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:

The distance of COM from mass m is 2d3. Thus, m is moving in uniform circular motion of radius 2d3Gravitational force on m is providing centripetal force.⇒G(m)(2m)d2=m×ω2×2d3⇒2Gmd2=ω2×2d3⇒ω2=3Gmd3⇒ω=3Gmd3 Hence, T=2πω=2πd33Gm