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| In [[astronomy]], a '''resonant trans-Neptunian object''' is a [[trans-Neptunian object]] (TNO) in mean motion [[orbital resonance]] with [[Neptune]]. The orbital periods of the resonant objects are in a simple integer relations with the period of Neptune e.g. 1:2, 2:3 etc. Resonant TNOs can be either part of the main [[Kuiper belt]] population, or the more distant [[scattered disc]] population.<ref>Hahn J. Malhotra R.''Neptune's migration into a stirred-up Kuiper Belt'' The Astronomical Journal, '''130''', pp.2392-2414, Nov.2005.[http://arxiv.org/abs/astro-ph/0507319 Full text on arXiv].</ref>
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| ==Distribution==
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| [[File:TheTransneptunians 73AU.svg|right|thumb|450px|Distribution of trans-Neptunian objects. Resonant objects are in red.]]
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| The diagram illustrates the distribution of the known trans-Neptunian objects (up to 70 AU) in relation to the orbits of the planets together with [[Centaur (planetoid)|centaurs]] for reference.
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| Resonant objects are plotted in red.
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| Orbital resonances with Neptune are marked with vertical bars; 1:1 marks the position of Neptune’s orbit (and its [[Neptune trojan|trojans]]), 2:3 marks the orbit of Pluto and [[plutinos]], and 1:2, 2:5 etc. mark a number of smaller families.
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| The designation ''2:3'' or ''3:2'' refer both to the same resonance for TNOs. There’s no confusion possible as TNOs, by definition, have periods longer than Neptune. The usage depends on the author and the field of research. The statement "Pluto is in '''2''':'''3''' resonance to Neptune" appears better to capture the meaning: Pluto completes '''2''' orbits for every '''3''' orbits of Neptune.
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| ==Origin==
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| {{For|details of the evolution of Neptune's orbit|Nice model}}
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| Detailed analytical and numerical studies<ref name="Malhotra96">Malhotra, Renu ''The Phase Space Structure Near Neptune Resonances in the Kuiper Belt''. Astronomical Journal v.111, p.504 [http://arxiv.org/abs/astro-ph/9509141 preprint]</ref><ref name="Chiang2002">E. I. Chiang and A. B. Jordan, ''On the Plutinos and Twotinos of the Kuiper Belt'', The Astronomical Journal, '''124''' (2002), pp.3430–3444. [http://www.iop.org/EJ/article/1538-3881/124/6/3430/202320.html (html)]</ref>
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| of Neptune’s resonances have shown that they are quite "narrow" (i.e. the objects must have a relatively precise range of energy). If the object [[semi-major axis]] is outside these narrow ranges, the orbit becomes chaotic, with widely changing orbital elements.
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| As TNOs were discovered, a substantial (more than 10%) proportion were found to be in 2:3 resonances, far from a random distribution. It is now believed that the objects have been ''collected'' from wider distances by sweeping resonances during the migration of Neptune.<ref name="Malhotra95">Renu Malhotra, ''The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune'', The Astronomical Journal, '''110''' (1995), p. 420 [http://arxiv.org/abs/astro-ph/9504036 Preprint].</ref>
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| Well before the discovery of the first TNO, it was suggested that interaction between [[giant planet]]s and a massive disk of small particles would, via [[angular momentum|momentum]] transfer, make Jupiter migrate inwards while Saturn, Uranus and especially Neptune would migrate outwards. During this relatively short period of time, Neptune’s resonances would be ''sweeping'' the space, trapping objects on initially-varying heliocentric orbits into resonance.<ref name="Mahotra2000">
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| Malhotra, R.; Duncan, M. J.; Levison, H. F. ''Dynamics of the Kuiper Belt''. Protostars and Planets IV, University of Arizona Press, p. 1231 [http://arxiv.org/abs/astro-ph/9901155 preprint]</ref>
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| ==Known populations==
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| ===2:3 resonance ("plutinos", period ~250 years)===
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| {{main|Plutino}}
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| [[File:Orcus-motion.png|thumb|right|150px|The motion of [[90482 Orcus|Orcus]] in a [[rotating frame]] with a period equal to [[Neptune]]'s [[orbital period]]. (Neptune is held stationary.)]]
