How Do You Calculate Orbital Speed in Different Galactic Density Models?

[CaptainEvil]

Orbital Speed of a Star - Please Help!

Homework Statement

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.

Homework Equations

M(r) = v(r)²r/G

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.

Any help please?

 

[underalus]

That Els Peeters, she's got some tough questions, eh?