Resonant trans-Neptunian object

Last updated December 26, 2024

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.^[1]

Distribution
Origin
Known populations
1:1 resonance (Neptune trojans, period 164.7 years)
2:3 resonance ("plutinos", period 247.0 years)
3:5 resonance (period 274.5 years)
4:7 resonance (period 288.2 years)
1:2 resonance ("twotinos", period 329.4 years)
2:5 resonance (period 411.7 years)
1:3 resonance (period 494.1 years)
Other resonances
Haumea
Coincidental versus true resonances
Toward a formal definition
Classification methods
References
Further reading

Distribution

The diagram illustrates the distribution of the known trans-Neptunian objects. Resonant objects are plotted in red. Orbital resonances with Neptune are marked with vertical bars: 1:1 marks the position of Neptune's orbit and its trojans; 2:3 marks the orbit of Pluto and plutinos; and 1:2, 2:5, etc. mark a number of smaller families. The designation 2:3 or 3:2 both refer to the same resonance for TNOs. There is no ambiguity, because TNOs have, by definition, periods longer than Neptune's. The usage depends on the author and the field of research.

Origin

Detailed analytical and numerical studies of Neptune's resonances have shown that the objects must have a relatively precise range of energies.^[2]^[3] If the object's semi-major axis is outside these narrow ranges, the orbit becomes chaotic, with widely changing orbital elements. As TNOs were discovered, more than 10% 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.^[4] Well before the discovery of the first TNO, it was suggested that interaction between giant planets and a massive disk of small particles would, via angular-momentum transfer, make Jupiter migrate inwards and make Saturn, Uranus, and especially Neptune 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.^[5]

Known populations

1:1 resonance (Neptune trojans, period 164.7 years)

A few objects have been discovered following orbits with semi-major axes similar to that of Neptune, near the Sun–Neptune Lagrangian points. These Neptune trojans, termed by analogy to the (Jupiter) Trojan asteroids, are in 1:1 resonance with Neptune. 28 are known as of February 2020.^[6]^[7] Only 5 objects are near Neptune's L₅ Lagrangian point, and the identification of one of these is insecure; the others are located in Neptune's L₄ region.^[8]^[7] In addition, (316179) 2010 EN65 is a so-called "jumping trojan", currently transitioning from librating around L₄ to librating around L₅, via the L₃ region.^[9]

Leading Trojans at L₄

Following Trojans at L₅

(530664) 2011 SO277
2008 LC18
2011 HM102
2012 UD185
2013 KY18 ?

2:3 resonance ("plutinos", period 247.0 years)

The motions of Orcus (in grey) and Pluto (in red) in a rotating frame with a period equal to Neptune's orbital period (holding Neptune stationary) OrcusandPlutoRotatingFrame.gif — The motions of Orcus (in grey) and Pluto (in red) in a rotating frame with a period equal to Neptune's orbital period (holding Neptune stationary)

The 2:3 resonance at 39.4 AU is by far the dominant category among the resonant objects. As of February 2020, it includes 383 confirmed and 99 possible member bodies (such as (175113) 2004 PF115 ).^[6] Of these 383 confirmed plutinos, 338 have their orbits secured in simulations run by the Deep Ecliptic Survey.^[7] The objects following orbits in this resonance are named plutinos after Pluto, the first such body discovered. Large, numbered plutinos include:

3:5 resonance (period 274.5 years)

As of February 2020, 47 objects are confirmed to be in a 3:5 orbital resonance with Neptune at 42.2 AU. Among the numbered objects there are:^[7]^[6]

(15809) 1994 JS
(126154) 2001 YH140
(149349) 2002 VA131
(434709) 2006 CJ69
(469420) 2001 XP254
(469584) 2003 YW179
(470523) 2008 CS190
(503883) 2001 QF331
(523677) 2013 UF15
(523688) 2014 DK143
(523731) 2014 OK394
(523743) 2014 TA86
(530839) 2011 UK411
(531683) 2012 UC178
(534074) 2014 QZ441
(534314) 2014 SJ349

