Resonant trans-Neptunian object

{{Short description|Trans-Neptunian object in a mean-motion orbital resonance with Neptune}}

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.{{Cite journal|last1=Hahn|first1=Joseph M.|last2=Malhotra|first2=Renu|author-link2=Renu Malhotra|date=November 2005|title=Neptune's Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations|journal=The Astronomical Journal|volume=130|issue=5|pages=2392–2414|arxiv=astro-ph/0507319|bibcode=2005AJ....130.2392H|doi=10.1086/452638|s2cid=14153557}}

Distribution

File: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; 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.{{Cite journal|last=Malhotra|first=Renu|author-link=Renu Malhotra|date=January 1996|title=The Phase Space Structure Near Neptune Resonances in the Kuiper Belt|url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970021298.pdf|url-status=live|journal=The Astronomical Journal|type=preprint|volume=111|page=504|arxiv=astro-ph/9509141|bibcode=1996AJ....111..504M|doi=10.1086/117802|archive-url=https://web.archive.org/web/20180723131740/https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970021298.pdf|archive-date=23 July 2018|via=the NASA Technical Report Server|hdl=2060/19970021298|s2cid=41919451}}{{Cite journal|last1=Chiang|first1=E. I.|last2=Jordan|first2=A. B.|date=December 2002|title=On the Plutinos and Twotinos of the Kuiper Belt|journal=The Astronomical Journal|volume=124|issue=6|pages=3430–3444|arxiv=astro-ph/0210440|bibcode=2002AJ....124.3430C|doi=10.1086/344605|s2cid=13928812}} 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.{{Cite journal|last=Malhotra|first=Renu|author-link=Renu Malhotra|date=July 1995|title=The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune|url=https://archive.org/details/nasa_techdoc_19970005091|journal=The Astronomical Journal|volume=110|issue=1|pages=420–429|arxiv=astro-ph/9504036|bibcode=1995AJ....110..420M|doi=10.1086/117532|via=the Internet Archive|hdl=2060/19970005091|s2cid=10622344}} 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.{{Cite book|title=Protostars and Planets IV|last1=Malhotra|first1=Renu|last2=Duncan|first2=Martin J.|last3=Levison|first3=Harold F.|publisher=University of Arizona Press|isbn=978-0816520596|editor-last=Mannings|editor-first=Vincent|series=Space Science Series|date=May 2000|page=1231|chapter=Dynamics of the Kuiper Belt|type=preprint|arxiv=astro-ph/9901155|bibcode=2000prpl.conf.....M|lccn=99050922|author-link=Renu Malhotra|author-link3=Harold F. Levison|editor-last2=Boss|editor-first2=Alan P.|editor-link2=Alan Boss|editor-last3=Russell|editor-first3=Sara S.|editor-link3=Sara Russell|chapter-url=https://www.lpl.arizona.edu/~renu/malhotra_preprints/kbd_ppiv.pdf|archive-url=https://web.archive.org/web/20170811213115/https://www.lpl.arizona.edu/~renu/malhotra_preprints/kbd_ppiv.pdf|archive-date=11 August 2017|url-status=live|via=the Lunar and Planetary Laboratory}}

Known populations

= {{anchor|1:1}} 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. 31 are known as of February 2024.{{cite web | url= http://www.johnstonsarchive.net/astro/tnoslist.html | title= List of Known Trans-Neptunian Objects (and other outer solar system objects) | date= 27 February 2024 | author= Johnston's Archive}} Only 3 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. In addition, {{mpl|(316179) 2010 EN|65}} is a so-called "jumping trojan", currently transitioning from librating around {{L4}} to librating around {{L5}}, via the {{L3}} region.{{Cite journal |first1 = C. |last1 = de la Fuente Marcos |first2 = R. |last2 = de la Fuente Marcos |date = November 2012 |title = Four temporary Neptune co-orbitals: (148975) 2001 XA255, (310071) 2010 KR59, (316179) 2010 EN65, and 2012 GX17 |journal = Astronomy and Astrophysics |volume = 547 |page = 7 |bibcode = 2012A&A...547L...2D |doi = 10.1051/0004-6361/201220377 |arxiv = 1210.3466 |s2cid = 118622987 }} [http://www.aanda.org/articles/aa/full_html/2012/11/aa20377-12/F1.html (rotating frame)]

