Mass of each star in a binary star system?

A binary star is composed of two stars that orbit around their centre of mass under the influence of gravity. Consider such a system in which two stars have identical mass. In the centre of mass frame, each star moves in a circular orbit with a speed of 200 km/s. If the orbital period is 15 days, what is the approximate mass of the star?

a) 10^32 kg b) 10^30 kg c) 10^34 kg d) 10^28 kg e) 10^26 kg

Attempt: Centripetal force = m*v^2/r Gravitational force = Gm1m2/r^2 (m1=m2)

m*v^2/r = Gm1m2/r^2

v = rw; w = angular velocity w = 2*pi/T (T, time period)

substituting

4*pi^2/T^2 = Gm/r^3

I am stuck here since r is not given.

Using the centre of mass equation, mr=m(R-r) [R is the total distance between the stars and r is the distance from COM to each star]. Don't know how to go beyond this. Please help with the solution!

• Yes but i am not sure how to make the substitution so as to get rid of the r. – rahul rj Mar 8 '17 at 9:19
• That was trivial indeed, I was solely thinking in terms of centripetal force and gravitational force , and along the way completely ignored that its circle with C = 2pi r. Thank you! – rahul rj Mar 8 '17 at 11:00