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

AI Thread Summary
The discussion focuses on the principles of momentum conservation in binary star systems. It explains that the total momentum remains constant due to the absence of external forces acting on the stars. The stars must be positioned diametrically opposite to maintain a constant net momentum, as their velocity vectors need to counterbalance each other. This configuration leads to a common period of rotation, with the more massive star being the inner one. Understanding these dynamics is crucial for analyzing the behavior of binary systems.
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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..
 
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