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| [[File:ThePlutinos Size Albedo Color2.svg|thumb|right|150px|Pluto and its moons (top) compared in size, [[albedo]] and [[color index|colour]] with [[90482 Orcus|Orcus]] and [[28978 Ixion|Ixion]].]]
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| The 2:3 resonance at 39.4 AU is by far the dominant category among the resonant objects, with 92 confirmed and 104 possible member bodies.<ref>[http://www.johnstonsarchive.net/astro/tnos.html Trans-Neptunian objects<!-- Bot generated title -->]</ref> The objects following orbits in this resonance are named [[plutino]]s after [[Pluto]], the first such body discovered. Large, numbered plutinos include:<ref name="MPC_classified">List of the classified orbits [http://cfa-www.harvard.edu/mpec/K08/K08S05.html from MPC] October, 2008</ref>
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| *[[90482 Orcus]]
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| *{{mpl|(84922) 2003 VS|2}}
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| *{{mpl|2003 AZ|84}}
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| *[[28978 Ixion]]
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| *[[38628 Huya]]
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| ===3:5 resonance (period ~275 years)===
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| A population of 10 objects at 42.3 AU as of October, 2008, including:<ref name="MPC_classified"/>
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| * {{mpl|126154|2001 YH|140}}
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| * {{mpl|(15809) 1994 JS|}}
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| * {{mp|(143751) 2003 US|292}}
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| ===4:7 resonance (period ~290 years)===
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| Another important population of objects (20 identified as of October 2008) is orbiting the Sun at 43.7 AU (in the midst of the [[Cubewano|classical objects]]). The objects are rather small (with a single exception, [[absolute magnitude|H]]>6) and most of them follow orbits close to the [[ecliptic]].
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| Objects with well established orbits include:<ref name="MPC_classified"/>
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| * [[1999 CD158|{{mp|1999 CD|158}}]], the largest
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| * {{mp|(119956) 2002 PA|149}}
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| <!-- in order of H. Commented out to avoid red links
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| * {{mpl|(160147) 2001 KN|76}}
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| * {{mpl|(119067) 2001 KP|76}}
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| * {{mpl|(119066) 2001 KJ|76}}
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| * {{mpl|(135024) 2001 KO|76}}
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| -->
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| * {{mpl|(119070) 2001 KP|77}}
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| <!--
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| * {{mpl|(135742) 2002 PB|171}}
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| -->
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| * {{mpl|(118378) 1999 HT|11}}
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| <!--
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| * {{mpl|(134568) 1999 RH|215}}
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| -->
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| * {{mp|(118698) 2000 OY|51}}
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| ===1:2 resonance ("twotinos", period ~330 years)===
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| This resonance at 47.8 AU is often considered as the outer "edge" of the [[Kuiper belt]] and the objects in this resonance are sometimes referred to as ''twotinos''. Twotinos have inclinations less than 15 degrees and generally moderate eccentricities (0.1 < e < 0.3).<ref name="Malhotra2008"/> An unknown number of the 2:1 resonants likely did not originate in a planetesimal disk that was swept by the resonance during Neptune's migration.<ref name="LykDyn">{{cite journal|author=Lykawka, Patryk Sofia & Mukai, Tadashi|year=2007| title= Dynamical classification of trans-neptunian objects: Probing their origin, evolution, and interrelation|journal = Icarus|volume=189|issue=1|month=July |pages=213–232| doi=10.1016/j.icarus.2007.01.001|bibcode=2007Icar..189..213L}}</ref>
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|
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| There are far fewer objects in this resonance (a total of 14 as of October, 2008) than plutinos.
