How Does Binary Star Mass Affect Orbital Period Calculation?

[kari82]

In a certain binary-star system, each star has the same mass as our Sun, and they revolve about their center of mass. The distance between them is the same as the distance between Earth and the Sun. What is their period of revolution in years?
T^2=(4pi^2/GM)*r^3
I know that the mass of the sun is 1.9x10^30. I also found in my book that the distance between the Earth and the sun is 1.5 x 10^11. If I plug those numbers into the equation and I solve for the ratio between T/1y in seconds, I don't get the correct answer, which is 0.7 years. I'm assuming my mistake has to do with the distance between these two planets. Can anyone help me please?

 

[gneill]

The problem is that the given expression for the period assumes that one of the masses is dominant (M >> m) and that the mass m of the smaller body can be ignored. Here both objects have the same mass.

The gravitational parameter μ = G*M is an approximation for when m << M. When this is not the case, take μ = G*(M + m), which in this instance will be G*(M + M), or μ = 2*G*M, since they are of equal mass M.