Kepler 3rd law for circular orbits

[Silviu]

Hello! I am a bit confused about Kepler 3rd law for circular orbits. So assume you have 2 bodies of masses M>m orbiting in circles around their center of mass. As the center of mass passes through the line connecting them, they must have the same period. But according to Kepler's 3rd law, this means that, as they rotate around the same center, they must also have the same radius of the orbits. But this is not possible as they have different masses. So how does this work? Thank you!

 

[Orodruin]

Kepler's third law holds for the system as a whole with the distance between the objects as the radius.

If you only look at each individual body, you do not have a Kepler problem.