4:7 resonance (period 288.2 years)

Another population of objects is orbiting the Sun at 43.6 AU (in the midst of the classical objects). The objects are rather small (with two exceptions, H>6) and most of them follow orbits close to the ecliptic.^[7]As of February 2020^[update], 55 4:7-resonant objects have had their orbits secured by the Deep Ecliptic Survey.^[6]^[7] Objects with well established orbits include:^[7]

(119956) 2002 PA149
(119066) 2001 KJ76
(135024) 2001 KO76
(119070) 2001 KP77
(181871) 1999 CO153
(118378) 1999 HT11
(118698) 2000 OY51
385446 Manwë
(385527) 2004 OK14
(500828) 2013 GR136
(523742) 2014 TZ85

1:2 resonance ("twotinos", period 329.4 years)

This resonance at 47.7 AU is often considered to be 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 between 0.1 and 0.3.^[10] 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, but were captured when they had already been scattered.^[11]

There are far fewer objects in this resonance than plutinos. Johnston's Archive counts 99 while simulations by the Deep Ecliptic Survey have confirmed 73 as of February 2020.^[6]^[7] Long-term orbital integration shows that the 1:2 resonance is less stable than the 2:3 resonance; only 15% of the objects in 1:2 resonance were found to survive 4 Gyr as compared with 28% of the plutinos.^[10] Consequently, it might be that twotinos were originally as numerous as plutinos, but their population has dropped significantly below that of plutinos since.^[10]

Objects with well established orbits include (in order of the absolute magnitude):^[6]

2:5 resonance (period 411.7 years)

There are 57 confirmed 2:5-resonant objects at 55.3 AU as of February 2020.^[6]^[7]

Objects with well established orbits at 55.4 AU include:

(495603) 2015 AM281
(26375) 1999 DE9
(143707) 2003 UY117
(471172) 2010 JC80
(471151) 2010 FD49
472235 Zhulong
(119068) 2001 KC77
(60621) 2000 FE8
(38084) 1999 HB12
(135571) 2002 GG32
(69988) 1998 WA31
(84522) 2002 TC302 , dwarf candidate

1:3 resonance (period 494.1 years)

Johnston's Archive counts 14 1:3-resonant objects as of February 2020 at 62.5 AU.^[6] A dozen of these are secure according to the Deep Ecliptic Survey:^[7]

(136120) 2003 LG7
(385607) 2005 EO297
2004 VU130
(613469) 2006 QJ181
2006 SF369
2011 US411
2014 FX71
2015 BZ517 ?
2015 GA55
2015 KY173
2015 RA278
2015 RZ277 ?
2015 VM166
2015 VN166

Other resonances

As of February 2020, the following higher-order resonances are confirmed for a limited number of objects:^[7]

