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.
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..