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Birth of Stars

Two stars of ...

Question

Two stars of mass M each, move in circular orbits about their center of mass C.The distance between them is 2R. A very small body A of mass m(m<<M) also rotates about the point C, such that its relative position with respect to the stars remains constant.If the distance between a star and the small mass A is nR, find the value of n.

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Solution

Since it lies in between the two stars $M$ and $M^{'}$ then only it can be equidistant and it is at a distance $R$ from each star.
$∴ n = 1$

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