Ratio	Semimajor AU	Period years	Count	Examples
4:5	34.9	205.9	11 confirmed	(432949) 2012 HH2 , (127871) 2003 FC128 , (308460) 2005 SC278 , (79969) 1999 CP133 , (427581) 2003 QB92 , (131697) 2001 XH255
3:4	36.4	219.6	30 confirmed	(143685) 2003 SS317 , (15836) 1995 DA2
5:8	41.1	263.5	1 confirmed	(533398) 2014 GA54
7:12	43.0	282.3	1 confirmed	and 2015 RP278
5:9	44.5	296.5	6 confirmed	(437915) 2002 GD32
6:11	45.0	301.9	4 confirmed	(523725) 2014 MC70 and (505477) 2013 UM15 . (182294) 2001 KU76 is also likely.
5:11	50.8	362.3	1 confirmed	2013 RM109
4:9	51.6	370.6	3 confirmed	(42301) 2001 UR163 , (182397) 2001 QW297
3:7	52.9	384.3	10 confirmed	(495297) 2013 TJ159 , (181867) 1999 CV118 , (131696) 2001 XT254 , (95625) 2002 GX32 , (183964) 2004 DJ71 , (500882) 2013 JN64
5:12	53.9	395.3	6 confirmed	(79978) 1999 CC158 , (119878) 2002 CY224
3:8	57.8	439.2	3 confirmed	(82075) 2000 YW134 , (542258) 2013 AP183 , 2014 UE228
4:11	59.0	452.9	1 confirmed	(500879) 2013 JH64
4:13	65.9	535.3	1 confirmed	2009 DJ143
3:10	67.0	549.0	2 confirmed	225088 Gonggong
2:7	69.3	576.4	10 confirmed	471143 Dziewanna, (160148) 2001 KV76
3:11	71.4	603.9	2 confirmed	(534627) 2014 UV224 , 2013 AR183
1:4	75.7	658.8	7 confirmed	2003 LA7 , 2011 UP₄₁₁
5:21	78.2	691.7	1 confirmed	(574372) 2010 JO179 ^[12]
2:9	81.9	741.1	3 confirmed	(523794) 2015 RR245 , 2003 UA414 , 2018 VG18
1:5	87.9	823.5	2 confirmed	2007 FN51 , (667161) 2011 BP170
2:11	93.6	905.8	3 confirmed	(613037) 2005 RP43 , 2011 HO60
1:6	99.2	988.2	2 confirmed	(528381) 2008 ST291 , (668381) 2011 WJ157
1:9	130.0	1482.3	2 confirmed	2007 TC434 , 2015 KE172

Haumea

The libration of Haumea's nominal orbit in a rotating frame, with Neptune stationary (see 2 Pallas for an example of non-librating)

The libration angle

\phi

of Haumea's weak 7:12 resonance with Neptune,

\phi ={\rm {12\cdot \lambda -{\rm {7\cdot \lambda _{\rm {N}}-{\rm {5\cdot \varpi -{\rm {1\cdot \Omega }}}}}}}}

, over the next 5 million years

Haumea is thought to be in an intermittent 7:12 orbital resonance with Neptune.^[13] Its ascending node $\Omega$ precesses with a period of about 4.6 million years, and the resonance is broken twice per precession cycle, or every 2.3 million years, only to return a hundred thousand years or so later.^[14] Marc Buie qualifies it as non-resonant.^[15]

Coincidental versus true resonances

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 periods of more than 300 years and most have only been observed over a relatively short observation arc of a few 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 coincidental. A true resonance will smoothly oscillate while a coincidental near resonance will circulate.^{[ citation needed ]} (See Toward a formal definition)

Simulations by Emel'yanenko and Kiseleva in 2007 show that (131696) 2001 XT254 is librating in a 3:7 resonance with Neptune.^[16] This libration can be stable for less than 100 million to billions of years.^[16]

Emel'yanenko and Kiseleva also show that (48639) 1995 TL8 appears to have less than a 1% probability of being in a 3:7 resonance with Neptune, but it does execute circulations near this resonance.^[16]

Toward a formal definition

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 formal definition of classical KBO)

In general, the mean-motion resonance may involve not only orbital periods of the form

{\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}}}}}

where p and q are small integers, λ and λ_N are respectively the mean longitudes of the object and Neptune, but can also involve the longitude of the perihelion and the longitudes of the nodes (see orbital resonance, for elementary examples)

An object is resonant if for some small integers (p,q,n,m,r,s), the argument (angle) defined below is librating (i.e. is bounded):^[17]

\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}}}}}}}}}}}}}}

where the $\varpi$ are the longitudes of perihelia and the $\Omega$ are the longitudes of the ascending nodes, for Neptune (with subscripts "N") and the resonant object (no subscripts).

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 $\phi$ librates around 180° with an amplitude of around 86.6° degrees, i.e. the angle changes periodically from 93.4° to 266.6°.^[18]

All new plutinos discovered during the Deep Ecliptic Survey proved to be of the type

\phi ={\rm {3\cdot \lambda -{\rm {2\cdot \lambda _{\rm {N}}-\varpi }}}}

similar to Pluto's mean-motion resonance.

