How to Solve Stellar Structure Equations for a Constant Density Star?

[fu11meta1]

Homework Statement

Consider a star of radius R, with density p that is constant, composed of classical, nonrelativistic, idealg gas of fully ionized hydrogen.
a. Solve the equations of stellar structure for the pressure profile, P(r) with the boundary condition P(R)=0
b. Find the temperature profile T(r)
c. Assume that the nuclear energy production rate depends on temperature as E==T^4. At what radius does E decrease to 0.1 of its central value, and what fraction of the star's volume is included within this radius?

Homework Equations

A) dP(r)=-G*M(r)*ρ(r)*dr/r^2
B)dT(r)/dr = -3/4 *( L(r)*k(r)*ρ(r))/(4∏r^24acT(r)^3)
C) I'm not sure about the formulas for C

The Attempt at a Solution

I think I get A part. You have to integrate from r to R of
dP(r)=-G*M(r)*ρ*dr/r^2 ;ρ= M(r)/(4/3)∏r^3, solve for M(r)
=-G*ρ^2*(4/3)*∏*integration of r

b part: I have no idea. Which values will be constant and why?

c part: I'm also not sure which equations to use

Please help and explain thoroughly or set me on the right track! Also please explain the concepts too! Thanks

 

[SteamKing]

For part c, you have to solve part b and figure out the radial distribution of temperature within the star.

 

[fu11meta1]

Thanks!
any idea on part b?

 

[SteamKing]

Thanks!
any idea on part b?

B)dT(r)/dr = -3/4 *( L(r)*k(r)*ρ(r))/(4∏r^24acT(r)^3)

You've got a first order ODE to solve here. It's not clear what functions L(r) and k(r) are and how they vary with r, nor what boundary conditions to apply.

 

[fu11meta1]

Yeah, that's what I'm trying to figure out. Would the luminosity be constant in this case? or would I need another equation to substitute it with?