(adsbygoogle = window.adsbygoogle || []).push({}); 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

Please deduct a relation between period T and density a, your answer should be

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

2. Relevant equations

hydrostatic equilibrium

(Pressure of the surface-Pressure of the core)/Radius = GMa(average density)/Radius^2

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!!

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# Homework Help: Deducting period-density law

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