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sl2382
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Homework Statement
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.
Homework Equations
hydrostatic equilibrium
(Pressure of the surface-Pressure of the core)/Radius = GMa(average density)/Radius^2
so that's
ΔP=GMa/R
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!