# Resonant trans-Neptunian object <!-- SOLSIM:BEGIN g31 — Solar System explorer state (hand-built on wt-core, specs/solar/); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *The Kuiper belt in the Solar System explorer* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/solar/Solar_System.html?obj=kuiper&embed=1" data-title="The Kuiper belt in the Solar System explorer"></div> *The Solar System explorer locked on this article's state (`?obj=kuiper`); every object and population of the [[PORTAL_Solar_System|Solar System portal]] has its own state in the same scene.* <!-- SOLSIM:END --> *Try: under show, choose small bodies and locate the plutino ring at 39.4 AU, the one resonance the explorer draws; scroll out until the belt's outer edge near 50 AU is in view, close to where the 1:2 resonance lies at 47.7 AU; then set show back to everything and the speed to 100 years/s and time Neptune's laps, about 1.6 seconds each, against which every resonance here is a simple ratio.* A **resonant trans-Neptunian object** is a body beyond [[Neptune]], a [[Trans-Neptunian_object|trans-Neptunian object]] or TNO, that is locked in a mean-motion [[Resonance|resonance]] with the planet: its orbital period stands in a ratio of small whole numbers, such as 2:3 or 1:2, to Neptune's.[^elliot2005][^hahn2005] Resonant objects occur both in the main [[Kuiper_belt|Kuiper belt]] and in the more distant [[Scattered_disc|scattered disc]].[^hahn2005] The best-known are the [[Plutino|plutinos]], including [[Pluto]], which orbit twice for every three orbits of Neptune. Resonance protects. Many resonant objects, Pluto among them, cross Neptune's orbit in projection, yet the timing locked in by the resonance keeps them from meeting the planet.[^malhotra1995] Their concentration in resonances, far from random, is widely taken as evidence that Neptune migrated outward early in the Solar System's history and swept objects into its resonances as it went.[^malhotra1995][^malhotra2000] Proving that a particular object is resonant requires integrating its orbit forward and showing that a characteristic angle oscillates rather than circulating.[^elliot2005][^gladman2008] The explorer at the top of this page is locked on the Kuiper belt. It draws the belt as a cloud of ILLUSTRATIVE points and marks only one resonance, the 2:3, with a ring at 39.4 AU; the other resonances described here lie within and beyond the cloud but are not drawn.[^jpl-t1] ## Distribution Each resonance sits at a definite distance. If an object's period is q/p times Neptune's 164.8 years, [[Kepler's_laws_of_planetary_motion|Kepler's third law]] puts its semi-major axis at 30.07 × (q/p)^(2/3) AU.[^jpl-t1][^nasa-fs-n] The main resonances therefore fall at the following positions (all derived): | Resonance | Semi-major axis (AU) | Period (years) | Common name | |---|---|---|---| | 1:1 | 30.1 | 164.8 | Neptune trojans | | 3:4 | 36.4 | 219.7 | | | 2:3 | 39.4 | 247.2 | plutinos | | 3:5 | 42.3 | 274.6 | | | 4:7 | 43.7 | 288.4 | | | 1:2 | 47.7 | 329.6 | twotinos | | 2:5 | 55.4 | 412.0 | | | 1:3 | 62.5 | 494.4 | | A plot of known TNOs by semi-major axis shows resonant objects stacked in narrow vertical columns at these values, spanning a wide range of eccentricities, while non-resonant [[Classical_Kuiper_belt_object|classical objects]] fill the gaps between 42 and 48 AU at low eccentricity.[^elliot2005] Some authors write the plutino resonance as 3:2 rather than 2:3; there is no ambiguity, since a TNO's period is always the longer. ## Origin Analytical and numerical studies show that a resonance can hold an object only within a narrow range of orbital energies, and so of semi-major axes. Outside that range the orbit becomes chaotic, its elements wandering widely.[^malhotra1996][^chiang2002] When TNOs began to be found, more than 10% turned out to lie in the 2:3 resonance, far more than chance would allow.[^malhotra1995] The accepted explanation predates most of the discoveries. Exchanges of [[Angular_momentum|angular momentum]] between the giant planets and a massive disc of planetesimals would push [[Jupiter]] slightly inward and [[Saturn]], [[Uranus]] and especially Neptune outward.