Binary Star system common period

AI Thread Summary
In a binary star system, the two stars are always diametrically opposite due to the requirement of equal gravitational forces acting on each star, which allows for stable circular motion. They share a common orbital period because they must maintain the same angular velocity to remain in equilibrium, ensuring they remain opposite each other. The inner star is typically more massive due to conservation of momentum, which dictates that the more massive star will have a smaller orbital radius. This relationship is essential for understanding the dynamics of binary systems, as it directly influences their gravitational interactions. Overall, the principles of gravitational force and centripetal motion are key to explaining these phenomena in binary star systems.
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Homework Statement


The questions are about binary star system.


Homework Equations


Why the two stars in a binary star system are always diametrically opposite positions?
Why the two stars have common period?
Why the inner star is more massive?

The Attempt at a Solution


For the period question, I'm thinking that they have same angular velocity, but I know that I should use force to explain why, but I don't know how to explain using gravitational force.
For the mass question, I think it's because of conservation of momentum, but don't know if it is right or how to explain.
 
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Let us look at the definition of a binary star system: "a star system consisting of two stars orbiting around their common center of mass" according to Wikipedia. This succinct description in fact encodes all that you need to know to solve the question.
1. If the two stars are not diametrically opposite each other, what is the direction of the gravitational force acting on each of them? Can it possibly allow them to undergo circular motion?
2. This is linked to the first question. If they do not have the same period, then they would not always be diametrically opposite each other.
3. Based on the above two ideas, you can easily prove this using the fact that centripetal force acting on each is the gravitational force acting on it.
 
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