An Enclosed Mass Profile problem

[bluejazz]

Homework Statement

Find the enclosed mass profile M(r) in terms of R* and the total mass M* of the star.

Homework Equations

dM_r/dr = 4(pi)r²(density)

density is given as: rho(r) = (rho_c)[1-(r/R*)²]
Where rho_c is the central density and R* is the radius of the star.

3. Attempt at a solution

I plugged the given density into the enclosed mass formula, took the integral in terms of r, and ended up with the result:

M(r) = 4(pi)(rho_c)[r³/3 - r⁵/(5R*²)]

My problem is, I'm not sure how to put this in terms of M_star. What I think is I have to take the central density and the expression for volume [4/3 * (pi) * r³] and get M_star. I guess my real question is this: what is the definition of central density?

 

[bluejazz]

bump! Hope this question doesn't get lost!

 

[bluejazz]

Nevermind, I found the answer! Thanks anyways guys!