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Binary Star Mass

  1. Jun 4, 2014 #1
    1. The problem statement, all variables and given/known data

    96yhwo.png


    How do I show that for a binary star system, if one star has mass ##M_s##, speed ##V_s##, period ##P##, the mass of the other star is given by: ##M_P^3 \approx \frac{V_s^3}{2\pi G} PM_s^2##?

    2. Relevant equations



    3. The attempt at a solution

    [tex]\frac{GM_pM_s}{(a_p+a_s)^2} = \frac{M_s v_s^2}{a_s}[/tex]
    Substituting in ##PV_s=2\pi a_s##:
    [tex]M_p = \frac{2\pi(a_p+a_s)^2V_s}{PG}[/tex]
    Using kepler's second law: ## P^2 = \frac{(a_p+a_s)^3(2\pi)^2}{G(M_p+M_s)} ##:
    [tex]M_p^3 = \frac{V_s^3}{2\pi G} P (M_p+M_s)^2[/tex]
     
  2. jcsd
  3. Jun 4, 2014 #2
    Seems correct to me. The mass of the planet is more often than not negligible compared to the mass of a star, so [itex] M_{p} << M_{S}[/itex]
     
  4. Jun 4, 2014 #3
    Thanks alot! I'm doing an introductory course to my first ever astrophysics module, so I'm not quite familiar with these things.
     
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