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Binary Star System Period of Revolution

  1. Feb 13, 2013 #1
    1. The problem statement, all variables and given/known data
    (a) Consider a binary star system in which the two stars have masses M1 and M2 and the stars move on circular orbits separated by a distance R. Derive the formula for the period of revolution.

    (b) Suppose M1= 1.22M and M2= 0.64M (where M = mass of the sun) and R= 0.63 AU. Calculate the period of revolution.


    2. Relevant equations
    Centripetal Force: F_c = (mv^2)/r
    Gravitational Force: F_g = (GM1M2)/r^2
    v = (w^2)r

    3. The attempt at a solution
    I set the gravitational force equal to the centripetal force, then used the centripetal forces of each star to solve an equation for the R and r. The overall equation so far is:
    (GM1M2)/R^2 = M1(w^2)*((rM2)/(M1+M2))

    Solving for w^2, I get: w^2 = (G(M1+M2)/R^3)

    Now, taking the period to be T = 2∏/w, the equation for period is:

    T = √((4∏^2R^3)/(G(M1+M2)))

    This is not correct, and I can't seem to figure out why. I'm sure my derivation went wrong somewhere, any help would be appreciated.
     
  2. jcsd
  3. Feb 13, 2013 #2
    The stars revolve around their mutual center of mass. What does that mean with respect to the acceleration of each star?
     
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