# Barycenter

The barycenter (from the Greek βαρύκεντρον) is the center of mass of two or more bodies which are orbiting each other, and is the point around which both of them orbit.

In the case where one of the two objects is much larger and more massive than the other, the barycenter will be located within the larger object and rather than appearing to orbit it will simply be seen to "wobble" slightly. This is the case for the Moon and Earth, where the barycenter is located on average 4,671 km from Earth's center, well within the planet's radius of 6,378 km. When the two bodies are of similar masses (or at least the mass ratio is less extreme), however, the barycenter will be located outside of either of them and both bodies will follow an orbit around it. This is the case for Pluto and Charon, Jupiter and the Sun, and many binary asteroids and binary stars.

The distance from the center of a body (thought of as a point-mass) to the barycenter in a simple two-body case can be calculated as follows:

[itex]r_1 = r_{\rm tot} {m_2 \over m_1 + m_2}[itex]

where :

r1 is the distance from body 1 to the barycenter
rtot is the distance between the two bodies
m1 and m2 are the masses of the two bodies.

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