Two stars each of mass M form a binary star system such that both stars move in the same circular orbit of radius R. The universal gravitational constant is G. Required:
a. Use Newton's laws of motion and gravitation to find an expression for the speed v of either star in terms of R, G, and M.
b. Express the total energy E of the binary star system in terms of R, G, and M. Suppose, instead, one of the stars had a mass 2M.
c. Find the ratio of the speeds, v2M/vM.