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| Long-term orbital integration shows that the 1:2 resonance is less stable than 2:3 resonance; only 15% of the objects in 1:2 resonance were found to survive 4 [[Gya|Gyr]] as compared with 28% of the plutinos.<ref name="Malhotra2008"/> Consequently it might be that twotinos were originally as numerous as plutinos, but their population has dropped significantly below that of plutinos since.<ref name="Malhotra2008">{{cite journal
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| |author=M. Tiscareno, R. Malhotra
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| |title=Chaotic Diffusion of Resonant Kuiper Belt Objects
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| |volume=194|date=April 2008
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| |id=
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| |arxiv=0807.2835
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| |bibcode = 2009AJ....138..827T |doi = 10.1088/0004-6256/138/3/827
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| |journal=The Astronomical Journal
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| |issue=3
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| |pages=827–837 }}</ref>
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| Objects with well established orbits include (in order of the [[absolute magnitude]]):<ref name="MPC_classified"/>
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| * {{mpl|(119979) 2002 WC|19}}
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| * {{mpl| (26308) 1998 SM|165}}
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| * {{mpl|(137295) 1999 RB|216}}
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| * {{mpl| (20161) 1996 TR|66}}
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| * {{mpl|(130391) 2000 JG|81}}
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| <!-- unnumbered {{mpl|1997 SZ|10}}
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| * {{mpl|1999 RB|216}}-->
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| [[File:TheResonantTNO 90AU.svg|right|thumb|500px|Selected resonant objects (in red).]]
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| ===2:5 resonance (period ~410 years)===
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| Objects with well established orbits at 55.4 AU include:<ref name="MPC_classified"/>
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| *{{mpl|(84522) 2002 TC|302}}, a large dwarf-planet candidate
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| *{{mp|(143707) 2003 UY|117}}
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| *{{mpl|(119068) 2001 KC|77}}
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| *{{mp|(135571) 2002 GG|32}}
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| *{{mpl|(69988) 1998 WA|31}}
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| In total, the orbits of 11 objects are classified as 2:5 as of October, 2008.
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| ===Other resonances===
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| [[File:Haumea.GIF|250px|thumb|right|The nominal 7:12 libration of [[Haumea (dwarf planet)|Haumea]] in a [[rotating frame]]. Where red turns to green is where it crosses the ecliptic.]]
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| So called higher-order resonances are known for a limited number of objects, including the following numbered objects<ref name="MPC_classified"/>
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| *'''4:5''' (35 AU, ~205 years) {{mpl+|131697|2001 XH|255}}
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| *'''3:4''' (36.5 AU, ~220 years) {{mp|(143685) 2003 SS|317}}, {{mpl+|15836|1995 DA|2}}
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| *'''5:9''' (44.5 AU, ~295 years) {{mp|2002 GD|32}}<ref name=GD32>{{cite web
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| |author=[[Marc W. Buie]]
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| |date=2005-04-11 using 20 observations
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| |title=Orbit Fit and Astrometric record for 02GD32
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| |publisher=SwRI (Space Science Department)
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| |url=http://www.boulder.swri.edu/~buie/kbo/astrom/02GD32.html
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| |accessdate=2009-02-05}}</ref>
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| *'''4:9''' (52 AU, ~370 years) {{mpl+|42301|2001 UR|163}}, {{mp|(182397) 2001 QW|297}}<ref name=QW197>{{cite web
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| |author=[[Marc W. Buie]]
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| |date=2007-11-09 using 23 observations
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| |title=Orbit Fit and Astrometric record for 182397
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| |publisher=SwRI (Space Science Department)
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| |url=http://www.boulder.swri.edu/~buie/kbo/astrom/182397.html
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| |accessdate=2009-01-29}}</ref>
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| *'''3:7''' (53 AU, ~385 years) {{mpl+|131696|2001 XT|254}}, {{mpl+|95625|2002 GX|32}}, {{mp|(183964) 2004 DJ|71}}, {{mp|(181867) 1999 CV|118}}
