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.^{†}

## Distribution

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 Centaurs for reference. 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 Neptune Trojans), 2:3 marks the orbit of Pluto and plutinos, 1:2, 2:5 etc. a number of smaller families).

^{†}The designation *2:3* or *3:2* refer both to the same resonance for TNOs. There’s no confusion possible as TNO, 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 to better capture the meaning: Pluto completes **2** orbits for every **3** orbits of Neptune.

## Origin

Detailed analytical and numerical studies^{[1]}
^{[2]}
of the Neptune’s resonances have shown that they are quite narrow i.e. the objects must have a relatively precise range of energy (i.e. semi-major axes). If the object semi-major axis is outside these narrow ranges, the orbit becomes chaotic (widely changing orbital elements).
Curiously, substantial numbers^{†} of TNO being discovered appeared to be in 2:3 resonances , the proportion far from random distribution.
It is now believed that the objects have been *collected* from wider distances by the sweeping resonances during the migration of Neptune. ^{[3]}
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 momentum transfer, make Jupiter migrate inwards and 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.^{[4]}

^{†}More than 10% are classified or suspected plutinos

## Known populations

### 2:3 resonance (Plutinos)

The 2:3 resonance is by far the dominant category among the resonant objects, with 92 confirmed and 104 possible member bodies.^{[5]} The objects following orbits in this resonance are named plutinos, after Pluto which has the first known orbit of this type. Large, numbered plutinos include:^{[6]}

### 1:2 resonance

This resonance is often considered as the outer "edge" of the Kuiper Belt and the objects in this resonance are sometimes referred to as *twotinos*.
There are far fewer objects in this resonance than plutinos.(Total of 14 as of September 27, 2006)^{[7]}

Objects with well established orbits include:^{[6]}

### 2:5 resonance

Objects with well established orbits, include:^{[6]}

- (84522) 2002 TC
_{302}, the largest - (38084) 1999 HB
_{12} - (60621) 2000 FE
_{8} - (69988) 1998 WA
_{31} - (119068) 2001 KC
_{77}

### Neptune trojans

A few objects follow orbits with similar semi-major axis as Neptune, near Lagrangian points. These Neptune Trojans, so called par analogy with Trojan asteroids. They can be formally considered in 1:1 resonance with Neptune. Five are known as of December 2006:^{[8]}

- 2001 QR
_{322} - 2004 UP
_{10} - 2005 TN
_{53} - 2005 TO
_{74} - 2006 RJ
_{103}

### Other resonances

So called higher-order resonances are known for a limited number of objects, including the following numbered objects^{[6]}

- 3:4 (15836) 1995 DA
_{2} - 3:5 (15809) 1994 JS
_{} - 4:7 (119070) 2001 KP
_{77}, (118698) 2000 OY_{51} - 3:7 (95625) 2002 GX
_{32}

## 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)

It should be noted that in general, the mean motion resonance can 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 repectively 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)^{[9]}

- $ \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 82° degrees, ie. the angle changes periodically from 180°-82° to 180°+82°.

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 or Pluto's mean motion resonance.

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.^{[3]} 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.^{[3]}
The object is protected from the perturbation by keeping its perihelion far from Neptune provided $ \phi\, $ librates around an angle far from 0°.

^{†}Capital R is used to refer to this formally defined class as opposed to common meaning of resonant

## References

- ↑
Malhotra, Renu
*The Phase Space Structure Near Neptune Resonances in the Kuiper Belt*. Astronomical Journal v.111, p.504 preprint - ↑ E. I. Chiang and A. B. Jordan,
*On the Plutinos and Twotinos of the Kuiper Belt*, The Astronomical Journal,**124**(2002), pp.3430–3444. (html) - ↑
^{3.0}^{3.1}^{3.2}Renu Malhotra,*The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune*, The Astronomical Journal,**110**(1995), p. 420 Preprint. - ↑
Malhotra, R.; Duncan, M. J.; Levison, H. F.
*Dynamics of the Kuiper Belt*. Protostars and Planets IV, University of Arizona Press, p. 1231 preprint - ↑ http://www.johnstonsarchive.net/astro/tnos.html
- ↑
^{6.0}^{6.1}^{6.2}^{6.3}List of the classified orbits from MPC - ↑ http://www.johnstonsarchive.net/astro/tnos.html
- ↑ List of Neptune Trojans from MPC
- ↑
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

## Further reading

- (2004-08-03) John K. Davies and Luis H. Barrera
*The First Decadal Review of the Edgeworth-Kuiper Belt*. Springer. ISBN 1-4020-1781-2. - E. I. Chiang, J. R. Lovering, R. L. Millis, M. W. Buie, L. H. Wasserman, and K. J. Meech (June 2003). "Resonant and Secular Families of the Kuiper Belt".
*Earth, Moon, and Planets***92**(1–4): 49–62. DOI:10.1023/B:MOON.0000031924.20073.d0. - 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 (2003-01-21). "Resonance occupation in the Kuiper Belt: case examples of the 5:2 and trojan resonances".
*The Astronomical Journal***126**: 430–443. - Renu Malhotra. "
*The Kuiper Belt as a Debris Disk*" (PDF). (as HTML)

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