A certain triple star system, known as trinary, consists of two stars, each of m
ID: 2255173 • Letter: A
Question
A certain triple star system, known as trinary, consists of two stars, each of mass m, orbiting a third star of mass M (whose center is located at the center of mass of the three star system) at a radius of R. The two stars of mass m orbit directly across from one another, so that all three stars always form a straight line. Derive an expression for the period of revolution of the two stars. (Note: You must completely simplify your answer - this mainly means that any quantities, such as m, M, G, and R can appear at most once in the answer.)
Explanation / Answer
Balancing the forces of both the stars on one of the smaller star
mv^2/R= GmM/R^2 + Gmm/(2R)^2
Time period of revo T is
T = 2xpixR/v
solving above two equation
T will come to be
T= {4xpixR^3/2}/(G(4M+m))^1/2
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