Calculating the Mass of a Binary Star System

[coltsamuel96]

mass of a star...

given is a binary star system, with mass m1=6*1.99*10^30kg, radius =r1, v=270km/s, orbital period, T=1.7days... the other star of the binary system(compact and dense)with mass m2, and radius r2 orbits around a same common point... (r1>r2, G=6.67*10^-11Nm^2kg^-2) calculate, 1.)approximate mass of m2 2.)what type of star is m2?
attempt at the question, i used this equation, G*m1m2/(r1+r2)^2=m1(2pi/T)^2*r1 and furthermore i did, v=r(2pi/T), with this i get r1... but how do i get r2?so that i can get m2 from the above equation of G*m2/(r1+r2)^2=(2pi/T)^2*r1

 

[Delphi51]

Did you know the period is the same for both stars?
I was convinced by looking at the animation in Wikipedia (binary stars).
And, of course, the force. Anyway, you can write that
F = 4π²m1*r1/T² = 4π²m2*r2/T².
That gives you 2 equations and 3 unknowns, I think. Maybe use the other formula for the force in the same way to get a 3rd equation?