More generally, this 2:3 resonance is an example of the resonances p:(p+1) (for example 1:2, 2:3, 3:4) that have proved to lead to stable orbits.^[4] Their resonant angle is

\phi ={\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}-({\rm {p-{\rm {q)\cdot \varpi }}}}}}}}

In this case, the importance of the resonant angle $\phi \,$ can be understood by noting that when the object is at perihelion, i.e. $\lambda =\varpi$ , then

\phi =q\cdot (\varpi -\lambda _{\rm {N}})

i.e. $\phi \,$ gives a measure of the distance of the object's perihelion from Neptune.^[4] The object is protected from the perturbation by keeping its perihelion far from Neptune provided $\phi \,$ librates around an angle far from 0°.

Classification methods

As the orbital elements are known with a limited precision, the uncertainties may lead to false positives (i.e. classification as resonant of an orbit which is not). A recent approach^[19] 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. 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 formal definition), the classification as a resonant object is considered secure.^[19] 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.^[19] 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 deviations. 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%. The method is applicable to objects with observations spanning at least 3 oppositions.^[19]

Related Research Articles

A classical Kuiper belt object, also called a cubewano ( "QB1-o"), is a low-eccentricity Kuiper belt object (KBO) that orbits beyond Neptune and is not controlled by an orbital resonance with Neptune. Cubewanos have orbits with semi-major axes in the 40–50 AU range and, unlike Pluto, do not cross Neptune's orbit. That is, they have low-eccentricity and sometimes low-inclination orbits like the classical planets.

The Kuiper belt is a circumstellar disc in the outer Solar System, extending from the orbit of Neptune at 30 astronomical units (AU) to approximately 50 AU from the Sun. It is similar to the asteroid belt, but is far larger—20 times as wide and 20–200 times as massive. Like the asteroid belt, it consists mainly of small bodies or remnants from when the Solar System formed. While many asteroids are composed primarily of rock and metal, most Kuiper belt objects are composed largely of frozen volatiles, such as methane, ammonia, and water. The Kuiper belt is home to most of the objects that astronomers generally accept as dwarf planets: Orcus, Pluto, Haumea, Quaoar, and Makemake. Some of the Solar System's moons, such as Neptune's Triton and Saturn's Phoebe, may have originated in the region.

In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Neptune and Pluto. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large planetary system bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.

In astronomy, the plutinos are a dynamical group of trans-Neptunian objects that orbit in 2:3 mean-motion resonance with Neptune. This means that for every two orbits a plutino makes, Neptune orbits three times. The dwarf planet Pluto is the largest member as well as the namesake of this group. The next largest members are Orcus, (208996) 2003 AZ84, and Ixion. Plutinos are named after mythological creatures associated with the underworld.

A trans-Neptunian object (TNO), also written transneptunian object, is any minor planet in the Solar System that orbits the Sun at a greater average distance than Neptune, which has an orbital semi-major axis of 30.1 astronomical units (AU).

The Deep Ecliptic Survey (DES) is a project to find Kuiper belt objects (KBOs), using the facilities of the National Optical Astronomy Observatory (NOAO). The principal investigator is Robert L. Millis.

(84522) 2002 TC₃₀₂ (provisional designation 2002 TC₃₀₂) is a mid-sized trans-Neptunian object located in the outermost region of the Solar System. It was discovered on 9 October 2002, by American astronomers Mike Brown, Chad Trujillo and David Rabinowitz at the Palomar Observatory in California. The resonant trans-Neptunian object stays in a 2:5 resonance with Neptune. It has a reddish color, a rotation period of 56.1 hours and measures at least 500 kilometers (310 miles) in diameter.