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| *'''5:12''' (55 AU, ~395 years) {{mpl+|79978|1999 CC|158}}, {{mp|(119878) 2001 CY|224}}<ref name=CY224>{{cite web
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| |author=[[Marc W. Buie]]
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| |date=2005-12-06 using 41 observations
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| |title=Orbit Fit and Astrometric record for 119878
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| |publisher=SwRI (Space Science Department)
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| |url=http://www.boulder.swri.edu/~buie/kbo/astrom/119878.html
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| |accessdate=2009-01-29}}</ref> (84% probability according to Emel’yanenko)
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| *'''3:8''' (57 AU, ~440 years) {{mpl+|82075|2000 YW|134}}<ref name=YW134>{{cite web
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| |author=[[Marc W. Buie]]
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| |date=2004-04-16 using 62 of 63 observations
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| |title=Orbit Fit and Astrometric record for 82075
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| |publisher=SwRI (Space Science Department)
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| |url=http://www.boulder.swri.edu/~buie/kbo/astrom/82075.html
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| |accessdate=2009-01-29}}</ref> (84% probability according to Emel’yanenko)
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| *'''3:10''' (67 AU, ~549 years) {{mpl+|225088|2007 OR|10}}
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| *'''2:7''' (70 AU, ~580 years) {{mp|2006 HX|122}}<ref name=MPC2008-K28>{{cite web
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| |title=MPEC 2008-K28 : 2006 HX122
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| |date=2008-05-23
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| |publisher=Minor Planet Center
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| |url=http://www.cfa.harvard.edu/mpec/K08/K08K28.html
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| |accessdate=2009-01-30}}</ref> (The preliminary orbit suggests a weak 2:7 resonance. Further observations will be required.)
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| A few objects are known on simple, distant resonances<ref name="MPC_classified"/>
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| *'''1:3''' (62.5 AU, ~495 years) {{mpl+|136120|2003 LG|7}}
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| *'''1:4''' (76 AU, ~660 years) {{mpl|2003 LA|7}}<ref name=LA7>{{cite web
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| |author=[[Marc W. Buie]]
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| |date=2007-04-21 using 13 of 14 observations
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| |title=Orbit Fit and Astrometric record for 03LA7
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| |publisher=SwRI (Space Science Department)
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| |url=http://www.boulder.swri.edu/~buie/kbo/astrom/03LA7.html
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| |accessdate=2009-01-29}}</ref>
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| *'''1:5''' (88 AU, ~820 years) {{mp|2003 YQ|179}} ([[Orbital resonance#Coincidental 'near' ratios of mean motion|likely coincidental]])<ref name=YQ179>{{cite web
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| |author=[[Marc W. Buie]]
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| |date=2008-03-03 using 23 of 24 observations
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| |title=Orbit Fit and Astrometric record for 03YQ179
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| |publisher=SwRI (Space Science Department)
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| |url=http://www.boulder.swri.edu/~buie/kbo/astrom/03YQ179.html
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| |accessdate=2009-01-29}}</ref>
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| Some notable ''unproven'' (they could be coincidental) [[dwarf planet]] resonances include:
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| *'''7:12''' (43 AU, ~283 years) [[Haumea (dwarf planet)|Haumea]]<ref name="candidate">
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| {{cite journal
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| |title=Candidate Members and Age Estimate of the Family of Kuiper Belt Object 2003 EL<sub>61</sub>
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| |author=D. Ragozzine; M. E. Brown
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| |journal=The Astronomical Journal
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| |volume=134|issue=6|pages= 2160–2167
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| |date=2007-09-04
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| |bibcode=2007AJ....134.2160R
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| |accessdate=2008-09-19
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| |doi=10.1086/522334
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| |arxiv=0709.0328}}</ref> (nominal orbit very likely in resonance)
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| *'''6:11''' (45 AU, ~302 years) [[Makemake (dwarf planet)|Makemake]]<ref name=Dunn/> ({{mpl|(182294) 2001 KU|76}} appears to be in the 6:11 resonance)
