Editing Orbital resonance (section)

==== N-body mean motion resonance ====
MMRs involving more than two bodies have been observed in the Solar System. For example, there are [[three-body problem|three-body]] MMRs involving Jupiter, Saturn, and some main-belt asteroids. These three-body MMRs are unstable and main-belt asteroids involved in these three-body MMRs have [[Chaos theory|chaotic]] orbital evolutions.<ref name="Nesvorny1998"/> 

A ''Laplace resonance'' is a three-body MMR with a 1:2:4 orbital period ratio (equivalent to a 4:2:1 ratio of orbits). The term arose because [[Pierre-Simon Laplace]] discovered that such a resonance governed the motions of Jupiter's moons [[Io (moon)|Io]], [[Europa (moon)|Europa]], and [[Ganymede (moon)|Ganymede]]. It is now also often applied to other 3-body resonances with the same ratios,<ref name="Gargaud2011">{{cite book |last1=Barnes |first1=R. |year=2011 |chapter=Laplace Resonance |editor-last=Gargaud |editor-first=M. |title=Encyclopedia of Astrobiology |chapter-url=https://books.google.com/books?id=oEq1y9GIcr0C&pg=PA905 |pages=905–906 |publisher=[[Springer Science+Business Media]] |isbn=978-3-642-11271-3 |doi=10.1007/978-3-642-11274-4_864}}</ref> such as that between the [[extrasolar planet]]s [[Gliese 876]] c, b, and e.<ref name="rivera2010" /><ref>{{cite journal |last1=Nelson |first1=B. E. |last2=Robertson |first2=P. M. |last3=Payne |first3=M. J. |last4=Pritchard |first4=S. M. |last5=Deck |first5=K. M. |last6=Ford |first6=E. B. |last7=Wright |first7=J. T. |last8=Isaacson |first8=H. T. |date=2015 |title=An empirically derived three-dimensional Laplace resonance in the Gliese 876 planetary system |journal=Monthly Notices of the Royal Astronomical Society |volume=455 |issue=3 |pages=2484–2499 |doi=10.1093/mnras/stv2367 |doi-access=free |arxiv=1504.07995 }}</ref><ref name="MartiGiuppone2013">{{cite journal |last1=Marti |first1=J. G. |last2=Giuppone |first2=C. A. |last3=Beauge |first3=C. |year=2013 |title=Dynamical analysis of the Gliese-876 Laplace resonance |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=433 |issue=2 |pages=928–934 |arxiv=1305.6768 |bibcode=2013MNRAS.433..928M |doi=10.1093/mnras/stt765|doi-access=free |s2cid=118643833 }}</ref> Three-body resonances involving other simple integer ratios have been termed "Laplace-like"<ref name="ShowalterHamilton2015" /> or "Laplace-type".<ref name="MurrayDermott1999">{{cite book |last1=Murray |first1=C. D. |last2=Dermott |first2=S. F. |year=1999 |title=Solar System Dynamics |url=https://books.google.com/books?id=aU6vcy5L8GAC&pg=PA17 |page=17 |publisher=[[Cambridge University Press]] |isbn=978-0-521-57597-3}}</ref>