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I Hydrostatic equilibirum in slowly rotating star

  1. Jul 25, 2017 #1
    Hello, in article Slowly relativistic stars by James B. Hartle (http://adsabs.harvard.edu/full/1967ApJ...150.1005H) is equation of newtonian hydrostatic equilibrium, eq. (5). $$const.=\int_0^p\frac{dp}{\rho}-1/2(\Omega \times r)^2+\Phi,$$ where ##p## is pressure, ##\rho## is desinty, ##\Omega## angular velocity of star and ##\Phi## is graviational potential.
    How may I derive it? I can derive eq. for hydrostatic equilibrium of non rotating star, but here is in result only potetntial and it suggests some other start than I know.
    My idea is that all forces have to be in equilibrium, so if I take some small piece of matter let's call it ##dm##. Than $$Fp_b-Fp_t+Fg+Fc=0,$$ where ##Fp_b## is preassure force from the bottom, ##Fp_t## is preassure force from the top of ##dm##, ##Fg## is gravitational force and ##Fc## is centrifugal force. But how to proceed further, I'm not sure.
    Can anybody suggest something?
     
  2. jcsd
  3. Jul 25, 2017 #2

    haruspex

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    Try comparing it with the Bernoulli equation.
     
  4. Jul 26, 2017 #3
    Aha, thank you.
     
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