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Homework Help: What does momentum conservation reveal about period and mass of binary systems?

  1. Mar 18, 2010 #1
    1. The problem statement, all variables and given/known data
    A binary star consists of two stars that are orbiting a common centre. The only force acting on the stars is the gravitational force of attraction in a direction along the line joining the stars.

    a) Explain carefully why the total momentum of the binary is constant.

    b) Explain why the two stars are always in a diametrically opposite position.

    c) Hence explain why the two stars have a common period of rotation and why the inner star is the more massive of the two.

    2. Relevant equations

    No equations needed.

    3. The attempt at a solution

    a) The total momentum p = m1 x v1 + m2 x v2. Since there are no external forces acting on the binary system, momentum is by definition conserved.

    --> Does that also imply that the momentum is constant? Because I think that the momentum could vary during one complete revolution and still be conserved right?

    b) They must be in a diametrically opposite position in order for their velocity vectors to have opposite directions. If the were not diametrically opposite, the net momentum would not be constant.

    c) I have no clue here..
  2. jcsd
  3. Mar 18, 2010 #2
    A quick hint'd suffice..
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