651:, 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.
558:
221:
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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
762:
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
639:
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.
310:
859:
210:
165:
1049:
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".
944:
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".
256:) 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
1437:
1356:
798:
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.
1587:
477:). However, the mentioned study is only in preprint form on arXiv, and it has not yet been peer reviewed and published in a reputable scientific journal.
320:
There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near
Jupiter's Lagrangian points, the traditional
534:), and the proto-Earth. Their orbits were perturbed by other planets, bringing Theia out of its trojan position and causing the collision.
100:
occurs when two co-orbital objects are of similar masses and thus exert a non-negligible influence on each other. The objects can exchange
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604:
Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral
Lagrangian points, i.e. L
557:
1028:
1002:
168:
59:
271:
1130:
Dvorak, R.; Pilat-Lohinger, E.; Schwarz, R.; Freistetter, F. (2004). "Extrasolar Trojan planets close to habitable zones".
647:
A small number of asteroids have been found which are co-orbital with Earth. The first of these to be discovered, asteroid
1108:
926:
1609:
1051:
312:= (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity.
117:
546:
510:
The reason why no trojan planets have been definitively detected could be that tides destabilize their orbits.
177:
268:, but do remain relatively close to it, appearing to slowly orbit it. In technical terms, they librate around
238:, highlighted in red, on the orbital path of the secondary object (blue), around the primary object (yellow).
519:
243:
130:
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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
1184:
1596:
Web page of group of astronomers searching for extrasolar trojan planets at
Appalachian State University
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435:: it wanders as far as ±30° from its Lagrangian point and ±2% from its mean orbital radius, along a
89:, in which objects librate around 180° from the larger body. Objects librating around 0° are called
39:
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1301:"The Hungaria region as a possible source of Trojans and satellites in the inner Solar system"
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767:, 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
1526:"Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets"
768:
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599:
550:
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101:
90:
86:
54:) orbiting at the same, or very similar, distance from their primary; i.e., they are in a
1551:
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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
735:
631:
500:
393:
359:
125:
1161:
1082:
1218:
473:, close to the star GJ 3470 (this star has been known to have a confirmed planet
462:
was studied but the conclusion was that the transit-signal was a false-positive.
1023:
997:
329:
439:
in 790 days (288 times its orbital period around Saturn, the same as Dione's).
805:
777:
659:
459:
452:
85:, 60° ahead of and behind the larger body respectively. Another class is the
65:
There are several classes of co-orbital objects, depending on their point of
1469:
1433:"Asteroid (469219) 2016 HO3, the smallest and closest Earth quasi-satellite"
1432:
1388:
1351:
1335:
1300:
891:
854:
675:
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448:
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66:
31:
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17:
1486:"Exchange orbits: a possible application to extrasolar planetary systems?"
530:, thought to have had about 10% of the mass of Earth (about as massive as
1593:
1144:
714:
703:
364:
43:
833:
697:
257:
627:
481:
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380:) 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).
1350:
de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl (2014).
484:
was announced. This debris cloud could be evidence of a Trojan
745:
261:
388:
The
Saturnian system contains two sets of trojan moons. Both
1105:"Does this exoplanet have a sibling sharing the same orbit?"
855:"Asteroids in retrograde resonance with Jupiter and Saturn"
1588:
Cassini
Observes the Orbital Dance of Epimetheus and Janus
1403:
Agle, DC; Brown, Dwayne; Cantillo, Laurie (15 June 2016).
860:
Monthly
Notices of the Royal Astronomical Society Letters
526:
formed after a collision between two co-orbital objects:
469:
reported two new exoplanet candidates co-orbiting , in a
1352:"Asteroid 2014 OL339: yet another Earth quasi-satellite"
264:. Trojan objects do not orbit exactly at one of either
712:
which exist in resonant orbits similar to
Cruithne's.
305:{\displaystyle ({\Delta }{\lambda },{\Delta }\varpi )}
274:
180:
133:
1183:
Dobrovolskis, Anthony R.; Lissauer, Jack J. (2022).
304:
204:
159:
1490:Monthly Notices of the Royal Astronomical Society
1438:Monthly Notices of the Royal Astronomical Society
1357:Monthly Notices of the Royal Astronomical Society
1305:Monthly Notices of the Royal Astronomical Society
1246:Monthly Notices of the Royal Astronomical Society
1024:"The Extrasolar Planet Encyclopaedia — GJ 3470 e"
998:"The Extrasolar Planet Encyclopaedia — GJ 3470 d"
658:(NEOs) have since been discovered. These include
27:Configuration of two or more astronomical objects
1242:"A long-lived horseshoe companion to the Earth"
1405:"Small Asteroid Is Earth's Constant Companion"
73:, which librates around one of the two stable
69:. The most common and best-known class is the
910:
908:
906:
904:
902:
8:
915:Dynamics of two planets in co-orbital motion
1524:Eric B. Ford and Matthew J. Holman (2007).
