The combined center of mass of a two-body system.
It is located on a line between centers, at a point such that the product of the
mass of a body and its distance to the barycenter is the same for both bodies.
We usually say that the moon revolves around the earth, but in fact, both the
moon and the earth revolve around their barycenter, which is 4700 km from the
center of the earth on the side toward the moon. The earth wobbles. Also, not
the earth, but the barycenter of the earth-moon system is in elliptical orbit
around the sun.