640:, orbits the Sun with a period slightly less than one Earth year, resulting in an orbit that (from the point of view of Earth) appears as a bean-shaped orbit centered on a position ahead of the position of Earth. This orbit slowly moves further ahead of Earth's orbital position. When Cruithne's orbit moves to a position where it trails Earth's position, rather than leading it, the gravitational effect of Earth increases the orbital period, and hence the orbit then begins to lag, returning to the original location. The full cycle from leading to trailing Earth takes 770 years, leading to a horseshoe-shaped movement with respect to Earth.
547:
210:
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share their orbits, the difference in semi-major axes being less than either's mean diameter. This means the moon with the smaller semi-major axis slowly catches up with the other. As it does this, the moons gravitationally tug at each other, increasing the semi-major axis of the moon that has caught
751:
Quasi-satellites are co-orbital objects that librate around 0° from the primary. Low-eccentricity quasi-satellite orbits are highly unstable, but for moderate to high eccentricities such orbits can be stable. From a co-rotating perspective the quasi-satellite appears to orbit the primary like a
628:
up and decreasing that of the other. This reverses their relative positions proportionally to their masses and causes this process to begin anew with the moons' roles reversed. In other words, they effectively swap orbits, ultimately oscillating both about their mass-weighted mean orbit.
299:
199:
154:
1038:
Balsalobre-Ruza, O.; de
Gregorio-Monsalvo, I.; et al. (July 2023). "Tentative co-orbital submillimeter emission within the Lagrangian region L5 of the protoplanet PDS 70 b".
933:
Placek, Ben; Knuth, Kevin H.; Angerhausen, Daniel; Jenkins, Jon M. (2015). "Characterization of Kepler-91B and the
Investigation of a Potential Trojan Companion Using Exonest".
245:) a more massive object, both in orbit around an even more massive central object. The best known examples are the large population of asteroids that orbit ahead of or behind
848:
787:
In addition to swapping semi-major axes like Saturn's moons
Epimetheus and Janus, another possibility is to share the same axis, but swap eccentricities instead.
1576:
466:). However, the mentioned study is only in preprint form on arXiv, and it has not yet been peer reviewed and published in a reputable scientific journal.
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1345:
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There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near
Jupiter's Lagrangian points, the traditional
523:), and the proto-Earth. Their orbits were perturbed by other planets, bringing Theia out of its trojan position and causing the collision.
89:
occurs when two co-orbital objects are of similar masses and thus exert a non-negligible influence on each other. The objects can exchange
1570:
593:
Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral
Lagrangian points, i.e. L
260:
1119:
Dvorak, R.; Pilat-Lohinger, E.; Schwarz, R.; Freistetter, F. (2004). "Extrasolar Trojan planets close to habitable zones".
636:
A small number of asteroids have been found which are co-orbital with Earth. The first of these to be discovered, asteroid
915:
301:= (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity.
1017:
991:
157:
499:
The reason why no trojan planets have been definitively detected could be that tides destabilize their orbits.
166:
48:
257:, but do remain relatively close to it, appearing to slowly orbit it. In technical terms, they librate around
1097:
227:, highlighted in red, on the orbital path of the secondary object (blue), around the primary object (yellow).
119:
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were found to be one of the possible sources for co-orbital objects of the Earth with a lifetime up to ~58
546:
1173:
1598:
1040:
1585:
Web page of group of astronomers searching for extrasolar trojan planets at
Appalachian State University
106:
424:: it wanders as far as ±30° from its Lagrangian point and ±2% from its mean orbital radius, along a
78:, in which objects librate around 180° from the larger body. Objects librating around 0° are called
535:
508:
232:
1514:
1290:"The Hungaria region as a possible source of Trojans and satellites in the inner Solar system"
756:, although at distances so large that it is not gravitationally bound to it. Two examples of
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In July 2023, the possible detection of a cloud of debris co-orbital with the proto-planet
94:
1515:"Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets"
43:) orbiting at the same, or very similar, distance from their primary; i.e., they are in a
8:
221:
214:
28:
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Orbital parameters that are used to describe the relation of co-orbital objects are the
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difference. The longitude of the periapsis is the sum of the mean longitude and the
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462:, close to the star GJ 3470 (this star has been known to have a confirmed planet
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was studied but the conclusion was that the transit-signal was a false-positive.
90:
79:
75:
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in 790 days (288 times its orbital period around Saturn, the same as Dione's).
390:
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110:
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637:
425:
402:
378:
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74:, 60° ahead of and behind the larger body respectively. Another class is the
54:
There are several classes of co-orbital objects, depending on their point of
1458:
1422:"Asteroid (469219) 2016 HO3, the smallest and closest Earth quasi-satellite"
1421:
1377:
1340:
1324:
1289:
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843:
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724:
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382:
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114:
1475:"Exchange orbits: a possible application to extrasolar planetary systems?"