;Leading Trojans at {{L4}}:

{{mpl|385571 Otrera}}
{{mpl|385695 Clete}}
{{mpl|(527604) 2007 VL|305}}
{{mpl|(530664) 2011 SO|277}}
{{mpl|(530930) 2011 WG|157}}
{{mpl|(612243) 2001 QR|322}}
{{mpl|(613490) 2006 RJ|103}}
{{mpl|(666739) 2010 TS|191}}
{{mpl|2005 TN|53}}
{{mpl|2010 TT|191}}
{{mpl|2012 UV|177}}
{{mpl|2012 UD|185}}
{{mpl|2013 RL|124}}
{{mpl|2013 RC|158}}
{{mpl|2013 TZ|187}}
{{mpl|2013 TK|227}}
{{mpl|2013 VX|30}}
{{mpl|2014 QO|441}}
{{mpl|2014 QP|441}}
{{mpl|2014 RO|74}}
{{mpl|2014 SC|374}}
{{mpl|2014 UU|240}}
{{mpl|2014 YB|92}}
{{mpl|2015 RW|277}}
{{mpl|2015 VV|165}}
{{mpl|2015 VW|165}}
{{mpl|2015 VX|165}}
{{mpl|2015 VU|207}}

;Following Trojans at {{L5}}:

{{mpl|2008 LC|18}}
{{mpl|2011 HM|102}}
{{mpl|2013 KY|18}}

= {{anchor|2:3}} 2:3 resonance ("plutinos", period 247.0 years) =

File:OrcusandPlutoRotatingFrame.gif (in grey) and Pluto (in red) in a rotating frame with a period equal to Neptune's orbital period (holding Neptune stationary)]]

File:ThePlutinos Size Albedo Color2.svg and colour with Orcus, {{mpl-|208996|2003 AZ|84}}, 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 {{mpl|(175113) 2004 PF|115}}). Of these 383 confirmed plutinos, 338 have their orbits secured in simulations run by the Deep Ecliptic Survey. The objects following orbits in this resonance are named plutinos after Pluto, the first such body discovered. Large, numbered plutinos include:

{{mpl|Pluto}}
{{mpl|90482 Orcus}}
{{mpl|(208996) 2003 AZ|84}}
{{mpl|(455502) 2003 UZ|413}}
{{mpl|(84922) 2003 VS|2}}
{{mpl|28978 Ixion}}
{{mpl|(84719) 2002 VR|128}}
{{mpl|(469372) 2001 QF|298}}
{{mpl|38628 Huya}}
{{mpl|(33340) 1998 VG|44}}
{{mpl|(15789) 1993 SC|}}
{{mpl|(444745) 2007 JF|43}}
{{mpl|(532092) 2013 HU|156}}
{{mpl|(523760) 2014 WQ|509}}
{{mpl|(523768) 2014 WQ|510}}
{{mpl|(469421) 2001 XD|255}}
{{mpl|(533209) 2014 DR|143}}
{{mpl|(523655) 2011 VJ|24}}
{{mpl|(120216) 2004 EW|95}}
{{mpl|(523715) 2014 KU|101}}
{{mpl|47171 Lempo}}
{{mpl|(523644) 2010 VX|11}}
{{mpl|(524216) 2001 RU|143}}
{{mpl|(525258) 2004 VT|75}}
{{mpl|(531077) 2012 DB|99}}
{{mpl|(504555) 2008 SO|266}}
{{mpl|(307463) 2002 VU|130}}
{{mpl|(55638) 2002 VE|95}}
{{mpl|(524460) 2002 GF|32}}
{{mpl|(523717) 2014 KY|101}}
{{mpl|(450265) 2003 WU|172}}
{{mpl|(535029) 2014 WG|510}}
{{mpl|(385445) 2003 QH|91}}
{{mpl|(469987) 2006 HJ|123}}
{{mpl|(523697) 2014 GY|53}}
{{mpl|(523618) 2007 RT|15}}
{{mpl|(535231) 2014 YJ|50}}
{{mpl|(508823) 2001 RX|143}}
{{mpl|(469506) 2003 FF|128}}
{{mpl|(523766) 2014 WF|510}}
{{mpl|(529938) 2010 TM|182}}
{{mpl|(133067) 2003 FB|128}}
{{mpl|(523751) 2014 UU|224}}
{{mpl|(306792) 2001 KQ|77}}
{{mpl|(469704) 2005 EZ|296}}

