# Deducting period-density law

1. Oct 19, 2011

### sl2382

1. The problem statement, all variables and given/known data

Consider a start of mass M and radius R.
1.It can be modeled as a single shell in hydrostatic equilibrium
The star's pressure is given by P(core)/2
The star's density is average density a
2.Period=star's diameter/speed
3.Speed=sqrt(γP/a)
γ=5/3
P is the average pressure

T=Ka^(-1/2) where K is a constant you should be able to calculate.

2. Relevant equations

hydrostatic equilibrium

so that's
ΔP=GMa/R

3. The attempt at a solution

I've been trying it for numerous times but just can't get the right answer. I assume that:
according to hydrostatic equilibirum rule
P(core)/2=(GMa)/R
and
T=2R/speed = 2R/sqrt((5/4)P/a) since average pressure should be (P/2 + P)/2

So from the first equation, I get that P=(2GMa)/R so plug this into the second equation

It's too complicated to put here but I just can't get the right answer.. is any of those steps wrong so I can make corrections?? Thanks a lot!!