energy, but I don't know how the density is going to come into play. I also don't understand what the isotropic distribution is going to change in my answer and derivation.
    upload_2016-11-6_13-27-4.png
     
  2. jcsd
  3. Nov 6, 2016 #2
    I recommend that you read the Wikipedia article https://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation, especially the section "Gravitational field". It seems like the formula you are using is not correct, since it is valid for ##r>R## (##R## being the radius of the sphere). Density is defined as the mass per volume.
     
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