519:, thought to have had about 10% of the mass of Earth (about as massive as
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648:
448:
441:
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369:) that are known to exist. No Saturnian trojans have been observed.
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de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl (2016).
1339:
de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl (2014).
616:
473:
was announced. This debris cloud could be evidence of a Trojan
470:
40:
932:
761:
377:
The
Saturnian system contains two sets of trojan moons. Both
1094:"Does this exoplanet have a sibling sharing the same orbit?"
1398:
844:"Asteroids in retrograde resonance with Jupiter and Saturn"
520:
512:
493:
1577:
Cassini
Observes the Orbital Dance of Epimetheus and Janus
1392:
Agle, DC; Brown, Dwayne; Cantillo, Laurie (15 June 2016).
849:
Monthly
Notices of the Royal Astronomical Society Letters
734:
515:
formed after a collision between two co-orbital objects:
458:
reported two new exoplanet candidates co-orbiting , in a
250:
1341:"Asteroid 2014 OL339: yet another Earth quasi-satellite"
253:. Trojan objects do not orbit exactly at one of either
701:
which exist in resonant orbits similar to
Cruithne's.
294:{\displaystyle ({\Delta }{\lambda },{\Delta }\varpi )}
502:
263:
169:
122:
1172:
Dobrovolskis, Anthony R.; Lissauer, Jack J. (2022).
1171:
794:
293:
193:
148:
1479:Monthly Notices of the Royal Astronomical Society
1427:Monthly Notices of the Royal Astronomical Society
1391:
1346:Monthly Notices of the Royal Astronomical Society
1294:Monthly Notices of the Royal Astronomical Society
1235:Monthly Notices of the Royal Astronomical Society
1013:"The Extrasolar Planet Encyclopaedia — GJ 3470 e"
987:"The Extrasolar Planet Encyclopaedia — GJ 3470 d"
647:(NEOs) have since been discovered. These include
16:Configuration of two or more astronomical objects
1590:
841:
1287:
1231:"A long-lived horseshoe companion to the Earth"
1394:"Small Asteroid Is Earth's Constant Companion"
62:, which librates around one of the two stable
58:. The most common and best-known class is the
1385:
1228:
899:
897:
895:
893:
891:
631:
904:Dynamics of two planets in co-orbital motion
1513:Eric B. Ford and Matthew J. Holman (2007).
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1439:
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1358:
1323:
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1174:"Do tides destabilize Trojan exoplanets?"
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194:{\displaystyle (\varpi =\Omega +\omega )}
156:and the mean longitude is the sum of the
1571:QuickTime animation of co-orbital motion
1332:
545:
530:
208:
1413:
542:exchange orbits of Janus and Epimetheus
304:
1591:
1229:Christou, A. A.; Asher, D. J. (2011).
1086:
447:The possibility of a trojan planet to
420:Polydeuces is noticeable for its wide
213:Trojan points are the points labelled
149:{\displaystyle ({\lambda }=\varpi +M)}
1288:Galiazzo, M. A.; Schwarz, R. (2014).
916:"Two planets found sharing one orbit"
440:was proposed to be orbiting the star
1472:
237:Trojan objects orbit 60° ahead of (L
842:Morais, M.H.M.; F. Namouni (2013).
604:
526:
13:
782:
740:
503:Formation of the Earth–Moon system
477:or one in the process of forming.
281:
268:
179:
27:is a configuration of two or more
14:
1610:
1564:
1519:The Astrophysical Journal Letters
431:
1500:10.1111/j.1365-2966.2010.17453.x
1266:10.1111/j.1365-2966.2011.18595.x
1018:Extrasolar Planets Encyclopaedia
992:Extrasolar Planets Encyclopaedia
797:
554:orbit - Rotating reference frame
444:, but this was later retracted.
313:. As of 2015, there are also 13
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1281:
1222:
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823:Chinese Space Station Telescope
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158:longitude of the ascending node
97:when they approach each other.
