Editing Three-body problem (section)

=={{mvar|n}}-body problem==
The three-body problem is a special case of the [[n-body problem|{{mvar|n}}-body problem]], which describes how {{mvar|n}} objects move under one of the physical forces, such as [[gravity]]. These problems have a global analytical solution in the form of a convergent power series, as was proven by [[Karl F.&nbsp;Sundman]] for {{math|''n'' {{=}} 3}} and by [[Qiudong Wang]] for {{math|''n'' > 3}} (see [[n-body problem|{{mvar|n}}-body problem]] for details). However, the Sundman and Wang series converge so slowly that they are useless for practical purposes;<ref>[[Florin Diacu]]. [http://www.math.uvic.ca/faculty/diacu/diacuNbody.pdf "The Solution of the ''n''-body Problem"], ''[[The Mathematical Intelligencer]]'', 1996.</ref> therefore, it is currently necessary to approximate solutions by [[numerical analysis]] in the form of [[numerical integration]] or, for some cases, classical [[trigonometric series]] approximations (see [[N-body simulation|{{mvar|n}}-body simulation]]). Atomic systems, e.g. atoms, ions, and molecules, can be treated in terms of the quantum {{mvar|n}}-body problem. Among classical physical systems, the {{mvar|n}}-body problem usually refers to a [[galaxy]] or to a [[cluster of galaxies]]; [[planetary systems]], such as [[stars]], [[planets]], and their [[satellites]], can also be treated as {{mvar|n}}-body systems. Some applications are conveniently treated by [[perturbation (astronomy)|perturbation]] theory, in which the system is considered as a two-body problem plus additional forces causing deviations from a hypothetical unperturbed two-body trajectory.