barycentre

The barycenter is the common center of mass around which two or more celestial bodies orbit. For the Earth-Moon system, this point lies within Earth, about 4,700 km (2,900 miles) from its center. It is this barycenter, not the center of Earth, that follows an elliptical path around the Sun according to Kepler's laws.1

In mechanics, the center of mass is a conceptual point where an object's entire mass can be considered concentrated. This simplifies the analysis of motion for complex bodies by treating them as single particles located at their center of mass. This concept is crucial for understanding the dynamics of systems, from planets orbiting stars to collections of atoms within a rigid body. A center-of-mass system is a frame of reference where this common center of mass is at rest.23