Two stars of masses `m_(1)` and `m_(2)` distance r apart, revolve about their centre of mass. The period of revolution is :

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :

In a double star system, two stars of masses m_1 and m_2 separated by a distance x rotate about their centre of mass. Find the common angular velocity and Time period of revolution.

In a double star, two stars (one of mass m and the other of mass 2m ) distance d apart rotate about their common centre of mass., Deduce an expressioin for the period of revolution. Show that te ratio of their angular momenta about the centre of mass is the same as the ratio of their kinetic energies.

In a double star system one of mass m_(1) and another of mass m_(2) with a separation d rotate about their common centre of mass. Then rate of sweeps of area of star of mass m_(1) to star of mass m_(2) about their common centre of mass is

In a double star, two stars one of mass m_(1) and another of mass m_(2) , with a separation d, rotate about their common centre of mass. Find (a) an expression for their time period of eavolution. (b) the ratio of rheir kintic energies. (c) the ratio of their angular momenta about the centre of mass. (d) the total angular momentum of the system. (e) the kinetic energy of the system.

Two stars of mass M_(1) & M_(2) are in circular orbits around their centre of mass The star of mass M_(1) has an orbit of radius R_(1) the star of mass M_(2) has an orbit of radius R_(2) (assume that their centre of mass is not acceleration and distance between starts is fixed) (a) Show that the ratio of orbital radii of the two stars equals the reciprocal of the ratio of their masses, that is R_(1)//R_(2) = M_(2)//M_(1) (b) Explain why the two stars have the same orbital period and show that the period T=2pi((R_(1)+R_(2))^(3//2))/(sqrt(G(M_(1)+M_(2)))) .

Consider a binary star system consisting of two stars of masses M_(1) and M_(2) separated by a distance of 30AU with a period of revolution equal to 30 years. If one of the two stars is 5 times farther from the centre of mass than the other, show that the masses of the two stars are 5 and 25 times that of the sun.