Editing Celestial mechanics (section)

==Examples of problems==
Celestial motion, without additional forces such as [[drag force]]s or the [[thrust]] of a [[rocket]], is governed by the reciprocal gravitational acceleration between masses. A generalization is the [[n-body problem|''n''-body problem]],<ref>{{Cite journal|last1=Trenti|first1=Michele|last2=Hut|first2=Piet|date=2008-05-20|title=N-body simulations (gravitational)|journal=Scholarpedia|language=en|volume=3|issue=5|pages=3930|doi=10.4249/scholarpedia.3930|bibcode=2008SchpJ...3.3930T|issn=1941-6016|doi-access=free}}</ref> where a number ''n'' of masses are mutually interacting via the gravitational force. Although analytically not [[integrable]] in the general case,<ref>{{cite arXiv|last=Combot|first=Thierry|date=2015-09-01|title=Integrability and non integrability of some n body problems|class=math.DS|eprint=1509.08233}}</ref> the integration can be well approximated numerically.

:Examples:
:*4-body problem: spaceflight to Mars (for parts of the flight the influence of one or two bodies is very small, so that there we have a 2- or 3-body problem; see also the [[patched conic approximation]])
:*3-body problem:
:**[[Quasi-satellite]]
:**Spaceflight to, and stay at a [[Lagrangian point]]

In the <math>n=2</math> case ([[two-body problem]]) the configuration is much simpler than for <math>n>2</math>. In this case, the system is fully integrable and exact solutions can be found.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Two-Body Problem -- from Eric Weisstein's World of Physics|url=https://scienceworld.wolfram.com/physics/Two-BodyProblem.html|access-date=2020-08-28|website=scienceworld.wolfram.com|language=en}}</ref>

:Examples:
:*A [[binary star]], e.g., [[Alpha Centauri]] (approx. the same mass)
:*A [[binary asteroid]], e.g., [[90 Antiope]] (approx. the same mass)

A further simplification is based on the "standard assumptions in astrodynamics", which include that one body, the [[orbiting body]], is much smaller than the other, the [[central body]]. This is also often approximately valid.

:Examples:
:*The [[Solar System]] orbiting the center of the [[Milky Way]]
:*A planet orbiting the Sun
:*A moon orbiting a planet
:*A spacecraft orbiting Earth, a moon, or a planet (in the latter cases the approximation only applies after arrival at that orbit)