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Stellar Orbital Speed, please help

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Calculate [tex]\Omega[/tex](r) and v(r) for the following density models:
    (a) all the mass M is at the center of the galaxy;
    (b) a constant density adding up to a mass M(R0) at the Sun’s orbit and no mass beyond.


    2. Relevant equations

    M(r) = v(r)2r/G


    3. The attempt at a solution

    a) Using the above eqn, I can rewrite for v(r) = [tex]\sqrt{}GM(r)/r[/tex] but since all the mass M is in the center, it is constant, and M(r) = M so

    v(r) = [tex]\sqrt{}GM/r[/tex] and [tex]\Omega[/tex](r) = v(r)/r

    b) For a constant density, radius would extend from 0 to R0 and mass would increase from 0 to M(R0). So I'm thinking I have to integrate my equation from part (a) to account for this summation. But I'm a bit lost and don't know how to get it done.

    Any help please?
     
  2. jcsd
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