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87. Problem 16.61 (RHK) A certain triple-star system consists of two stars, each of mass m, revolving about a central star, mass M, in the same circular orbit. The two stars stay at opposite ends of a diameter of the circular orbit. We have to derive expression for the period of revolution of the stars; we are given that the radius of the orbit is r.
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Solution: Click For PDF Version Force on any one of the stars of mass m due to the other star of mass m and the third star of mass M is
As this star is revolving in a circular orbit of radius r, the
gravitational force F on it has to be equal to the centripetal force for
uniform circular motion,
Substituting
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. That is
, where
T is the orbital period of stars of mass m, we get