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Deducting period-density law

  1. Oct 19, 2011 #1
    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!!
     
  2. jcsd
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