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

[FelixISF]

Homework Statement

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.

Homework Equations

No equations needed.

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..

 

[FelixISF]

A quick hint'd suffice..