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611:Epimetheus (moon) § Orbit
288:
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1:
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100:
1208:10.1016/j.icarus.2022.115087
1121:Astronomy & Astrophysics
1041:Astronomy & Astrophysics
723:are the only two identified
385:have two trojan moons each,
7:
1583:A Search for Trojan Planets
1151:10.1051/0004-6361:200400075
1072:10.1051/0004-6361/202346493
965:10.1088/0004-637X/814/2/147
790:
10:
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632:Earth co-orbital asteroids
608:
586:
454:In April 2023, a group of
230:
204:
107:longitude of the periapsis
47:. (or 1:-1 if orbiting in
935:The Astrophysical Journal
45:1:1 mean-motion resonance
480:One possibility for the
460:horseshoe exchange orbit
25:co-orbital configuration
1573:from Murray and Dermott
1143:2004A&A...426L..37D
1064:2023A&A...675A.172B
550:Animation of Epimetheus
509:giant impact hypothesis
233:Trojan (celestial body)
584:
543:
295:
228:
195:
150:
1579:The Planetary Society
1459:10.1093/mnras/stw1972
1378:10.1093/mnras/stu1978
1325:10.1093/mnras/stu2016
881:10.1093/mnrasl/slt106
549:
534:
436:A pair of co-orbital
296:
212:
196:
162:argument of periapsis
151:
754:retrograde satellite
305:Trojan minor planets
261:
167:
120:
29:astronomical objects
1541:2007ApJ...664L..51F
1491:2011MNRAS.410..455F
1450:2016MNRAS.462.3441D
1369:2014MNRAS.445.2961D
1316:2014MNRAS.445.3999G
1257:2011MNRAS.414.2965C
1200:2022Icar..38515087D
957:2015ApJ...814..147P
922:. 24 February 2011.
872:2013MNRAS.436L..30M
475:planetary-mass body
456:amateur astronomers
109:difference and the
49:opposite directions
1599:Co-orbital objects
777:469219 Kamoʻoalewa
731:Hungaria asteroids
645:near-Earth objects
585:
544:
401:respectively, and
291:
229:
191:
146:
66:(Trojan points), L
1473:Funk, B. (2010).
818:Kordylewski cloud
538:depiction of the
507:According to the
255:Lagrangian points
64:Lagrangian points
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676:(419624) 2010 SO
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364:(614689) 2020 XL
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786:
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729:
642:
635:
614:
592:
574:
563:
506:
498:
490:giant planet
485:
479:
468:
453:
446:
435:
419:
409:in Dione's L
376:
373:Trojan moons
319:Mars trojans
308:
236:
115:mean anomaly
104:
86:
84:
53:
24:
18:
1300:(4): 3999.
1241:(4): 2965.
856:: L30–L34.
249:around the
1441:1608.01518
1307:1612.00275
1191:2206.07097
1184:: 115087.
1055:2307.12811
1024:2023-04-28
998:2023-04-28
948:1511.01068
941:(2): 147.
829:References
649:54509 YORP
625:Epimetheus
609:See also:
449:Kepler-91b
442:Kepler-223
438:exoplanets
407:Polydeuces
101:Parameters
1532:0705.0356
1360:1409.5588
1248:1104.0036
1216:248979920
1080:259684169
973:118366565
863:1308.0216
617:Saturnian
540:horseshoe
464:GJ 3470 b
422:libration
347:), and 2
286:ϖ
282:Δ
274:λ
269:Δ
186:ω
180:Ω
174:ϖ
135:ϖ
128:λ
56:libration
33:asteroids
31:(such as
21:astronomy
1593:Category
1557:14285948
1275:13832179
1159:15637771
1048:: A172.
791:See also
471:PDS 70 b
160:and the
1537:Bibcode
1487:Bibcode
1446:Bibcode
1405:15 June
1365:Bibcode
1312:Bibcode
1253:Bibcode
1196:Bibcode
1139:Bibcode
1104:19 July
1060:Bibcode
953:Bibcode
868:Bibcode
767:2014 OL
760:of the
704:2010 TK
693:2015 SO
687:2009 BD
665:2002 AA
391:Calypso
387:Telesto
354:2010 TK
247:Jupiter
205:Trojans
41:planets
1555:
1273:
1214:
1178:Icarus
1157:
1078:
971:
690:, and
619:moons
580:
575:·
573:
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564:·
562:
558:
552:'s
511:, the
403:Helene
379:Tethys
60:trojan
1553:S2CID
1527:arXiv
1436:arXiv
1355:arXiv
1302:arXiv
1271:S2CID
1243:arXiv
1212:S2CID
1186:arXiv
1155:S2CID
1129:arXiv
1076:S2CID
1050:arXiv
969:S2CID
943:arXiv
858:arXiv
762:Earth
621:Janus
597:and L
577:
566:
517:Theia
488:of a
484:is a
413:and L
397:and L
383:Dione
70:and L
39:, or
37:moons
1407:2016
1399:NASA
1106:2023
775:and
764:are
735:kyrs
712:and
623:and
615:The
521:Mars
513:Moon
494:star
405:and
389:and
381:and
362:and
336:and
321:, 2
317:, 7
220:and
23:, a
1545:doi
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1495:doi
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1454:doi
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1373:doi
1351:445
1320:doi
1298:445
1261:doi
1239:414
1204:doi
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1147:doi
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