# Addition of grav potentials / Orbital velocity

1. Mar 14, 2012

### ValarDohaeris

3. The attempt at a solution

I think I may of been too general with the volume in finding $$M_0$$
I'm assuming $$r_0 = r_M$$ although I'm not sure why different notation is used thougj

http://imageshack.us/photo/my-images/3/gravscan.jpg/

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2. Mar 14, 2012

### Staff: Mentor

Yup. You need to integrate to find the mass due to the dark matter since its density is not constant with r.

3. Mar 15, 2012

### ValarDohaeris

I integrated betwee r0 and 0 and got.

M(r) = 4∏ρ0r30

v2 = GM/r
Not sure where to go from here to get the second term.

4. Mar 15, 2012

### Staff: Mentor

That doesn't look quite right. What happened to the constant ro from the density function?
You should have two mass terms to add together. The first one is the trivial M for the central stars, while the second is due to the mass of the dark matter.

5. Mar 15, 2012

### ValarDohaeris

Ah cheers got it now, misread the question was thinking M was the total mass of sphere rather than just the stars contributions.. $$M(r)_{dm} = 4πρ_0r^2_0r$$

Last edited: Mar 15, 2012