A certain triple-star system consists of two stars, each of mass m, re

1.	A certain triple-star system consists of two stars, each of mass m, revolving in the same circular orbit of radius r around a central star of mass m (fig. 13-54).The two orbiting stars are always at opposite ends of a diameter of the orbit. Derive an expression for the period of revolution of the stars
Answer» The CENTRIPETAL force is obtained from the net GRAVITATIONAL force acting on the system. Thus, $F_{net} = F_c$ Substitute, $\frac {Gm}{r^2}[2M+\frac {m}{4}] = \frac {4\pi^2 mr }{T^2}$ Where G = Universal Gravitational Constant = $6.67408 \times 10^{-11}m^3 kg^{-1}s^{-2}$ T = PERIOD of revolution of the stars So, $T = \frac {\sqrt {16\pi^2 r^3}}{G[8M+m]}$ Therefore, the expression for the period of revolution of stars is $\frac {\sqrt {16\pi^2 r^3}}{G[8M+m]}$