[^malhotra2000] As Neptune moved, its resonances moved with it, sweeping through the disc. Objects overtaken by a resonance were captured and carried outward, and while they were carried their eccentricities grew.[^malhotra1995] Renu Malhotra used this mechanism in 1995 to explain Pluto's eccentric, Neptune-crossing orbit, and it predicted a population of objects sharing Pluto's resonance.[^malhotra1995] Planet migration of this kind is part of broader models such as the [[Nice_model|Nice model]]. Not every resonant object need have been swept up: some twotinos, for example, were probably captured after they had already been scattered.[^lykawka2007] ## Known populations Counts of resonant objects depend on the classification method and grow as orbits improve; the figures below are those reported by the Deep Ecliptic Survey (DES) and Johnston's Archive.[^buie-des][^johnston] ### 1:1 resonance (Neptune trojans, period 164.7 years) Neptune trojans share Neptune's orbit, librating around the Lagrangian points 60° ahead (L4) or behind (L5) the planet, like the [[Jupiter_trojan|Jupiter trojans]].[^chiang2003] Thirty-one were known in February 2024, almost all near L4; only three are near L5, and one of those is uncertain.[^mpc-nt][^buie-des] One object, 2001 XA255, is a "jumping trojan", currently moving from L4 to L5.[^delafuente2012] ### 2:3 resonance ("plutinos", period 247.0 years) The 2:3 resonance at 39.4 AU is by far the most populated. In February 2020 it held 383 confirmed and 99 possible members, 338 of them secured by DES simulations.[^johnston][^buie-des] Its members are named plutinos after Pluto; large ones include [[Orcus_(dwarf_planet)|Orcus]], Achlys, Ixion, Huya and Lempo.[^johnston] ### 3:5 resonance (period 274.5 years) In February 2020, 47 objects were confirmed in the 3:5 resonance at about 42.2 AU.[^buie-des][^johnston] ### 4:7 resonance (period 288.2 years) The 4:7 resonance at 43.6 AU lies in the midst of the classical belt. Its members are mostly small, with only two brighter than absolute magnitude 6, and most orbit close to the ecliptic; 55 had secured orbits in February 2020, including 385446 Manwë.[^buie-des][^johnston] ### 1:2 resonance ("twotinos", period 329.4 years) The 1:2 resonance at 47.7 AU is often taken as the outer edge of the Kuiper belt, and its members are sometimes called twotinos. They have inclinations under 15° and eccentricities of about 0.1–0.3.[^tiscareno2009] The DES had confirmed 126 in February 2020, far fewer than the plutinos.[^buie-des] Long integrations suggest why: only about 15% of twotinos survive 4 billion years, against 28% of plutinos, so the twotinos may once have been about as numerous.[^tiscareno2009] ### 2:5 resonance (period 411.7 years) Fifty-seven objects were confirmed in the 2:5 resonance at 55.4 AU in February 2020, including 472235 Zhulong.[^buie-des][^johnston] This resonance lies well beyond the main belt, among the scattered objects. ### 1:3 resonance (period 494.1 years) Johnston's Archive counted 14 objects in the 1:3 resonance at 62.5 AU in February 2020, a dozen of them secure according to the DES.[^johnston][^buie-des] ### Other resonances Many higher-order resonances hold smaller numbers of confirmed members. Examples include 4:5 at 34.9 AU and 3:4 at 36.4 AU inside the plutinos, 3:7 at 52.9 AU, and 2:7 at 69.3 AU, which holds 471143 Dziewanna; the dwarf planet [[Gonggong_(dwarf_planet)|Gonggong]] is in the 3:10 resonance at 67 AU.[^buie-des] Resonances extend at least as far as 1:9 near 130 AU. One large object, 2010 JO179, with a semi-major axis of 78.3 AU and an estimated diameter of 600–900 km, librates in the unusually high-order 5:21 resonance.[^holman2018] ### Haumea [[Haumea]] probably occupies a 7:12 resonance with Neptune, but only intermittently.[^ragozzine2007] The orientation of its orbit, measured by the longitude of the ascending node, turns full circle roughly every 4.6 million years; twice in each such cycle, or every 2.3 million years, the resonance lapses, and it re-establishes itself after roughly a hundred thousand years. Marc Buie's orbit fit classes it as non-resonant.