- #1
CaptainEvil
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Homework Statement
I'm to prove that the central pressure of a particular star is
Pc = (15/16[tex]\pi[/tex])(GM2/R4)
I am given the density as a function of r
[tex]\rho[/tex](r) = [tex]\rho[/tex]0[1 - (r/R)2]
In part a I found the Mass by integrating the equation of hydrostatic equilibrium and found
M = (8[tex]\pi[/tex]R3[tex]\rho[/tex]0)/15
mean density [tex]\rho[/tex] was found to be 2[tex]\rho[/tex]0/5
Using these results, I have to prove the central pressure from above.
Homework Equations
The Attempt at a Solution
I know since density is changing, I can integrate the equation of hydrostatic equilibrium and plug in [tex]\rho[/tex](r). But what do I plug in for M(r)? Do I use the mass I calculated? I'm confused and often get very close to the answer but cannot get the 15[tex]\pi[/tex]/16 and instead get another fraction.
Please help