= {{anchor|3:5}} 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:

{{mpl|(15809) 1994 JS}}
{{mpl|(126154) 2001 YH|140}}
{{mpl|(143751) 2003 US|292}}
{{mpl|(149349) 2002 VA|131}}
{{mpl|(434709) 2006 CJ|69}}
{{mpl|(469420) 2001 XP|254}}
{{mpl|(469584) 2003 YW|179}}
{{mpl|(470523) 2008 CS|190}}
{{mpl|(503883) 2001 QF|331}}
{{mpl|(523677) 2013 UF|15}}
{{mpl|(523688) 2014 DK|143}}
{{mpl|(523731) 2014 OK|394}}
{{mpl|(523743) 2014 TA|86}}
{{mpl|(530839) 2011 UK|411}}
{{mpl|(531683) 2012 UC|178}}
{{mpl|(534074) 2014 QZ|441}}
{{mpl|(534314) 2014 SJ|349}}

= {{anchor|4:7}} 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. {{As of|February 2020}}, 55 4:7-resonant objects have had their orbits secured by the Deep Ecliptic Survey. Objects with well established orbits include:

{{mpl|(60620) 2000 FD|8}}
{{mpl|(118378) 1999 HT|11}}
{{mpl|(118698) 2000 OY|51}}
{{mpl|(119066) 2001 KJ|76}}
{{mpl|(119070) 2001 KP|77}}
{{mpl|(119956) 2002 PA|149}}
{{mpl|(129772) 1999 HR|11}}
{{mpl|(135024) 2001 KO|76}}
{{mpl|(135742) 2002 PB|171}}
{{mpl|(181871) 1999 CO|153}}
385446 Manwë
{{mpl|(385527) 2004 OK|14}}
{{mpl|(500828) 2013 GR|136}}
{{mpl|(523742) 2014 TZ|85}}
{{mpl|(525816) 2005 SF|278}}
{{mpl|(531917) 2013 BN|82}}
{{mpl|(532039) 2013 FR|28}}
{{mpl|(533028) 2014 AL|55}}

= {{anchor|1:2}} 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. 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.{{cite journal|author1=Lykawka, Patryk Sofia |author2=Mukai, Tadashi |name-list-style=amp |date=July 2007| title= Dynamical classification of trans-neptunian objects: Probing their origin, evolution, and interrelation |journal = Icarus |volume=189 |issue=1 |pages=213–232 |url= https://www.researchgate.net/publication/223445604 |doi=10.1016/j.icarus.2007.01.001 |bibcode=2007Icar..189..213L}}

There are far fewer objects in this resonance than plutinos. Johnston's Archive counts 111 while simulations by the Deep Ecliptic Survey have confirmed 126 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.{{cite journal

|author1=M. Tiscareno |author2=R. Malhotra |title=Chaotic Diffusion of Resonant Kuiper Belt Objects

|volume=194|year=2009

|arxiv=0807.2835

|bibcode = 2009AJ....138..827T |doi = 10.1088/0004-6256/138/3/827

|journal=The Astronomical Journal

|issue=3

|pages=827–837 |s2cid=1764121 }}

Objects with well established orbits include (in order of the diameter):

