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)
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!