# Orbital Speed of a Star -

1. Nov 25, 2009

### CaptainEvil

1. The problem statement, all variables and given/known data

Calculate $$\Omega$$(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) = $$\sqrt{}GM(r)/r$$ but since all the mass M is in the center, it is constant, and M(r) = M so

v(r) = $$\sqrt{}GM/r$$ and $$\Omega$$(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.