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Homework Help: Rotation Curve for a Galaxy

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data

    SUppose you have a galaxy with a spherically symmetric mass distribution with the mass density rho(r) = rho0 (r0/r)^5/3, where rho0 and r0 are constants. Derive the expression for M(r) the total mass interior to r, Then derive the rotation curve function.

    2. Relevant equations

    v2 = GM(r)/r

    3. The attempt at a solution

    I know that M(r) = the Integral from 0 to r of; 4/3 (pi) rho(r) r^2 dr

    I know that rho(r) is proportional, or goes as 1/r^2

    I also know that a rotation curve for a galaxy flattens out, so for this to be true then M(r) is proportional to r; thus I get the answer of

    v2 = 4/3 (pi) G M(r)/ r

    which should simplify to v2 = 4/3 (pi) G

    But this doesnt seem right to me...perhaps Im messing up the part for the M(r) and the r...or maybe the rho and 1/r^2

    Assistance if possible? THank you
  2. jcsd
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