Celestial Mechanics - The N-body Problem

The n-body problem

For systems of n gravitationally interacting bodies where n = 3 to thousands, that is, multiple stars and star clusters where the member stars are of comparable mass, the Virial Theorem, by working with a systems gravitational potential energy and the kinetic energies of the member stars, can give some insight into the system's stability and evolution. However, the theorem gives mainly information of a statistical nature about the system; it cannot define the space trajectory of a specific star in the system over an extended time interval, and therefore, it cannot predict close encounters of it with other stars nor whether or not this specific star will remain part of the system or will be ejected from it.