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Center of mass

The center of mass of a group of points is defined as the weighted mean of the points' positions. The weight applied to each point is the point's mass. It is also called the center of inertia.

For mass that is distributed according to a continuous, nonnegative density over a body V in space, the center of mass is:

, where total mass .

In , . Each of the center of mass's components can be computed by


The origin from which positions are calculated has no effect on the result. As long as the same unit is used for all the points, any length and mass unit can be used.


When talking about celestial bodies, the center of mass has a special relevance: when a moon orbits around planet, or a planet orbits around a star, both of them are actually orbiting around their center of mass, called the barycenter. There are some interesting consequences:

from the Earth's center. We can see that the Earth is far from standing "still" and the Moon moving: both of them move around a point more than 1,000 km below the Earth surface.

See also: Center of gravity, Pappus's theorem