The three-body problem is a special case of the n -body problem, which describes how 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. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n -body problem for details). However, the Sundman and Wang series converge so slowly that they are useless for practical purposes; 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). Atomic systems, e.g. atoms, ions, and molecules, can be treated in terms of the quantum n -body problem. Among classical physical systems, the 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 n -body systems. Some applications are conveniently treated by 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.