{{mpl|(119979) 2002 WC|19}}
{{mpl|(612931) 2005 CA|79}}
{{mpl|(312645) 2010 EP|65}}
{{mpl|(576256) 2012 JH|67}}
{{mpl|(523617) 2007 PS|45}}
{{mpl|(523691) 2014 DO|143}}
{{mpl|(308379) 2005 RS|43}}
{{mpl|(26308) 1998 SM|165}}
{{mpl|(554856) 2013 CF|229}}
{{mpl|(554102) 2012 KW|51}}
{{mpl|(612892) 2004 TV|357}}
{{mpl|(495189) 2012 VR|113}}
{{mpl|(534626) 2014 UT|224}}
{{mpl|(469505) 2003 FE|128}}
{{mpl|(535025) 2014 WT|509}}
{{mpl|(137295) 1999 RB|216}}
{{mpl|(524179) 2001 FQ|185}}
{{mpl|(500880) 2013 JJ|64}}
{{mpl|(20161) 1996 TR|66}}
{{mpl|(583751) 2016 NZ|90}}
{{mpl|(531074) 2012 DX|98}}
{{mpl|(612524) 2002 VD|130}}
{{mpl|(470083) 2006 SG|369}}
{{mpl|(612176) 2000 QL|251}}
{{mpl|(130391) 2000 JG|81}}
{{mpl|(577578) 2013 GW|136}}
{{mpl|(581804) 2015 KN|167}}
{{mpl|(612051) 1997 SZ|10}}
{{mpl|(500877) 2013 JE|64}}

= {{anchor|2:5}} 2:5 resonance (period 411.7 years) =

There are 57 confirmed 2:5-resonant objects at 55.3 AU as of February 2020.

Objects with well established orbits at 55.4 AU include:

{{mpl|(26375) 1999 DE|9}}
{{mpl|(38084) 1999 HB|12}}
{{mpl|(60621) 2000 FE|8}}
{{mpl|(69988) 1998 WA|31}}
{{mpl|(84522) 2002 TC|302}}
{{mpl|(119068) 2001 KC|77}}
{{mpl|(135571) 2002 GG|32}}
{{mpl|(143707) 2003 UY|117}}
{{mpl|(471151) 2010 FD|49}}
{{mpl|(471172) 2010 JC|80}}
472235 Zhulong
{{mpl|(495603) 2015 AM|281}}
{{mpl|(523769) 2014 WS|510}}
{{mpl|(523713) 2014 JX|80}}
{{mpl|(524365) 2001 XQ|254}}
{{mpl|(531017) 2012 BA|155}}
{{mpl|(535991) 2015 BD|519}}

= {{anchor|1:3}} 1:3 resonance (period 494.1 years) =

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

{{mpl|(136120) 2003 LG|7}}
{{mpl|(385607) 2005 EO|297}}
{{mpl|2004 VU|130}}
{{mpl|(613469) 2006 QJ|181}}
{{mpl|2006 SF|369}}
{{mpl|2011 US|411}}
{{mpl|2014 FX|71}}
{{mpl|2015 BZ|517}}?
{{mpl|2015 GA|55}}
{{mpl|2015 KY|173}}
{{mpl|2015 RA|278}}
{{mpl|2015 RZ|277}}?
{{mpl|2015 VM|166}}
{{mpl|2015 VN|166}}

= Other resonances =

File:2015RR245 resonance.gif]]

As of February 2024, the following higher-order resonances are confirmed for a limited number of objects:

