Does the orbits of stars in a binary system have a common focus, which is the center of mass of the stars?
Elliptic orbits with the focus at the centre of mass (the barycentre) are the solution to the "two body problem". 

The wikipedia page on the central force problem shows how the two body problem can be reduced to solving two central force problems. Therefore the elliptical solution to the central force problem also solves the two body problem, and in moreover Kepler's laws apply to such bodies.