(119070) 2001 KP₇₇ (provisional designation 2001 KP₇₇) is a resonant trans-Neptunian object in the Kuiper belt, a circumstellar disc located in the outermost region of the Solar System. It was discovered on 23 May 2001, by American astronomer Marc Buie at the Cerro Tololo Observatory in Chile. The object is locked in a 4:7 orbital resonance with Neptune. It has a red surface color and measures approximately 176 kilometers (110 miles) in diameter. As of 2021, it has not been named.

<span class="nowrap">(208996) 2003 AZ<sub>84</sub></span> Plutino

(208996) 2003 AZ₈₄ (provisional designation 2003 AZ₈₄) is a trans-Neptunian object with a possible moon located in the outer regions of the Solar System. It is approximately 940 kilometers across its longest axis, as it has an elongated shape. It belongs to the plutinos – a group of minor planets named after its largest member Pluto – as it orbits in a 2:3 resonance with Neptune in the Kuiper belt. It is the third-largest known plutino, after Pluto and Orcus. It was discovered on 13 January 2003, by American astronomers Chad Trujillo and Michael Brown during the NEAT survey using the Samuel Oschin telescope at Palomar Observatory.

(84922) 2003 VS₂ is a trans-Neptunian object discovered by the Near Earth Asteroid Tracking program on 14 November 2003. Like Pluto, it is in a 2:3 orbital resonance with Neptune and is thus a plutino. Analysis of light-curve suggests that it is not a dwarf planet.

<span class="nowrap">(15875) 1996 TP<sub>66</sub></span> Resonant trans-Neptunian object

(15875) 1996 TP₆₆ (provisional designation 1996 TP₆₆) is a resonant trans-Neptunian object of the plutino population, located in the outermost region of the Solar System, approximately 154 kilometers (96 miles) in diameter. It was discovered on 11 October 1996, by astronomers Jane Luu, David C. Jewitt and Chad Trujillo at the Mauna Kea Observatories, Hawaii, in the United States. The very reddish RR-type with a highly eccentric orbit has been near its perihelion around the time of its discovery. This minor planet was numbered in 2000 and has since not been named. It is probably not a dwarf planet candidate.

(119951) 2002 KX₁₄ (provisional designation 2002 KX₁₄) is a medium-sized trans-Neptunian object (TNO) residing within the Kuiper belt. It was discovered on 17 May 2002 by Michael E. Brown and Chad Trujillo.

15810 Arawn (provisional designation 1994 JR₁) is a trans-Neptunian object (TNO) from the inner regions of the Kuiper belt, approximately 133 kilometres (83 mi) in diameter. It belongs to the plutinos, the most populous class of resonant TNOs. It was named after Arawn, the ruler of the Otherworld in Welsh mythology, and was discovered on 12 May 1994, by astronomers Michael Irwin and Anna Żytkow with the 2.5-metre Isaac Newton Telescope at Roque de los Muchachos Observatory in the Canary Islands, Spain.

Detached objects are a dynamical class of minor planets in the outer reaches of the Solar System and belong to the broader family of trans-Neptunian objects (TNOs). These objects have orbits whose points of closest approach to the Sun (perihelion) are sufficiently distant from the gravitational influence of Neptune that they are only moderately affected by Neptune and the other known planets: This makes them appear to be "detached" from the rest of the Solar System, except for their attraction to the Sun.

<span class="nowrap">(120216) 2004 EW<sub>95</sub></span>

(120216) 2004 EW₉₅ (provisional designation 2004 EW₉₅) is a resonant trans-Neptunian object in the Kuiper belt located in the outermost regions of the Solar System. It measures approximately 291 kilometers in diameter. It has more carbon than typical of KBOs, and the first to be confirmed as having this composition in this region of space. It is thought to have originated closer to the Sun, perhaps even in the main asteroid belt.