[^buie-haumea] ## Coincidental versus true resonances A semi-major axis close to a resonance is not enough. Orbits of distant TNOs are known imperfectly: periods exceed 300 years, while many objects have been followed for only a few years, so a weak resonance can be hard to prove and an apparent one may be an accident.[^gladman2008] The test is the behaviour of the resonant angle over time. In a true resonance the angle oscillates, or librates, smoothly about a fixed value; in a coincidental near-resonance it circulates through all values from 0° to 360°.[^elliot2005] Vladimir Emel'yanenko and E. L. Kiseleva applied this test to high-eccentricity objects near the 3:7 resonance. They found that 2001 XT254 librates in the resonance, in a state that can last from under 100 million years to billions of years, whereas another nearby object has less than a 1% probability of being resonant and circulates near the resonance without being caught.[^emelyanenko2008] Decades more observation will be needed to settle many cases. ## Toward a formal definition No universally accepted definitions exist for TNO classes, and the notion of resonance is not always stated precisely. The DES introduced formal dynamical classes based on integrating each orbit forward under the perturbations of all four giant planets.[^elliot2005] For a resonance in which the object makes p orbits while Neptune makes q, the simplest resonant angle is φ = qλ − pλ_N − (q − p)ϖ, where λ and λ_N are the mean longitudes of the object and of Neptune and ϖ is the object's longitude of perihelion. More general resonant angles also include the longitudes of perihelion and of the ascending nodes of both bodies; an object counts as resonant when one such angle, built from small integers, librates.[^elliot2005] For the plutinos the angle is φ = 3λ − 2λ_N − ϖ.[^malhotra1995] The meaning of φ becomes clear at perihelion, where λ = ϖ: then φ = 2(ϖ − λ_N), twice the angle between the object's perihelion and Neptune (derived). If φ librates about 180°, the object always reaches perihelion about 90° away from Neptune and never approaches it closely.[^malhotra1995] Pluto's resonant angle librates about 180° with an amplitude of about 86.6°, ranging from about 93.4° to 266.6°.[^buie-pluto] All new plutinos found by the DES proved to have librating angles of this same type.[^elliot2005] ## Classification methods Because orbital elements carry uncertainties, a naive classification can produce false positives. Brett Gladman, Brian Marsden and Christa Van Laerhoven proposed a method that integrates not one orbit but three: the best fit and two orbits at the extremes of the semi-major-axis uncertainty, chosen at up to three standard deviations so that the true orbit has less than a 0.3% chance of lying outside the range.[^gladman2008] Each orbit is integrated for 10 million years. If all three show a librating resonant angle, the object is classed as securely resonant; if two do, it is probably resonant; if only one does, it is flagged as near the resonance for further observation.[^gladman2008] The method needs observations over at least three oppositions, which for a distant TNO means three years or more. It is a practical safeguard against the pitfalls described above, and it underlies many of the "secure" counts quoted for individual resonances. ## References [^elliot2005]: Elliot, J. L.; Kern, S. D.; Clancy, K. B.; et al. (2005). "The Deep Ecliptic Survey: a search for Kuiper belt objects and Centaurs. II. Dynamical classification, the Kuiper belt plane, and the core population". *The Astronomical Journal* 129: 1117–1162. https://doi.org/10.1086/427395 [^hahn2005]: Hahn, J. M.; Malhotra, R. (2005). "Neptune's migration into a stirred-up Kuiper belt: a detailed comparison of simulations to observations". *The Astronomical Journal* 130: 2392–2414. https://doi.org/10.1086/452638 [^malhotra1995]: Malhotra, R. (1995). "The origin of Pluto's orbit: implications for the Solar System beyond Neptune". *The Astronomical Journal* 110: 420–429. https://doi.org/10.1086/117532 [^malhotra2000]: Malhotra, R.; Duncan, M. J.; Levison, H. F. (2000). "Dynamics of the Kuiper belt". In Mannings, V.; Boss, A. P.; Russell, S. S. (eds.), *Protostars and Planets IV*. University of Arizona Press, p. 1231. ISBN 978-0-8165-2059-6. https://www.lpl.arizona.edu/~renu/malhotra_preprints/kbd_ppiv.pdf [^gladman2008]: Gladman, B.; Marsden, B. G.; Van Laerhoven, C. (2008). "Nomenclature in the outer Solar System". In *The Solar System Beyond Neptune*. University of Arizona Press, pp. 43–57. Bibcode 2008ssbn.book...43G. ISBN 978-0-8165-2755-7. [^jpl-t1]: JPL Solar System Dynamics. "Approximate Positions of the Planets", Table 1. https://ssd.jpl.nasa.gov/planets/approx_pos.html [^nasa-fs-n]: Williams, D. R. "Neptune Fact Sheet". NASA NSSDCA (last updated 3 October 2024). https://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html (fetched 2026-09-18). [^malhotra1996]: Malhotra, R. (1996). "The phase space structure near Neptune resonances in the Kuiper belt". *The Astronomical Journal* 111: 504. https://doi.org/10.1086/117802 [^chiang2002]: Chiang, E. I.; Jordan, A. B. (2002). "On the plutinos and twotinos of the Kuiper belt". *The Astronomical Journal* 124: 3430–3444. https://doi.org/10.1086/344605 [^lykawka2007]: Lykawka, P. S.; Mukai, T. (2007). "Dynamical classification of trans-neptunian objects: probing their origin, evolution, and interrelation". *Icarus* 189: 213–232. https://doi.org/10.1016/j.icarus.2007.01.001 [^buie-des]: Buie, M. W. "The Deep Ecliptic Survey object classifications". Southwest Research Institute. https://www.boulder.swri.edu/~buie/kbo/desclass.html [^johnston]: Johnston, W. R. (27 February 2024). "List of known trans-Neptunian objects (and other outer solar system objects)". *Johnston's Archive*. http://www.johnstonsarchive.net/astro/tnoslist.html [^chiang2003]: Chiang, E. I.; Jordan, A. B.; Millis, R. L.; et al. (2003). "Resonance occupation in the Kuiper belt: case examples of the 5:2 and Trojan resonances". *The Astronomical Journal* 126: 430–443. https://doi.org/10.1086/375207 [^mpc-nt]: Minor Planet Center (27 February 2024). "List of Neptune trojans". http://www.minorplanetcenter.org/iau/lists/NeptuneTrojans.html [^delafuente2012]: de la Fuente Marcos, C.; de la Fuente Marcos, R. (2012). "Four temporary Neptune co-orbitals: (148975) 2001 XA255, (310071) 2010 KR59, (316179) 2010 EN65, and 2012 GX17". *Astronomy & Astrophysics* 547: L2. https://doi.org/10.1051/0004-6361/201220377 [^tiscareno2009]: Tiscareno, M. S.; Malhotra, R. (2009). "Chaotic diffusion of resonant Kuiper belt objects". *The Astronomical Journal* 138: 827–837. https://doi.org/10.1088/0004-6256/138/3/827 [^holman2018]: Holman, M. J.; Payne, M. J.; Fraser, W.; et al. (2018). "A dwarf planet class object in the 21:5 resonance with Neptune". *The Astrophysical Journal Letters* 855: L6. https://doi.org/10.3847/2041-8213/aaadb3 [^ragozzine2007]: Ragozzine, D.; Brown, M. E. (2007). "Candidate members and age estimate of the family of Kuiper belt object 2003 EL61". *The Astronomical Journal* 134: 2160–2167. https://doi.org/10.1086/522334 [^buie-haumea]: Buie, M. W. (25 June 2008). "Orbit fit and astrometric record for 136108". Southwest Research Institute. https://www.boulder.swri.edu/~buie/kbo/astrom/136108.html [^emelyanenko2008]: Emel'yanenko, V. V.; Kiseleva, E. L. (2008). "Resonant motion of trans-Neptunian objects in high-eccentricity orbits". *Astronomy Letters* 34: 271–279. https://doi.org/10.1134/S1063773708040075 [^buie-pluto]: Buie, M. W. (12 November 2019). "Orbit fit and astrometric record for 134340". Southwest Research Institute. https://www.boulder.swri.edu/~buie/kbo/astrom/134340.html ## Further reading - Malhotra, R. (1995). "The origin of Pluto's orbit: implications for the Solar System beyond Neptune". *The Astronomical Journal* 110: 420–429. - Gladman, B.; Marsden, B. G.; Van Laerhoven, C. (2008). "Nomenclature in the outer Solar System". In *The Solar System Beyond Neptune*. University of Arizona Press. - JPL Small-Body Database. https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Resonant_trans-Neptunian_object) : [Wikitube](https://en.wikitube.io/wiki/Resonant_trans-Neptunian_object) · pinned revision [1370788373](https://en.wikipedia.org/w/index.php?oldid=1370788373) · 2026-09-18 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Solar_System]]. --- *Solar System portal child articles, wave 1 · 2026-09-18 · drafted · row SOL-068 · explorer state `?obj=kuiper`.* <!-- hub_tags: Life_Physics · PORTAL_Solar_System -->