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| *'''5:17''' (67 AU, ~560 years) [[Eris (dwarf planet)|Eris]]<ref name=Dunn>{{cite web
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| |title=Possible resonances of Eris (2003 UB<sub>313</sub>) and Makemake (2005 FY<sub>9</sub>)
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| |publisher=Gravity Simulator
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| |author=Tony Dunn
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| |url=http://www.orbitsimulator.com/gravity/articles/newtno.html
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| |accessdate=2009-01-29}}</ref> ({{mpl|2007 OR|10}} has a similar orbit)
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| ===1:1 resonance (Neptune trojans, period ~165 years)===
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| {{main|Neptune trojan}}
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| A few objects have been discovered following orbits with semi-major axes similar to that of Neptune, near the [[Sun]]–[[Neptune]] [[Lagrangian point]]s. These [[Neptune trojan]]s, termed by analogy to the [[Jupiter Trojan|(Jupiter) Trojan asteroids]], are in 1:1 resonance with Neptune. Nine are known as of October 2012:
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| *{{mpl|2001 QR|322}}
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| *{{mpl|2004 UP|10}}
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| *{{mpl|2005 TN|53}}
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| *{{mpl|2005 TO|74}}
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| *{{mpl|2006 RJ|103}}
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| *{{mpl|2007 VL|305}}
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| *{{mpl|2008 LC|18}}
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| *{{mpl|2004 KV|18}}
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| *{{mpl|2011 HM|102}}
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| Only the last three objects are near Neptune's {{L5}} [[Lagrangian point]]; the others are located in Neptune's {{L4}} region.<ref name=ntrojans>{{cite web
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| |title=List Of Neptune Trojans
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| |publisher=Minor Planet Center
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| |url=http://www.minorplanetcenter.org/iau/lists/NeptuneTrojans.html
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| |accessdate=2013-01-08}}</ref>
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| ==Coincidental versus true resonances==
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| One of the concerns is that weak resonances may exist and would be difficult to prove due to the current lack of accuracy in the orbits of these distant objects. Many objects have [[orbital period]]s of more than 300 years and most have only been observed over a short observation [[Arc (geometry)|arc]] of a couple years. Due to their great distance and slow movement against background stars, it may be decades before many of these distant orbits are determined well enough to confidently confirm whether a resonance is true or merely [[Orbital resonance#Coincidental 'near' ratios of mean motion|coincidental]]. A true resonance will smoothly oscillate while a coincidental near resonance will circulate. (See [[Resonant_trans-Neptunian_object#Toward_a_formal_definition|Toward a formal definition]])
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| Simulations by Emel’yanenko and Kiseleva in 2007 show that {{mpl|(131696) 2001 XT|254}} is librating in a 7:3 resonance with Neptune.<ref name=Emel2008>{{cite journal
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| |last=Emel’yanenko |first=V. V
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| |coauthors=Kiseleva, E. L.
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| |title=Resonant motion of trans-Neptunian objects in high-eccentricity orbits
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| |journal=Astronomy Letters
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| |volume=34 |pages=271–279 |year=2008
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| |bibcode=2008AstL...34..271E
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| |accessdate=2009-01-30
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| |doi=10.1134/S1063773708040075
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| |issue=4 }}</ref> This libration can be stable for less than 100 million to billions of years.<ref name=Emel2008/>
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| [[File:2001XT254 Resonance.jpg|400px|thumb|none|The orbital period of 2001 XT<sub>254</sub> around the 7:3 (2.333) resonance of Neptune.]]
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| Emel’yanenko and Kiseleva also show that {{mpl|(48639) 1995 TL|8}} appears to have less than a 1% probability of being in a 7:3 resonance with Neptune, but it does [[Orbital resonance#Coincidental 'near' ratios of mean motion|execute circulations near this resonance]].<ref name=Emel2008/>
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| [[File:1995TL8 Orbital Period.jpg|400px|thumb|none|The orbital period of 1995 TL<sub>8</sub> missing the 7:3 (2.333) resonance of Neptune.]]
