In
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
, a resonant trans-Neptunian object is a
trans-Neptunian object
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).
Typically, ...
(TNO) in mean-motion
orbital resonance
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 relationsh ...
with
Neptune
Neptune is the eighth planet from the Sun and the farthest known planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times ...
. 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
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 ...
population, or the more distant
scattered disc
The scattered disc (or scattered disk) is a distant circumstellar disc in the Solar System that is sparsely populated by icy small solar system bodies, which are a subset of the broader family of trans-Neptunian objects. The scattered-disc objec ...
population.
Distribution
![KBOs and resonances](https://upload.wikimedia.org/wikipedia/commons/0/05/KBOs_and_resonances.png)
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
Trojan or Trojans may refer to:
* Of or from the ancient city of Troy
* Trojan language, the language of the historical Trojans
Arts and entertainment Music
* ''Les Troyens'' ('The Trojans'), an opera by Berlioz, premiered part 1863, part 1890 ...
; 2:3 marks the orbit of
Pluto
Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...
and
plutino
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 lar ...
s; 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.
If the object's
semi-major axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the long ...
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.
Well before the discovery of the first TNO, it was suggested that interaction between
giant planet
The giant planets constitute a diverse type of planet much larger than Earth. They are usually primarily composed of low-boiling-point materials (volatiles), rather than rock or other solid matter, but massive solid planets can also exist. Ther ...
s 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.
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
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
–
Neptune
Neptune is the eighth planet from the Sun and the farthest known planet in the Solar System. It is the fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 times ...
Lagrangian point
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of th ...
s. These
Neptune trojan
Neptune trojans are bodies that orbit the Sun near one of the stable Lagrangian points of Neptune, similar to the Trojan (astronomy), trojans of other planets. They therefore have approximately the same orbital period as Neptune and follow rough ...
s, termed by analogy to the
(Jupiter) Trojan asteroids, are in 1:1 resonance with Neptune. 28 are known as of February 2020.
Only 5 objects are near Neptune's
Lagrangian point
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of th ...
, and the identification of one of these is insecure; the others are located in Neptune's region.
[ In addition, is a so-called "jumping trojan", currently transitioning from librating around to librating around , via the region.][(rotating frame)]
/ref>
;Leading Trojans at :
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
;Following Trojans at :
*
*
*
*
* ''?''
2:3 resonance ("plutinos", period ~247.94 years)
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 ).[ Of these 383 confirmed plutinos, 338 have their orbits secured in simulations run by the ]Deep Ecliptic Survey
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.
Since 1998 through the end of 2003, the sur ...
. The objects following orbits in this resonance are named plutino
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 lar ...
s after Pluto
Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the S ...
, 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:[
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
]
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
The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic again ...
. , 55 4:7-resonant objects have had their orbits secured by the Deep Ecliptic Survey. Objects with well established orbits include:
*
*
*
*
*
*
*
* 385446 Manwë
385446 Manwë , or (385446) Manwë–Thorondor , is a binary resonant Kuiper belt object in a 4:7 mean-motion resonance with Neptune. It was discovered on 25 August 2003, by American astronomer Marc Buie at Cerro Tololo Observatory in northern ...
*
*
*
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
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 ...
, 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. 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.
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.
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. Consequently, it might be that twotinos were originally as numerous as plutinos, but their population has dropped significantly below that of plutinos since.
Objects with well established orbits include (in order of the absolute magnitude
Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse Logarithmic scale, logarithmic Magnitude (astronomy), astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent mag ...
):[
*
*
*
*
*
*
*
*
*
*
*
*
]
2:5 resonance (period ~410 years)
There are 57 confirmed 2:5-resonant objects as of February 2020.[
Objects with well established orbits at 55.4 AU include:
* , dwarf candidate
*
*
*
*
*
* ]472235 Zhulong
47, 47 or forty-seven may refer to:
*47 (number)
*47 BC
*AD 47
* 1947
*2047
*'47 (brand), an American clothing brand
* ''47'' (magazine), an American publication
* 47 (song), a song by Sidhu Moose Wala
*47, a song by New Found Glory from the albu ...
*
*
*
*
*
1:3 resonance (period ~500 years)
Johnston's Archive counts 14 1:3-resonant objects as of February 2020.[ A dozen of these are secure according to the Deep Ecliptic Survey:]
*
*
*
*
*
*
*
* ?
*
*
*
* ?
*
*
Other resonances
As of February 2020, the following higher-order resonances are confirmed for a limited number of objects:
Haumea
Haumea is thought to be in an intermittent 7:12 orbital resonance with Neptune. Its ascending node
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of reference ...
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. Marc Buie
Marc William Buie (; born 1958) is an American astronomer and prolific discoverer of minor planets who works at the Southwest Research Institute in Boulder, Colorado in the Space Science Department. Formerly he worked at the Lowell Observatory ...
qualifies it as non-resonant.
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 period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...
s of more than 300 years and most have only been observed over a relatively short observation arc
ARC may refer to:
Business
* Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s
* Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services
* ...
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 coincidence is a remarkable concurrence of events or circumstances that have no apparent causal connection with one another. The perception of remarkable coincidences may lead to supernatural, occult, or paranormal claims, or it may lead to ...
. A true resonance will smoothly oscillate while a coincidental near resonance will circulate. (See Toward a formal definition)
Simulations by Emel'yanenko and Kiseleva in 2007 show that is librating in a 3:7 resonance with Neptune. This libration can be stable for less than 100 million to billions of years.[
]
Emel'yanenko and Kiseleva also show that 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.[
]
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
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.
Since 1998 through the end of 2003, the sur ...
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 longitude Mean longitude is the ecliptic longitude at which an orbiting body could be found if its orbit were circular and free of perturbations. While nominally a simple longitude, in practice the mean longitude does not correspond to any one physical angle ...
s of the object and Neptune, but can also involve the longitude of the perihelion and the longitudes of the nodes
In general, a node is a localized swelling (a "knot") or a point of intersection (a Vertex (graph theory), vertex).
Node may refer to:
In mathematics
*Vertex (graph theory), a vertex in a mathematical graph
*Vertex (geometry), a point where two ...
(see orbital resonance
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 relationsh ...
, 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):[
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
:
where the are the longitudes of perihelia and the are the longitudes of the ascending node
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained in the reference plane, has no nodes.
Planes of reference
Common planes of reference ...
s, 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°.
All new plutinos discovered during the Deep Ecliptic Survey
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.
Since 1998 through the end of 2003, the sur ...
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. 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.
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 positive
A false positive is an error in binary classification in which a test result incorrectly indicates the presence of a condition (such as a disease when the disease is not present), while a false negative is the opposite error, where the test result ...
s (i.e. classification as resonant of an orbit which is not). A recent approach[
] considers not only the current best-fit
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is ...
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
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to:
Dress code and events
* Formal wear, attire for formal events
* Semi-formal attire ...
), the classification as a resonant object is considered secure. 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. 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
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
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%. The method is applicable to objects with observations spanning at least 3 oppositions.
References
Further reading
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as HTML
{{DEFAULTSORT:Resonant Trans-Neptunian Object