Everything in the Solar System orbits the center of mass (it's rarely in the center of the Sun!)
The Earth-Moon Barycenter: The Moon doesn't orbit Earth's center and Earth doesn't stay still (3D!)
The barycenter is the center of mass of two or more bodies that orbit each other and is the point about which the bodies orbit. It is an important concept in fields such as astronomy and astrophysics. The distance from a body's center of mass to the barycenter can be calculated as a two-body problem.
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