Editing Orbital resonance (section)

== Possible past mean-motion resonances ==
A past resonance between Jupiter and Saturn may have played a dramatic role in early Solar System history. A 2004 [[Nice model|computer model]] by [[Alessandro Morbidelli (astronomer)|Alessandro Morbidelli]] of the [[Côte d'Azur Observatory|Observatoire de la Côte d'Azur]] in [[Nice]] suggested the formation of a 1:2 resonance between Jupiter and Saturn due to interactions with [[planetesimal]]s that caused them to migrate inward and outward, respectively. In the model, this created a gravitational push that propelled both Uranus and Neptune into higher orbits, and in some scenarios caused them to switch places, which would have doubled Neptune's distance from the Sun. The resultant expulsion of objects from the proto-Kuiper belt as Neptune moved outwards could explain the [[Late Heavy Bombardment]] 600&nbsp;million years after the Solar System's formation and the origin of Jupiter's [[Trojan asteroid]]s.<ref>{{cite web |last=Hansen |first=K. |date=7 June 2004 |title=Orbital shuffle for early solar system |url=http://www.geotimes.org/june05/WebExtra060705.html |work=[[Geotimes]] |access-date=26 August 2007}}</ref> An outward migration of Neptune could also explain the current occupancy of some of its resonances (particularly the 2:5 resonance) within the Kuiper belt.

While Saturn's mid-sized moons Dione and Tethys are not close to an exact resonance now, they may have been in a 2:3 resonance early in the Solar System's history. This would have led to orbital eccentricity and [[tidal heating]] that may have warmed Tethys' interior enough to form a subsurface ocean. Subsequent freezing of the ocean after the moons escaped from the resonance may have generated the extensional stresses that created the enormous [[graben]] system of [[Ithaca Chasma]] on Tethys.<ref name="Chen2008">{{cite conference |last1=Chen |first1=E. M. A. |last2=Nimmo |first2=F. |year=2008 |title=Thermal and Orbital Evolution of Tethys as Constrained by Surface Observations |url=http://www.lpi.usra.edu/meetings/lpsc2008/pdf/1968.pdf |book-title=Lunar and Planetary Science XXXIX |publisher=[[Lunar and Planetary Institute]] |id=#1968 |access-date=14 March 2008}}</ref>

The satellite system of Uranus is notably different from those of Jupiter and Saturn in that it lacks precise resonances among the larger moons, while the majority of the larger moons of Jupiter (3 of the 4 largest) and of Saturn (6 of the 8 largest) are in mean-motion resonances. In all three satellite systems, moons were likely captured into mean-motion resonances in the past as their orbits shifted due to [[Tidal acceleration|tidal dissipation]], a process by which satellites gain orbital energy at the expense of the primary's rotational energy, affecting inner moons disproportionately. In the Uranian system, however, due to the planet's lesser degree of [[Oblate spheroid|oblateness]], and the larger relative size of its satellites, escape from a mean-motion resonance is much easier. Lower oblateness of the primary alters its gravitational field in such a way that different possible resonances are spaced more closely together. A larger relative satellite size increases the strength of their interactions. Both factors lead to more chaotic orbital behavior at or near mean-motion resonances. Escape from a resonance may be associated with capture into a secondary resonance, and/or tidal evolution-driven increases in [[orbital eccentricity]] or [[inclination]].