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| ==Toward a formal definition==
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| The classes of TNO have no universally agreed precise definitions, the boundaries are often unclear and the notion of resonance is not defined precisely. The [[Deep Ecliptic Survey]] introduced formally defined dynamical classes based on long-term forward integration of orbits under the combined perturbations from all four giant planets. (see also [[cubewano#Toward a formal definition|formal definition of classical KBO]])
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| In general, the mean motion resonance may involve not only orbital periods of the form
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| :<math> \rm p\cdot\lambda - \rm q\cdot\lambda_{\rm N} </math>
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| where p and q are small integers, λ and λ<sub>N</sub> are respectively the [[mean longitude]]s of the object and Neptune, but can also involve the [[longitude of the periapsis|longitude of the perihelion]] and the longitudes of the [[orbital nodes|nodes]] (see [[orbital resonance#Mean motion resonances in the Solar System|orbital resonance]], for elementary examples)
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| An object is a Resonant if for some small integers p,q,n,m,r,s, the argument (angle) defined below is ''librating'' (i.e. is bounded)<ref name="DES_Elliot2006" >
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| J. L. Elliot, S. D. Kern, K. B. Clancy, A. A. S. Gulbis, R. L. Millis, M. W. Buie, L. H. Wasserman, E. I. Chiang, A. B. Jordan, D. E. Trilling, and K. J. Meech
| |
| ''The Deep Ecliptic Survey: A Search for Kuiper Belt Objects and Centaurs. II. Dynamical Classification, the Kuiper Belt Plane, and the Core Population.''
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| The Astronomical Journal, '''129''' (2006), pp.
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| [http://alpaca.as.arizona.edu/~trilling/des2.pdf preprint]</ref>
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| :<math> \phi = \rm p\cdot\lambda - \rm q\cdot\lambda_{\rm N} - \rm m\cdot\varpi - \rm n\cdot\Omega - \rm r\cdot\varpi_{\rm N} -\rm s\cdot\Omega_{\rm N}</math>
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| where the <math>\varpi</math> are the [[longitude of the periapsis|longitudes of perihelia]] and the <math>\Omega</math> are the longitudes of the [[ascending node]]s, for Neptune (with subscripts "N") and the resonant object (no subscripts).
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| The term ''libration'' denotes here periodic oscillation of the angle around some value and is opposed to ''circulation'' where the angle can take all values from 0 to 360°. For example, in the case of Pluto, the resonant angle <math>\phi</math> librates around 180° with an amplitude of around 82° degrees, i.e. the angle changes periodically from 180°-82° to 180°+82°.
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| All new plutinos discovered during the [[Deep Ecliptic Survey]] proved to be of the type
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| :<math> \phi = \rm 3\cdot\lambda - \rm 2\cdot\lambda_{\rm N} - \varpi </math>
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| similar to Pluto's mean motion resonance.
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| More generally, this 2:3 resonance is an example of the resonances p:(p+1) (example 1:2, 2:3, 3:4 etc.) that have proved to lead to stable orbits.<ref name="Malhotra95"/> Their resonant angle is
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| :<math> \phi = \rm p\cdot\lambda - \rm q\cdot\lambda_{\rm N} - (\rm p-\rm q)\cdot\varpi </math>
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| In this case, the importance of the resonant angle <math>\phi\,</math> can be understood by noting that when the object is at perihelion, i.e. <math>\lambda = \varpi </math>, then
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| :<math>\phi = q\cdot ( \varpi - \lambda_{\rm N})</math> | |
| i.e. <math>\phi\,</math> gives a measure of the distance of the object's perihelion from Neptune.<ref name="Malhotra95"/>
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| The object is protected from the perturbation by keeping its perihelion far from Neptune provided <math>\phi\,</math> librates around an angle far from 0°.
