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Binary star system

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data
    A binary star system has a period of 90 days. It consists of two equally massed stars each with a mass of twice that of the sun, that rotate like a dumbbell about the center of mass at the midpoint between them. How far apart are these stars?


    2. Relevant equations
    F = ma v = 2 pi r/T force of g = GMm/r^2 distance = 2r




    3. The attempt at a solution
    I set GMm/r^2 = m v^2/r then solve for r and d is 2 r. My problem is that my solution sheet uses force of g = GM^2/(2r)^2 and then force = to M v^2/r I know this has something to do with the fact that we have two stars and therefore, I guess M times M but I am confused... Could someone please explain why the equations used in the solution sheet are the correct ones and why in turn mine are incorrect??? Thanks, Frostking
     
  2. jcsd
  3. Oct 25, 2009 #2
    You used r^2 where the distance between them is 2r, they are orbiting about a common center of mass.
     
  4. Oct 25, 2009 #3

    ehild

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    Both stars revolve around their common centre of mass which is halfway between them, at distance r, so the centripetal force is mv2/r, but the other star is 2r distance apart, so the gravitational interaction between the stars is Gm2/(2r)2.

    ehild
     
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