Resonant trans-Neptunian object

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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. [1]



Distribution of trans-Neptunian objects. Objects occupying the stronger resonances are in red. KBOs and resonances.png
Distribution of trans-Neptunian objects. Objects occupying the stronger resonances are in red.

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.


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 ~164.8 years)

A few objects have been discovered following orbits with semi-major axes similar to that of Neptune, near the SunNeptune 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

2:3 resonance ("plutinos", period ~247.94 years)

The motions of Orcus and Pluto in a rotating frame with a period equal to Neptune's orbital period (holding Neptune stationary) OrcusandPlutoRotatingFrame.gif
The motions of Orcus and Pluto in a rotating frame with a period equal to Neptune's orbital period (holding Neptune stationary)
Pluto and its moons (top) compared in size, albedo and colour with Orcus and Ixion ThePlutinos Size Albedo Color2.svg
Pluto and its moons (top) compared in size, albedo and colour with Orcus and Ixion

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 ~275 years)

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

4:7 resonance (period ~290 years)

Another population of objects is orbiting the Sun at 43.7 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, 55 4:7-resonant objects have had their orbits secured by the Deep Ecliptic Survey. [6] [7] Objects with well established orbits include: [7]

1:2 resonance ("twotinos", period ~330 years)

This resonance at 47.8 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 has 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 ~410 years)

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

Objects with well established orbits at 55.4 AU include:

1:3 resonance (period ~500 years)

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

Other resonances

(523794) 2015 RR245's orbit librating in a 2:9 resonance with Neptune 2015RR245 resonance.gif
(523794) 2015 RR245's orbit librating in a 2:9 resonance with Neptune

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

4:535~20511 confirmed (432949) 2012 HH2 , (127871) 2003 FC128 , (308460) 2005 SC278 , (79969) 1999 CP133 , (427581) 2003 QB92 , (131697) 2001 XH255
3:436.5~22030 confirmed (143685) 2003 SS317 , (15836) 1995 DA2
5:841.1~2641 confirmed (533398) 2014 GA54
7:1243.1~2831 confirmed 2015 RP278
5:944.5~2956 confirmed (437915) 2002 GD32
6:1145~3034 confirmed (523725) 2014 MC70 and (505477) 2013 UM15 . (182294) 2001 KU76 is also likely.
5:1151~3631 confirmed 2013 RM109
4:952~3703 confirmed (42301) 2001 UR163 , (182397) 2001 QW297
3:753~38510 confirmed (495297) 2013 TJ159 , (181867) 1999 CV118 , (131696) 2001 XT254 , (95625) 2002 GX32 , (183964) 2004 DJ71 , (500882) 2013 JN64
5:1254~3956 confirmed (79978) 1999 CC158 , (119878) 2002 CY224
3:857~4403 confirmed (82075) 2000 YW134 , (542258) 2013 AP183 , 2014 UE228
4:1159~4531 confirmed (500879) 2013 JH64
4:1366~5371 confirmed 2009 DJ143
3:1067~5492 confirmed 225088 Gonggong
2:770~58010 confirmed 471143 Dziewanna, (160148) 2001 KV76
3:1172~6062 confirmed 2014 UV224 , 2013 AR183
1:476~6607 confirmed 2003 LA7 , 2011 UP411
5:2178~7061 confirmed [12] (574372) 2010 JO179
2:980~7302 confirmed (523794) 2015 RR245 , 2003 UA414
1:588~8252 confirmed 2007 FN51 , 2011 BP170
2:1194~9093 confirmed 2005 RP43 , 2011 HO60
1:699~10002 confirmed (528381) 2008 ST291 , 2011 WJ157
1:9129~15002 confirmed 2007 TC434 , 2015 KE172


The libration of Haumea's nominal orbit in a rotating frame, with Neptune stationary (see 2 Pallas for an example of non-librating)
Haumea resonant angle.png
The libration angle of Haumea's weak 7:12 resonance with Neptune, , over the next 5 million years

Haumea is thought to be in an intermittent 7:12 orbital resonance with Neptune. [13] Its ascending node 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]

The orbital period of 2001 XT254 around the 3:7 (2.333) resonance of Neptune. 2001XT254 Resonance.jpg
The orbital period of 2001 XT254 around the 3:7 (2.333) resonance of Neptune.

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]

The orbital period of 1995 TL8 missing the 3:7 (2.333) resonance of Neptune. 1995TL8 Orbital Period.jpg
The orbital period of 1995 TL8 missing the 3:7 (2.333) resonance of Neptune.

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

where p and q are small integers, λ and λN 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]

where the are the longitudes of perihelia and the 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 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

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

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

i.e. 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 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

Classical Kuiper belt object Kuiper belt object, not controlled by an orbital resonance with Neptune

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.

Kuiper belt Area of the Solar System beyond the planets, comprising small bodies

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.

Orbital resonance Regular and periodic gravitational influence by two orbiting celestial bodies exerted on each other

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 Pluto and Neptune. 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 solar 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.

Trans-Neptunian object Solar system objects beyond Neptune

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 a 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.

(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 is a trans-Neptunian object with a possible moon from 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.

<span class="nowrap">(15875) 1996 TP<sub>66</sub></span>

(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.

In astronomy, a co-orbital configuration is a configuration of two or more astronomical objects orbiting at the same, or very similar, distance from their primary, i.e. they are in a 1:1 mean-motion resonance..

(119951) 2002 KX<sub>14</sub>

(119951) 2002 KX14, also written as 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

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 largest class of resonant TNOs. It was named after Arawn, the ruler of the Celtic underworld, and 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 object Dynamical class of minor planets

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.

(131696) 2001 XT254, provisionally known as 2001 XT254, is a Kuiper belt object (KBO) that has a 3:7 resonance with Neptune.

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

(120216) 2004 EW95, provisionally known as 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 that it had originated closer to the Sun, maybe even the main asteroid belt.

(307463) 2002 VU130, prov. 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, is a binary trans-Neptunian object discovered on 8 September 2011 by the Pan-STARRS survey at the Haleakalā Observatory in Hawaii. It was found by Pan-STARRS on 20 November 2014 and was announced later in July 2016 after additional observations and precovery identifications. It is in the Kuiper belt, a region of icy objects orbiting beyond Neptune in the outer Solar System. It is classified as a plutino, a dynamical class of objects in a 2:3 orbital resonance with Neptune. On 1 December 2018, a team of astronomers observed a stellar occultation by the object, which revealed that it is a compact binary system consisting of two separate components in close orbit around each other. The primary and secondary components are estimated to have diameters of around 180 km (110 mi) and 140 km (87 mi), respectively.


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Further reading