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| == Classification methods ==
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| As the orbital elements are known with a limited precision, the uncertainties may lead to [[false positive]]s (i.e. classification as resonant of an orbit which is not).
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| A recent approach<ref name="ArizonaBook_Gladman2007">
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| {{cite journal
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| |author=[[Brett J. Gladman|B. Gladman]], [[Brian G. Marsden|B. Marsden]], C. VanLaerhoven
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| |title=Nomenclature in the Outer Solar System
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| |journal=In '''The Solar System Beyond Neptune''', ISBN 9780816527557
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| |year=2008
| |
| }}
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| </ref> considers not only the current [[best-fit]] orbit but also two additional orbits corresponding to the uncertainties of the observational data. In simple terms, the algorithm determines whether the object would be still classified as resonant if its actual orbit differed from the best fit orbit, as the result of the errors in the observations.
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| The three orbits are numerically integrated over a period of 10 million years. If all three orbits remain resonant (i.e. the argument of the resonance is librating, see [[Resonant_trans-Neptunian_object#Toward_a_formal_definition|formal definion]]), the classification as a resonant object is considered secure.<ref name="ArizonaBook_Gladman2007"/>
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| If only two out of the three orbits are librating the object is classified as ''probably'' in resonance. Finally, if only one orbit passes the test, the ''vicinity'' of the resonance is noted to encourage further observations to improve the data.<ref name="ArizonaBook_Gladman2007"/>
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| The two extreme values of the semi-major axis used in the algorithm are determined to correspond to uncertainties of the data of at most 3 [[standard deviation]]s. Such range of semi-axis values should, with a number of assumptions, reduce the probability that the actual orbit is beyond this range to less than 0.3%.
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| The method is applicable to objects with observations spanning at least 3 oppositions.<ref name="ArizonaBook_Gladman2007"/>
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| ==References==
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| {{reflist|2}}
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| == Further reading ==
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| <!-- Some of these will be progressively included as refs -->
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| *
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| * {{cite book|title=The First Decadal Review of the Edgeworth-Kuiper Belt|editor=John K. Davies and Luis H. Barrera|publisher=Springer|date=2004-08-03|isbn=1-4020-1781-2}}
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| * {{cite journal|title=Resonant and Secular Families of the Kuiper Belt|journal=Earth, Moon, and Planets|publisher=Springer Netherlands|volume=92|issue=1–4|date=June 2003|doi=10.1023/B:MOON.0000031924.20073.d0|pages=49–62|author=E. I. Chiang, J. R. Lovering, R. L. Millis, M. W. Buie, L. H. Wasserman, and K. J. Meech|bibcode = 2003EM&P...92...49C }}
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| * {{cite journal | journal=The [[Astronomical Journal]] | volume=126 | pages=430–443 | date=2003-01-21|publisher=The American Astronomical Society | url=http://www.iop.org/EJ/article/1538-3881/126/1/430/203022.html | title=Resonance occupation in the Kuiper Belt: case examples of the 5:2 and trojan resonances|author=E. I. Chiang, A. B. Jordan, R. L. Millis, M. W. Buie, L. H. Wasserman, J. L. Elliot, S. D. Kern, D. E. Trilling, K. J. Meech, and R. M. Wagner | doi=10.1086/375207 | bibcode=2003AJ....126..430C|arxiv = astro-ph/0301458 | issue=1}}
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| * {{cite journal|title=The Kuiper Belt as a Debris Disk|author=Renu Malhotra|url=http://www.lpl.arizona.edu/faculty/malhotra_preprints/04-TPF_Darwin.pdf}} ([http://www.lpl.arizona.edu/faculty/malhotra_preprints/ISP_Nov04.html as HTML])
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| {{Solar System}}
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| {{DEFAULTSORT:Resonant Trans-Neptunian Object}}
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| [[Category:Resonant trans-Neptunian objects| ]]
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