(307463) 2002 VU₁₃₀ (provisional designation 2002 VU₁₃₀) is a trans-Neptunian object, located in the circumstellar disc of the Kuiper belt in the outermost region of the Solar System. The resonant trans-Neptunian object belongs to the population of plutinos and measures approximately 253 kilometers (160 miles) in diameter. It was discovered on 7 November 2002, by American astronomer Marc Buie at the Kitt Peak Observatory near Tucson, Arizona. The object has not been named yet.

The hypothetical Planet Nine would modify the orbits of extreme trans-Neptunian objects via a combination of effects. On very long timescales exchanges of angular momentum with Planet Nine cause the perihelia of anti-aligned objects to rise until their precession reverses direction, maintaining their anti-alignment, and later fall, returning them to their original orbits. On shorter timescales mean-motion resonances with Planet Nine provides phase protection, which stabilizes their orbits by slightly altering the objects' semi-major axes, keeping their orbits synchronized with Planet Nine's and preventing close approaches. The inclination of Planet Nine's orbit weakens this protection, resulting in a chaotic variation of semi-major axes as objects hop between resonances. The orbital poles of the objects circle that of the Solar System's Laplace plane, which at large semi-major axes is warped toward the plane of Planet Nine's orbit, causing their poles to be clustered toward one side.

(523764) 2014 WC₅₁₀ (provisional designation 2014 WC₅₁₀) is a binary trans-Neptunian object and plutino discovered on 8 September 2011 by the Pan-STARRS survey at the Haleakalā Observatory in Hawaii. It orbits in the Kuiper belt, a region of icy objects orbiting beyond Neptune in the outer Solar System. Astronomers discovered the binary nature of 2014 WC₅₁₀ when its two components occulted a star on 1 December 2018. The components of the 2014 WC₅₁₀ binary system, which have diameters of 180 km (110 mi) and 140 km (87 mi), orbit each other at a separation distance of roughly 2,600 km (1,600 mi).