Mean-motion resonances that probably once existed in the Uranus System include (3:5) Ariel-Miranda, (1:3) Umbriel-Miranda, (3:5) Umbriel-Ariel, and (1:4) Titania-Ariel.<ref name="Tittemore1988">{{cite journal |last1=Tittemore |first1=W. C. |last2=Wisdom |first2=J. |year=1988 |title=Tidal Evolution of the Uranian Satellites I. Passage of Ariel and Umbriel through the 5:3 Mean-Motion Commensurability |journal=[[Icarus (journal)|Icarus]] |volume=74 |issue=2 |pages=172–230 |bibcode=1988Icar...74..172T |doi=10.1016/0019-1035(88)90038-3|hdl=1721.1/57632 |hdl-access=free }}</ref><ref name="Tittemore Wisdom 1990">{{cite journal |last1=Tittemore |first1=W. C. |last2=Wisdom |first2=J. |year=1990 |title=Tidal evolution of the Uranian satellites: III. Evolution through the Miranda-Umbriel 3:1, Miranda-Ariel 5:3, and Ariel-Umbriel 2:1 mean-motion commensurabilities |journal=[[Icarus (journal)|Icarus]] |volume=85 |issue=2 |pages=394–443 |bibcode=1990Icar...85..394T |doi=10.1016/0019-1035(90)90125-S |hdl=1721.1/57632 |hdl-access=free }}</ref> Evidence for such past resonances includes the relatively high eccentricities of the orbits of Uranus' inner satellites, and the anomalously high orbital inclination of Miranda. High past orbital eccentricities associated with the (1:3) Umbriel-Miranda and (1:4) Titania-Ariel resonances may have led to tidal heating of the interiors of Miranda and Ariel,<ref name="Tittemore 1990">{{cite journal |last=Tittemore |first=W. C. |year=1990 |title=Tidal heating of Ariel |journal=[[Icarus (journal)|Icarus]] |volume=87 |issue=1 |pages=110–139 |bibcode=1990Icar...87..110T |doi=10.1016/0019-1035(90)90024-4 }}</ref> respectively. Miranda probably escaped from its resonance with Umbriel via a secondary resonance, and the mechanism of this escape is believed to explain why its orbital inclination is more than 10 times those of the other [[Regular moon|regular]] Uranian moons (see [[Uranus' natural satellites]]).<ref name="Tittemore1989">{{cite journal |last1=Tittemore |first1=W. C. |last2=Wisdom |first2=J. |year=1989 |title=Tidal Evolution of the Uranian Satellites II. An Explanation of the Anomalously High Orbital Inclination of Miranda |journal=[[Icarus (journal)|Icarus]] |volume=78 |issue=1 |pages=63–89 |bibcode=1989Icar...78...63T |doi=10.1016/0019-1035(89)90070-5 |url=http://dspace.mit.edu/bitstream/1721.1/57632/2/19834233-MIT.pdf|hdl=1721.1/57632 |hdl-access=free }}</ref><ref>{{cite journal |last1=Malhotra |first1=R. |last2=Dermott |first2=S. F |year=1990 |title=The Role of Secondary Resonances in the Orbital History of Miranda |journal=[[Icarus (journal)|Icarus]] |volume=85 |issue=2 |pages=444–480 |bibcode=1990Icar...85..444M |doi=10.1016/0019-1035(90)90126-T|doi-access=free }}</ref>

Similar to the case of Miranda, the present inclinations of Jupiter's moonlets Amalthea and [[Thebe (moon)|Thebe]] are thought to be indications of past passage through the 3:1 and 4:2 resonances with Io, respectively.<ref name="Burns2004">{{cite book |last1=Burns |first1=J. A. |last2=Simonelli |first2=D. P. |last3=Showalter |first3=M. R. |last4=Hamilton |first4=D. P. |last5=Porco |first5=Carolyn C. |last6=Esposito |first6=L. W. |last7=Throop |first7=H. |year=2004 |chapter=Jupiter's Ring-Moon System |chapter-url=http://www.astro.umd.edu/~hamilton/research/preprints/BurSimSho03.pdf |editor=Bagenal, Fran |editor2=Dowling, Timothy E. |editor3=McKinnon, William B. |title=Jupiter: The Planet, Satellites and Magnetosphere |url=http://google.com/books?id=aMERHqj9ivcC&printsec=frontcover |publisher=[[Cambridge University Press]] |isbn=978-0-521-03545-3}}</ref>

Neptune's regular moons Proteus and Larissa are thought to have passed through a 1:2 resonance a few hundred million years ago; the moons have drifted away from each other since then because Proteus is outside a [[synchronous orbit]] and Larissa is within one. Passage through the resonance is thought to have excited both moons' eccentricities to a degree that has not since been entirely damped out.<ref name="ZhangHamilton2007" /><ref name="ZhangHamilton2008" />

In the case of [[Pluto]]'s satellites, it has been proposed that the present near resonances are relics of a previous precise resonance that was disrupted by tidal damping of the eccentricity of Charon's orbit (see [[Pluto's natural satellites]] for details). The near resonances may be maintained by a 15% local fluctuation in the Pluto-Charon gravitational field. Thus, these near resonances may not be coincidental.

The smaller inner moon of the [[dwarf planet]] [[Haumea (dwarf planet)|Haumea]], [[Namaka (moon)|Namaka]], is one tenth the mass of the larger outer moon, [[Hiʻiaka (moon)|Hiʻiaka]]. Namaka revolves around Haumea in 18 days in an eccentric, [[Osculating orbit|non-Keplerian]] orbit, and as of 2008 is inclined 13° from Hiʻiaka.<ref name="Ragozzine&Brown2009" /> Over the timescale of the system, it should have been tidally damped into a more circular orbit. It appears that it has been disturbed by resonances with the more massive Hiʻiaka, due to converging orbits as it moved outward from Haumea because of tidal dissipation. The moons may have been caught in and then escaped from orbital resonance several times. They probably passed through the 3:1 resonance relatively recently, and currently are in or at least close to an 8:3 resonance. Namaka's orbit is strongly [[Perturbation (astronomy)|perturbed]], with a current precession of about −6.5° per year.<ref name="Ragozzine&Brown2009" />