If I remember correctly, the masses I calculated were not disproportionately skewed so that one is much larger than the other.
Syo gave me this link for the full formula: http://en.wikipedia.org/wiki/Orbital_speed
, go down to "Taking into account the mass of the orbiting body"
I can't use that formula in this case, since there's not exactly an "orbiting body" in the problem (I got that much)...so why was it like that on the test? Or maybe I'm just remembering something wrong.
Also, if you assume that centripetal & gravitational forces are equal (work of syo as well):
Fg=Gm1m2/r^2=Fc=mv^2/r, Fc is the centripetal force towards the center of a circle, Fg is the gravitational force. If you solve for m1 and m2 you get that Gm2/r1^2=v1^2/r1 and Gm1/r2^2=v2^2/r2. That means that v1=sqrt(Gm2/r1) and v2=sqrt(Gm1/r2)
Side note: There's an animation on wikipedia somewhere...ah! here it is:
, scroll down to the section "Astrophysics" and it should be right there.
The stars' velocities increase as their orbits approach the barycenter. If you can imagine that the orbits are circular, would the stars' velocities be constant throughout their orbit? Or would it be something similar to what we're already seeing in the animation?
EDIT: orbital speed link was screwed up