Editing Orbital resonance (section)

=== Secular resonance ===
A ''[[secular resonance]]'' occurs when the [[precession#Astronomy|precession]] of two orbits is synchronised (usually a precession of the [[perihelion]] or [[ascending node]]). A small body in secular resonance with a much larger one (e.g. a [[planet]]) will precess at the same rate as the large body. Over long times (a million years, or so) a secular resonance will change the [[eccentricity (orbit)|eccentricity]] and [[inclination]] of the small body.

Several prominent examples of secular resonance involve Saturn. There is a near-resonance between the precession of Saturn's rotational axis and that of Neptune's orbital axis (both of which have periods of about 1.87 million years), which has been identified as the likely source of Saturn's large [[axial tilt]] (26.7°).<ref>{{cite web |last=Beatty |first=J. K. |title=Why Is Saturn Tipsy? |url=http://www.skyandtelescope.com/news/3306806.html?page=1&c=y |work=[[Sky & Telescope]] |date=23 July 2003 |access-date=25 February 2009 |archive-url=https://web.archive.org/web/20090903170550/http://www.skyandtelescope.com/news/3306806.html?page=1&c=y |archive-date=3 September 2009 |url-status=dead }}</ref><ref>{{cite journal |last1=Ward |first1=W. R. |last2=Hamilton |first2=D. P. |year=2004 |title=Tilting Saturn. I. Analytic Model |journal=[[The Astronomical Journal]] |volume=128 |issue=5 |pages=2501–2509 |bibcode=2004AJ....128.2501W |doi=10.1086/424533|doi-access=free }}</ref><ref>{{cite journal |last1=Hamilton |first1=D. P. |last2=Ward |first2=W. R. |year=2004 |title=Tilting Saturn. II. Numerical Model |journal=[[The Astronomical Journal]] |volume=128 |issue=5 |pages=2510–2517 |bibcode=2004AJ....128.2510H |doi=10.1086/424534|s2cid=33083447 }}</ref> Initially, Saturn probably had a tilt closer to that of Jupiter (3.1°). The gradual depletion of the Kuiper belt would have decreased the precession rate of Neptune's orbit; eventually, the frequencies matched, and Saturn's axial precession was captured into a spin-orbit resonance, leading to an increase in Saturn's obliquity. (The angular momentum of Neptune's orbit is 10<sup>4</sup> times that of Saturn's rotation rate, and thus dominates the interaction.) However, it seems that the resonance no longer exists. Detailed analysis of data from the [[Cassini spacecraft]] gives a value of the moment of inertia of Saturn that is just outside the range for the resonance to exist, meaning that the spin axis does not stay in phase with Neptune's orbital inclination in the long term, as it apparently did in the past. One theory for why the resonance came to an end is that there was another moon around Saturn whose orbit destabilized about 100 million years ago, perturbing Saturn.<ref>{{cite journal |last1=Maryame El Moutamid |title=How Saturn got its tilt and its rings |journal=Science |date=Sep 15, 2022 |volume=377 |issue=6612 |pages=1264–1265 |doi=10.1126/science.abq3184|pmid=36108002 |bibcode=2022Sci...377.1264E |s2cid=252309068 }}</ref><ref>{{cite journal|display-authors=etal |last1=Jack Wisdom |title=Loss of a satellite could explain Saturn's obliquity and young rings |journal=Science |date=Sep 15, 2022 |volume=377 |issue=6612 |pages=1285–1289 |doi=10.1126/science.abn1234|pmid=36107998 |bibcode=2022Sci...377.1285W |s2cid=252310492 |hdl=1721.1/148216 |hdl-access=free }}</ref>

The [[secular resonance#?6 resonance|perihelion secular resonance]] between [[asteroid]]s and [[Saturn]] (''ν<sub>6</sub>'' = ''g'' − ''g<sub>6</sub>'') helps shape the asteroid belt (the subscript "6" identifies Saturn as the sixth planet from the Sun). Asteroids which approach it have their eccentricity slowly increased until they become [[Mars-crossing asteroid|Mars-crossers]], at which point they are usually ejected from the [[asteroid belt]] by a close pass to [[Mars]]. This resonance forms the inner and "side" boundaries of the [[asteroid belt]] around 2 [[astronomical unit|AU]], and at inclinations of about 20°.

Numerical simulations have suggested that the eventual formation of a perihelion secular resonance between [[Mercury (planet)|Mercury]] and Jupiter (''g<sub>1</sub>'' = ''g<sub>5</sub>'') has the potential to greatly increase Mercury's eccentricity and possibly destabilize the inner Solar System several billion years from now.<ref name="Laskar2008">{{cite journal |last=Laskar |first=J. |year=2008 |title=Chaotic diffusion in the Solar System |journal=[[Icarus (journal)|Icarus]] |volume=196 |issue=1 |pages=1–15 |arxiv=0802.3371 |bibcode=2008Icar..196....1L |doi=10.1016/j.icarus.2008.02.017|s2cid=11586168 }}</ref><ref name="Laskar2009">{{cite journal |last1=Laskar |first1=J. |last2=Gastineau |first2=M. |year=2009 |title=Existence of collisional trajectories of Mercury, Mars and Venus with the Earth |journal=[[Nature (journal)|Nature]] |volume=459 |issue=7248 |pages=817–819 |bibcode=2009Natur.459..817L |doi=10.1038/nature08096 |pmid=19516336|s2cid=4416436 }}</ref>

The [[Rings of Saturn#Colombo Gap and Titan Ringlet|Titan Ringlet]] within Saturn's [[Rings of Saturn#C Ring|C Ring]] represents another type of resonance in which the rate of [[apsidal precession]] of one orbit exactly matches the speed of revolution of another. The outer end of this eccentric ringlet always points towards Saturn's major moon [[Titan (moon)|Titan]].<ref name="Porco1984">{{cite journal |last1=Porco |first1=C. |author-link=Carolyn Porco |last2=Nicholson |first2=P. D. |author-link2=Phil Nicholson |last3=Borderies |first3=N. |last4=Danielson |first4=G. E. |last5=Goldreich |first5=P. |author-link5=Peter Goldreich |last6=Holdberg |first6=J. B. |last7=Lane |first7=A. L. |year=1984 |title=The eccentric Saturnian ringlets at 1.29R<sub>s</sub> and 1.45R<sub>s</sub> |journal=[[Icarus (journal)|Icarus]] |volume=60 |issue=1 |pages=1–16 |bibcode=1984Icar...60....1P |doi=10.1016/0019-1035(84)90134-9}}</ref>

A ''[[Kozai resonance]]'' occurs when the inclination and eccentricity of a [[perturbation theory|perturbed]] orbit oscillate synchronously (increasing eccentricity while decreasing inclination and vice versa). This resonance applies only to bodies on highly inclined orbits; as a consequence, such orbits tend to be unstable, since the growing eccentricity would result in small [[Apsis|pericenters]], typically leading to a collision or (for large moons) destruction by [[tidal forces]].

In an example of another type of resonance involving orbital eccentricity, the eccentricities of Ganymede and Callisto vary with a common period of 181 years, although with opposite phases.<ref name=Musotto2002>{{cite journal |last1=Musotto |first1=S. |last2=Varad |first2=F. |last3=Moore |first3=W. |last4=Schubert |first4=G. |year=2002 |title=Numerical Simulations of the Orbits of the Galilean Satellites |journal=[[Icarus (journal)|Icarus]] |volume=159 |issue=2 |pages=500–504 |doi=10.1006/icar.2002.6939 |bibcode=2002Icar..159..500M}}</ref>