Question

A double star is a system of two stars rotating about their centre of mass, only under their mutual gravitational attraction. Let the stars have masses m and m2 and let their separation be l .Their time period of revolution about the centre of mass of the system will be proportional to.....

Answer 1

The masses will be rotating about their Center of Mass which is at distance of 2l/3 from the mass m. The force on mass m is the gravitational force which is also providing the force for circular motion.

m(2l/3)ω

2

=G

l

2

m×2m

ω=

G

l

3

3m

T=2π/ω