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, defined as:

where r_i and p_i 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.

External links

• The virial theorem made easy by John Baez
• A mathematical analysis of the virial theorem