Just use Kepler's Third Law.The spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 8.00 months. The lines of both stars shift by equal amounts, and the amount of the Doppler shift indicates that each star has an orbital speed of 9.00×10^4. What are the masses of the two stars? Assume that each of the two stars traces a circular orbit around their center of mass.
How would you solve this?
They give you the period in the first part (3/4 years), and with the period and the speed, you can find out the distance the stars travel (d=vt). Once you know that they are orbiting in circles, you can see that the distance in the circumference, and use that to find out the average separation of the stars. Now you have both t and a. By the fact that both stars are going the same speed, you can tell that they are the same mass, so you have all of the parts of the equation. Just make sure that your units are in years, solar masses, and AU.