# Barycenter

Two bodies of similar mass orbiting around a common barycenter.
Two bodies with a slight difference in mass orbiting around a common barycenter.
Two bodies with a major difference in mass orbiting around a common barycenter.
Two bodies with an extreme difference in mass orbiting around a common barycenter.
Two bodies with similar mass orbiting around a common barycenter with elliptic orbits.

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. It is an important concept in the fields of astronomy, astrophysics, and the like.

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. 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:

$r_1 = r_{\rm tot} {m_2 \over m_1 + m_2}$

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.