class="wikitable sortable" !Ratio	Semimajor AU	Period years	Count	Examples
4:5	34.9	205.9	17 confirmed	{{mpl\|(432949) 2012 HH\|2}}, {{mpl\|(127871) 2003 FC\|128}}, {{mpl\|(308460) 2005 SC\|278}}, {{mpl\|(79969) 1999 CP\|133}}, {{mpl\|(427581) 2003 QB\|92}}, {{mpl\|(131697) 2001 XH\|255}}
\|3:4	36.4	219.6	50 confirmed	{{mpl\|(143685) 2003 SS\|317}}, {{mpl\|15836\|1995 DA\|2}}
\|5:7	37.6	226.5	1 confirmed	{{mpl\|2013 RD\|157}}
\|7:10	38.6	240.2	1 confirmed	{{mpl\|2014 UF\|229}}
\|7:11	40.1	250.5	1 confirmed	{{mpl\|(555915) 2014 GX\|53}}
\|5:8	41.1	263.5	4 confirmed	{{mpl\|(533398) 2014 GA\|54}}
\|7:12	43.0	282.3	1 confirmed	{{mpl\|2015 RP\|278}}
\| 5:9	44.5	296.5	6 confirmed	{{mpl\|(437915) 2002 GD\|32}}
\|6:11	45.0	301.9	4 confirmed	{{mpl\| (523725) 2014 MC\|70}}, {{mpl\|(505477) 2013 UM\|15}}
\|3:6	46.6	314.2	1 confirmed	{{mpl\|2013 TA\|228}}
\| 5:11	50.8	362.3	1 confirmed	{{mpl\|2013 RM\|109}}
\| 4:9	51.6	370.6	5 confirmed	{{mpl\|42301\|2001 UR\|163}}, {{mpl\|(182397) 2001 QW\|297}}
\| 3:7	52.9	384.3	17 confirmed	{{mpl\|(495297) 2013 TJ\|159}}, {{mpl\|(181867) 1999 CV\|118}}, {{mpl\|(131696) 2001 XT\|254}}, {{mpl\|(95625) 2002 GX\|32}}, {{mpl\|(183964) 2004 DJ\|71}}, {{mpl\|(500882) 2013 JN\|64}}
\|5:12	53.9	395.3	6 confirmed	{{mpl\|79978\|1999 CC\|158}}, {{mpl\|(119878) 2002 CY\|224}}
\|3:8	57.8	439.2	5 confirmed	{{mpl\|82075\|2000 YW\|134}}, {{mpl\|(542258) 2013 AP\|183}}, {{mpl\|2014 UE\|228}}
\|4:13	65.9	535.3	3 confirmed	{{mpl\|2006 QH\|181}}, {{mpl\|2009 DJ\|143}}
\|3:10	67.0	549.0	2 confirmed	225088 Gonggong
\|2:7	69.3	576.4	17 confirmed	471143 Dziewanna, {{mpl\|(160148) 2001 KV\|76}}
\|3:11	71.4	603.9	5 confirmed	{{mpl\|534627\|2014 UV\|224}}, {{mpl\|2013 AR\|183}}
\|1:4	75.7	658.8	8 confirmed	{{mpl\|2003 LA\|7}}, {{mpl\|2011 UP\|411}}
\|5:21	78.2	691.7	1 confirmed	{{mpl\|(574372) 2010 JO\|179}}{{cite journal \|author1=Matthew J. Holman \|author2=Matthew J. Payne \|author3=Wesley Fraser \|author4=Pedro Lacerda \|author5=Michele T. Bannister \|author6=Michael Lackner \|author7=Ying-Tung Chen \|author8=Hsing Wen Lin \|author9=Kenneth W. Smith \|author10=Rosita Kokotanekova \|author11=David Young \|author12=K. Chambers \|author13=S. Chastel \|author14=L. Denneau \|author15=A. Fitzsimmons \|author16=H. Flewelling \|author17=Tommy Grav \|author18=M. Huber \|author19=Nick Induni \|author20=Rolf-Peter Kudritzki \|author21=Alex Krolewski \|author22=R. Jedicke \|author23=N. Kaiser \|author24=E. Lilly \|author25=E. Magnier \|author26=Zachary Mark \|author27=K. J. Meech \|author28=M. Micheli \|author29=Daniel Murray \|author30=Alex Parker \|author31=Pavlos Protopapas \|author32=Darin Ragozzine \|author33=Peter Veres \|author34=R. Wainscoat \|author35=C. Waters \|author36=R. Weryk \|title=A Dwarf Planet Class Object in the 21:5 Resonance with Neptune \|journal=The Astrophysical Journal Letters \|date=2018 \|volume=855 \|issue=1 \|at=L6 1 March 2018 \|doi=10.3847/2041-8213/aaadb3 \|arxiv=1709.05427 \|bibcode=2018ApJ...855L...6H \|doi-access=free}}
\|2:9	81.9	741.1	3 confirmed	{{mpl\|(523794) 2015 RR\|245}}, {{mpl\|2003 UA\|414}}, {{mpl\|2018 VG\|18}}
\|1:5	87.9	823.5	4 confirmed	{{mpl\|2007 FN\|51}}, {{mpl\|667161\|2011 BP\|170}}
\|2:11	93.6	905.8	3 confirmed	{{mpl\|613037\|2005 RP\|43}}, {{mpl\|2011 HO\|60}}
\|1:6	99.2	988.2	4 confirmed	{{mpl\|(528381) 2008 ST\|291}}, {{mpl\|668381\|2011 WJ\|157}}
\|1:8	120.0	1241.1	1 confirmed	{{mpl\|2014 RV\|86}}
\|1:9	130.0	1482.3	2 confirmed	{{mpl\|2007 TC\|434}}, {{mpl\|2015 KE\|172}}

