Gravity/Binary Star System

EbolaPox

Two stars in a binary system orbit each other with a period of 30 days. Each moves with velocity 30 km/s. A) What is the mass of each, and B) their seperation.

Ok, First thing I noticed was w*r=v this would mean though that the stars are the same distance from the center of mass. I used this radius and calculated the mass of the stars using 1/2mV^2=(-gMm)/r.

If the radius from the center of mass is equal for both stars that means that they would both have to be the same mass. I tried to use the center of mass equation and something relating to gravity to isolate just one variable and solve but couldn't come up with anything. Then I drew another picture for myself and realized that since they are both traveling at the same tangental velocity at the same period they are traveling the same distance. Does this make sense to anyone else? Or am I way off the mark. I wanted to try and use kepler's laws but had too many variables. Any ideas suggestions?

mezarashi

I agree. They would be circling the same path.