Estimating orbital seperation?

Question

Estimate the orbital seperation and velocity for a binary star system composed of solar mass stars that have an orbital period of 12 hours (assume circular orbits).

Please help :( so confused

Answer 1

You have two identical stars with orbital periods around one another of 12 hours - right?

They have to obey Kepler's laws - so P^2 = a^3

(as long as we have info in years, AU and solar masses - otherwise there is a proportionality constant).

You know the period, so you can calculate the semi-major axis of the orbits (a). Since the orbits are circular, semi-major axis = radius. And since the masses are the same both stars are equidistant from the center of mass, around which they orbit. And since you know the period and the radius of the orbit, you can use v = 2 pi R / P to get the speed.