This is a simulation for a double stars system in circular motion.

Assume the mass for stars are M,m.
The density is assume to be the same for both stars, so the radius for M will change when M is changed.
The distance between star is d,

The radius for the circular motion are r and d-r,
where $M\, r=(d-r)\,m$ , and $\frac{GMm}{d^2}=M\,r w^2=m(d-r) w^2$

The black dot is the center of mass (CM) for the binary stars ststem.