A binary star system consists of two equal mass stars that revolve in circular orbits about their center of mass. The period of the motion, T=29.6 days, and the orbital speed v= 220 km/s of the stars can be measured from telescopic observations. What is the mass (kg) of each star?

Answer 1

Each has a force holding it to the other.

F=GM^2/d^2

this is equal to centripetal acceleration.

GM^2/d^2=v^2/(d/2)^2

check my thinking. solve for M

Answer 2

Using Newton's law and the law of universal graviation:

F=ma
Acceleration is centripital acceleration, so a=(v^2)/r

so G(m^2/r^2)=m(v^2/r)