Center of Mass
The animations in the link shows how the barycenter shifts depending on the relative masses of the orbiting bodies (Wiki: http://en.wikipedia.org/wiki/Barycenter)
Originally shared by Tom Eigelsbach
The barycenter is the point in space around which two objects orbit. For the Moon and Earth, that point is about 1000 miles (1700 km) beneath your feet, or about three-quarters of the way from the Earth’s center to its surface. That means the Earth actually wobbles around a point deep in its interior, pulled around by the Moon.