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Virial theorem

The virial theorem states that the average kinetic energy of the objects in a stable, bounded, self-gravitating assembly is equal to -1/2 times the average gravitational potential energy.

The virial theorem is a remarkably useful simplifying result for otherwise very complex physical systems such as solar systems or galaxies, and is also applicable to a number of other similar scenarios.

The virial theorem takes its name from the quantity known as the virial (Latin for "force"), defined as:

where ri and pi are the position and momentum vectorss of the ith particle respectively.

The virial theorem can be derived by considering the properties of the virial in the limit over a long period of time.

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