=Haumea=

{{multiple image |direction=vertical |align=right |total_width=300

|image1=Haumea.GIF |caption1=The libration of Haumea's nominal orbit in a rotating frame, with Neptune stationary (see 2 Pallas for an example of non-librating)

|image2=Haumea resonant angle.png |caption2=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.{{cite journal |title=Candidate Members and Age Estimate of the Family of Kuiper Belt Object 2003 EL₆₁ |author1=D. Ragozzine |author2=M. E. Brown |journal=The Astronomical Journal |volume=134|issue=6|pages= 2160–2167 |date=2007-09-04 |bibcode=2007AJ....134.2160R |doi=10.1086/522334|arxiv=0709.0328|s2cid=8387493 }} 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.{{cite web |author = Marc W. Buie |author-link = Marc W. Buie |date = 2008-06-25 |title = Orbit Fit and Astrometric record for 136108 |publisher = Southwest Research Institute (Space Science Department) |url = http://www.boulder.swri.edu/~buie/kbo/astrom/136108.html |access-date = 2008-10-02 |url-status = live |archive-url = https://web.archive.org/web/20110518005546/http://www.boulder.swri.edu/~buie/kbo/astrom/136108.html |archive-date = 2011-05-18}} Marc Buie qualifies it as non-resonant.{{Cite web|title=Orbit and Astrometry for 136108|url=https://www.boulder.swri.edu/~buie/kbo/astrom/136108.html|access-date=2020-07-14|website=www.boulder.swri.edu}}

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|date=November 2019}} (See Toward a formal definition)

Simulations by Emel'yanenko and Kiseleva in 2007 show that {{mpl|(131696) 2001 XT|254}} is librating in a 3:7 resonance with Neptune.{{cite journal

|last=Emel'yanenko |first=V. V

|author2=Kiseleva, E. L.

|title=Resonant motion of trans-Neptunian objects in high-eccentricity orbits

|journal=Astronomy Letters

|volume=34 |pages=271–279 |year=2008

|bibcode=2008AstL...34..271E

|doi=10.1134/S1063773708040075

|issue=4 |s2cid=122634598

}} This libration can be stable for less than 100 million to billions of years.

File:2001XT254 Resonance.jpg

Emel'yanenko and Kiseleva also show that {{mpl|(48639) 1995 TL|8}} 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.

File:1995TL8 Orbital Period.jpg

{{anchor|Definition}}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):

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.

[http://alpaca.as.arizona.edu/~trilling/des2.pdf preprint] {{webarchive|url=https://web.archive.org/web/20060823112517/http://alpaca.as.arizona.edu/~trilling/des2.pdf |date=2006-08-23 }}

: $\phi = \rm p\cdot\lambda - \rm q\cdot\lambda_{\rm N} - \rm m\cdot\varpi - \rm n\cdot\Omega - \rm r\cdot\varpi_{\rm N} -\rm s\cdot\Omega_{\rm N}$

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°.{{Citation|url=https://www.boulder.swri.edu/~buie/kbo/astrom/134340.html|title=Orbit Fit and Astrometric record for 134340|author=Mark Buie|date=12 November 2019|archive-url=https://web.archive.org/web/20191111230750/https://www.boulder.swri.edu/~buie/kbo/astrom/134340.html|archive-date=11 November 2019|url-status=live}}

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. 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.

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

{{cite book

|author1=B. Gladman |author2=B. Marsden |author3=C. VanLaerhoven

|title=Nomenclature in the Outer Solar System

|journal=The Solar System Beyond Neptune

|isbn=9780816527557

|year=2008

|bibcode=2008ssbn.book...43G

}} 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. 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 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.

References

{{reflist|refs=

{{cite web

|title = List Of Neptune Trojans

|work = Minor Planet Center

|date = 27 February 2024

|url = http://www.minorplanetcenter.org/iau/lists/NeptuneTrojans.html

|access-date = 24 January 2025}}