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Question on Kepler's Law

  1. Apr 21, 2016 #1
    1. The problem statement, all variables and given/known data
    Three identical stars of mass M = 8.9 x 1030 kg form an equilateral triangle that rotates around the triangle's center as the stars move in a common circle about that center. The triangle has edge length L = 2.8 x 1010 m. What is the speed of the stars?

    2. Relevant equations
    Kepler's 3rd Law: T^2=(4*π^2/GM)*R^3
    v=2πR/T

    3. The attempt at a solution
    I used L to find an expression for R, namely R=L/sqrt(3), since its a equilateral triangle and L one of the sides (this is probably where I went wrong). I then used the two equations above to calculate the speed.
    Now I know that the correct solution to this question is v=(GM/L)^0.5=1.456*10^5,
    can someone pls explain to me why it is so?
     
  2. jcsd
  3. Apr 21, 2016 #2

    gneill

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    Start with the basics: centripetal force being provided by the net gravitational force on any given star in the system.
    upload_2016-4-22_0-36-55.png
     
  4. Apr 22, 2016 #3
    I had m*v^2/R = G*m*3M/R^2, this led me to
    v=sqrt(3GM/R)
    and L=sqrt(3)R, could u tell me where I went wrong?
     
  5. Apr 22, 2016 #4

    haruspex

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    That is the magnitude of the force exerted by (what exactly) in what direction?
     
  6. Apr 22, 2016 #5
    I think this is the force exerted by the three suns and that is towards the centre of the circular orbit?
     
  7. Apr 22, 2016 #6

    haruspex

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    Each sun is only pulled by two others. But anyway, it looks to me like you calculated the force exerted by a single sun towards itself (GMm/L2).
     
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