References

↑ Hahn, Joseph M.; Malhotra, Renu (November 2005). "Neptune's Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations". The Astronomical Journal . 130 (5): 2392–2414. arXiv: astro-ph/0507319 . Bibcode:2005AJ....130.2392H. doi:10.1086/452638. S2CID 14153557.
↑ Malhotra, Renu (January 1996). "The Phase Space Structure Near Neptune Resonances in the Kuiper Belt" (PDF). The Astronomical Journal (preprint). 111: 504. arXiv: astro-ph/9509141 . Bibcode:1996AJ....111..504M. doi:10.1086/117802. hdl:2060/19970021298. S2CID 41919451. Archived (PDF) from the original on 23 July 2018 – via the NASA Technical Report Server.
↑ Chiang, E. I.; Jordan, A. B. (December 2002). "On the Plutinos and Twotinos of the Kuiper Belt". The Astronomical Journal . 124 (6): 3430–3444. arXiv: astro-ph/0210440 . Bibcode:2002AJ....124.3430C. doi:10.1086/344605. S2CID 13928812.
1 2 3 Malhotra, Renu (July 1995). "The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune". The Astronomical Journal . 110 (1): 420–429. arXiv: astro-ph/9504036 . Bibcode:1995AJ....110..420M. doi:10.1086/117532. hdl:2060/19970005091. S2CID 10622344 – via the Internet Archive.
↑ Malhotra, Renu; Duncan, Martin J.; Levison, Harold F. (May 2000). "Dynamics of the Kuiper Belt" (PDF). In Mannings, Vincent; Boss, Alan P.; Russell, Sara S. (eds.). Protostars and Planets IV (preprint). Space Science Series. University of Arizona Press. p. 1231. arXiv: astro-ph/9901155 . Bibcode:2000prpl.conf.....M. ISBN 978-0816520596. LCCN 99050922. Archived (PDF) from the original on 11 August 2017 – via the Lunar and Planetary Laboratory.
1 2 3 4 5 6 7 8 Johnston's Archive (27 December 2019). "List of Known Trans-Neptunian Objects (and other outer solar system objects)".
1 2 3 4 5 6 7 8 9 10 11 Buie, M. W. "The Deep Ecliptic Survey Object Classifications" . Retrieved 9 November 2019.
↑ "List Of Neptune Trojans". Minor Planet Center. 10 July 2017. Retrieved 4 August 2017.
↑ de la Fuente Marcos, C.; de la Fuente Marcos, R. (November 2012). "Four temporary Neptune co-orbitals: (148975) 2001 XA255, (310071) 2010 KR59, (316179) 2010 EN65, and 2012 GX17". Astronomy and Astrophysics. 547: 7. arXiv: 1210.3466 . Bibcode:2012A&A...547L...2D. doi:10.1051/0004-6361/201220377. S2CID 118622987. (rotating frame)
1 2 3 M. Tiscareno; R. Malhotra (2009). "Chaotic Diffusion of Resonant Kuiper Belt Objects". The Astronomical Journal. 194 (3): 827–837. arXiv: 0807.2835 . Bibcode:2009AJ....138..827T. doi:10.1088/0004-6256/138/3/827. S2CID 1764121.
↑ Lykawka, Patryk Sofia & Mukai, Tadashi (July 2007). "Dynamical classification of trans-neptunian objects: Probing their origin, evolution, and interrelation". Icarus. 189 (1): 213–232. Bibcode:2007Icar..189..213L. doi:10.1016/j.icarus.2007.01.001.
↑ Matthew J. Holman; Matthew J. Payne; Wesley Fraser; Pedro Lacerda; Michele T. Bannister; Michael Lackner; Ying-Tung Chen; Hsing Wen Lin; Kenneth W. Smith; Rosita Kokotanekova; David Young; K. Chambers; S. Chastel; L. Denneau; A. Fitzsimmons; H. Flewelling; Tommy Grav; M. Huber; Nick Induni; Rolf-Peter Kudritzki; Alex Krolewski; R. Jedicke; N. Kaiser; E. Lilly; E. Magnier; Zachary Mark; K. J. Meech; M. Micheli; Daniel Murray; Alex Parker; Pavlos Protopapas; Darin Ragozzine; Peter Veres; R. Wainscoat; C. Waters; R. Weryk (2018). "A Dwarf Planet Class Object in the 21:5 Resonance with Neptune". The Astrophysical Journal Letters. 855 (1). L6 1 March 2018. arXiv: 1709.05427 . Bibcode:2018ApJ...855L...6H. doi: 10.3847/2041-8213/aaadb3 .
↑ D. Ragozzine; M. E. Brown (2007-09-04). "Candidate Members and Age Estimate of the Family of Kuiper Belt Object 2003 EL₆₁". The Astronomical Journal. 134 (6): 2160–2167. arXiv: 0709.0328 . Bibcode:2007AJ....134.2160R. doi:10.1086/522334. S2CID 8387493.
↑ Marc W. Buie (2008-06-25). "Orbit Fit and Astrometric record for 136108". Southwest Research Institute (Space Science Department). Archived from the original on 2011-05-18. Retrieved 2008-10-02.
↑ "Orbit and Astrometry for 136108". www.boulder.swri.edu. Retrieved 2020-07-14.
1 2 3 Emel'yanenko, V. V; Kiseleva, E. L. (2008). "Resonant motion of trans-Neptunian objects in high-eccentricity orbits". Astronomy Letters. 34 (4): 271–279. Bibcode:2008AstL...34..271E. doi:10.1134/S1063773708040075. S2CID 122634598.
↑ 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. The Astronomical Journal, 129 (2006), pp. preprint Archived 2006-08-23 at the Wayback Machine
↑ Mark Buie (12 November 2019), Orbit Fit and Astrometric record for 134340, archived from the original on 11 November 2019
1 2 3 4 B. Gladman; B. Marsden; C. VanLaerhoven (2008). Nomenclature in the Outer Solar System. Bibcode:2008ssbn.book...43G. ISBN 9780816527557.{{cite book}}: |journal= ignored (help)