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1185:"Do tides destabilize Trojan exoplanets?"
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205:{\displaystyle (\varpi =\Omega +\omega )}
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167:and the mean longitude is the sum of the
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1582:QuickTime animation of co-orbital motion
219:
845:
553:exchange orbits of Janus and Epimetheus
1240:Christou, A. A.; Asher, D. J. (2011).
458:The possibility of a trojan planet to
431:Polydeuces is noticeable for its wide
224:Trojan points are the points labelled
160:{\displaystyle ({\lambda }=\varpi +M)}
1299:Galiazzo, M. A.; Schwarz, R. (2014).
927:"Two planets found sharing one orbit"
451:was proposed to be orbiting the star
7:
248:Trojan objects orbit 60° ahead of (L
853:Morais, M.H.M.; F. Namouni (2013).
514:Formation of the Earth–Moon system
488:or one in the process of forming.
292:
279:
190:
38:is a configuration of two or more
25:
1530:The Astrophysical Journal Letters
1511:10.1111/j.1365-2966.2010.17453.x
1277:10.1111/j.1365-2966.2011.18595.x
1029:Extrasolar Planets Encyclopaedia
1003:Extrasolar Planets Encyclopaedia
808:
565:orbit - Rotating reference frame
455:, but this was later retracted.
324:. As of 2015, there are also 13
834:Chinese Space Station Telescope
169:longitude of the ascending node
108:when they approach each other.
622:Epimetheus (moon) § Orbit
299:
275:
199:
181:
154:
134:
1:
1219:10.1016/j.icarus.2022.115087
1132:Astronomy & Astrophysics
1052:Astronomy & Astrophysics
734:are the only two identified
396:have two trojan moons each,
1594:A Search for Trojan Planets
1162:10.1051/0004-6361:200400075
1083:10.1051/0004-6361/202346493
976:10.1088/0004-637X/814/2/147
1626:
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643:Earth co-orbital asteroids
619:
597:
465:In April 2023, a group of
241:
118:longitude of the periapsis
58:. (or 1:-1 if orbiting in
946:The Astrophysical Journal
56:1:1 mean-motion resonance
491:One possibility for the
471:horseshoe exchange orbit
36:co-orbital configuration
1584:from Murray and Dermott
1154:2004A&A...426L..37D
1075:2023A&A...675A.172B
561:Animation of Epimetheus
520:giant impact hypothesis
244:Trojan (celestial body)
595:
554:
306:
239:
206:
161:
1590:The Planetary Society
1470:10.1093/mnras/stw1972
1389:10.1093/mnras/stu1978
1336:10.1093/mnras/stu2016
892:10.1093/mnrasl/slt106
560:
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447:A pair of co-orbital
307:
223:
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173:argument of periapsis
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765:retrograde satellite
316:Trojan minor planets
272:
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131:
40:astronomical objects
1552:2007ApJ...664L..51F
1502:2011MNRAS.410..455F
1461:2016MNRAS.462.3441D
1380:2014MNRAS.445.2961D
1327:2014MNRAS.445.3999G
1268:2011MNRAS.414.2965C
1211:2022Icar..38515087D
968:2015ApJ...814..147P
933:. 24 February 2011.
883:2013MNRAS.436L..30M
486:planetary-mass body
467:amateur astronomers
120:difference and the
60:opposite directions
1610:Co-orbital objects
788:469219 Kamoʻoalewa
742:Hungaria asteroids
656:near-Earth objects
596:
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412:respectively, and
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77:(Trojan points), L
1484:Funk, B. (2010).
829:Kordylewski cloud
549:depiction of the
518:According to the
266:Lagrangian points
75:Lagrangian points
16:(Redirected from
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330:Mars trojans
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1009:2023-04-28
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840:References
660:54509 YORP
636:Epimetheus
620:See also:
460:Kepler-91b
453:Kepler-223
449:exoplanets
418:Polydeuces
112:Parameters
1543:0705.0356
1371:1409.5588
1259:1104.0036
1227:248979920
1091:259684169
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628:Saturnian
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475:GJ 3470 b
433:libration
358:), and 2
297:ϖ
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280:Δ
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191:Ω
185:ϖ
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482:PDS 70 b
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1115:19 July
1071:Bibcode
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879:Bibcode
778:2014 OL
771:of the
715:2010 TK
704:2015 SO
698:2009 BD
676:2002 AA
402:Calypso
398:Telesto
365:2010 TK
258:Jupiter
216:Trojans
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528:Theia
499:of a
495:is a
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