In binary star systems we can often measure the sum of the m

In binary star systems we can often measure the sum of the masses of the stars and the ratio of their masses. If m1 + m2 = Mtot, and m1/m2 = Y, derive an expression for the mass of each star in terms of just Mtot and Y.

Solution

=>m₁/m₂ = Y

m₁ =Ym₂-------------1

=>m₁+m₂ =M_tot

Ym₂+m₂ = M_tot

(Y+1)m₂ =M_tot

=>m₂=M_tot/(Y+1)

From 1

=>m₁= [Y/(Y+1)]M_tot