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Co-orbital configuration

January 01, 1970

In astronomy, a co-orbital configuration is a configuration of two or more astronomical objects (such as asteroids, moons, or planets) orbiting at the same, or very similar, distance from their primary; i.e., they are in a 1:1 mean-motion resonance. (or 1:−1 if orbiting in opposite directions).[1]

There are several classes of co-orbital objects, depending on their point of libration. The most common and best-known class is the trojan, which librates around one of the two stable Lagrangian points (Trojan points), L4 and L5, 60° ahead of and behind the larger body respectively. Another class is the horseshoe orbit, in which objects librate around 180° from the larger body. Objects librating around 0° are called quasi-satellites.[2]

An exchange orbit occurs when two co-orbital objects are of similar masses and thus exert a non-negligible influence on each other. The objects can exchange semi-major axes or eccentricities when they approach each other.

Parameters edit

Orbital parameters that are used to describe the relation of co-orbital objects are the longitude of the periapsis difference and the mean longitude difference. The longitude of the periapsis is the sum of the mean longitude and the mean anomaly   and the mean longitude is the sum of the longitude of the ascending node and the argument of periapsis  .

Trojans edit

 
Trojan points are the points labelled L4 and L5, highlighted in red, on the orbital path of the secondary object (blue), around the primary object (yellow).
Main article: Trojan (celestial body)

Trojan objects orbit 60° ahead of (L4) or behind (L5) 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 Jupiter around the Sun. Trojan objects do not orbit exactly at one of either Lagrangian points, but do remain relatively close to it, appearing to slowly orbit it. In technical terms, they librate around   = (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity.[2]

Trojan minor planets edit

There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near Jupiter's Lagrangian points, the traditional Jupiter trojans. As of 2015, there are also 13 Neptune trojans, 7 Mars trojans, 2 Uranus trojans (2011 QF99 and 2014 YX49), and 2 Earth trojans (2010 TK7 and (614689) 2020 XL5 ) that are known to exist. No Saturnian trojans have been observed.

Trojan moons edit

The Saturnian system contains two sets of trojan moons. Both Tethys and Dione have two trojan moons each, Telesto and Calypso in Tethys's L4 and L5 respectively, and Helene and Polydeuces in Dione's L4 and L5 respectively.

Polydeuces is noticeable for its wide libration: it wanders as far as ±30° from its Lagrangian point and ±2% from its mean orbital radius, along a tadpole orbit in 790 days (288 times its orbital period around Saturn, the same as Dione's).

Trojan planets edit

A pair of co-orbital exoplanets was proposed to be orbiting the star Kepler-223, but this was later retracted.[3]

The possibility of a trojan planet to Kepler-91b was studied but the conclusion was that the transit-signal was a false-positive.[4]

In April 2023, a group of amateur astronomers reported two new exoplanet candidates co-orbiting , in a horseshoe exchange orbit, close to the star GJ 3470 (this star has been known to have a confirmed planet GJ 3470 b). 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.[5][6]

In July 2023, the possible detection of a cloud of debris co-orbital with the proto-planet PDS 70 b was announced. This debris cloud could be evidence of a Trojan planetary-mass body or one in the process of forming.[7][8]

One possibility for the habitable zone is a trojan planet of a giant planet close to its star.[9]

The reason why no trojan planets have been definitively detected could be that tides destabilize their orbits.[10]

Formation of the Earth–Moon system edit

According to the giant impact hypothesis, the Moon formed after a collision between two co-orbital objects: Theia, thought to have had about 10% of the mass of Earth (about as massive as Mars), and the proto-Earth. Their orbits were perturbed by other planets, bringing Theia out of its trojan position and causing the collision.

Horseshoe orbits edit

 
Rotating-frame depiction of the horseshoe exchange orbits of Janus and Epimetheus
 
Animation of Epimetheus's orbit - Rotating reference frame
   Saturn ·    Janus  ·   Epimetheus
Main article: Horseshoe orbit

Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. L4 and L5.[2]

Co-orbital moons edit

See also: Epimetheus (moon) § Orbit

The Saturnian moons Janus and Epimetheus 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 will slowly catch 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 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.

Earth co-orbital asteroids edit

A small number of asteroids have been found which are co-orbital with Earth. The first of these to be discovered, asteroid 3753 Cruithne, 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.[11]

More resonant near-Earth objects (NEOs) have since been discovered. These include 54509 YORP, (85770) 1998 UP1, 2002 AA29, 2010 SO16, 2009 BD, and 2015 SO2 which exist in resonant orbits similar to Cruithne's. 2010 TK7 and 2020 XL5 are the only two identified Earth trojans.

Hungaria asteroids were found to be one of the possible sources for co-orbital objects of the Earth with a lifetime up to ~58 kyrs.[12]

Quasi-satellite edit

Main article: Quasi-satellite

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.[2] From a co-rotating perspective the quasi-satellite appears to orbit the primary like a retrograde satellite, although at distances so large that it is not gravitationally bound to it.[2] Two examples of quasi-satellites of the Earth are 2014 OL339[13] and 469219 Kamoʻoalewa.[14][15]

Exchange orbits edit

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.[16]

See also edit

References edit

  1. ^ Morais, M.H.M.; F. Namouni (2013). "Asteroids in retrograde resonance with Jupiter and Saturn". Monthly Notices of the Royal Astronomical Society Letters. 436: L30–L34. arXiv:1308.0216. Bibcode:2013MNRAS.436L..30M. doi:10.1093/mnrasl/slt106.
  2. ^ a b c d e Dynamics of two planets in co-orbital motion
  3. ^ "Two planets found sharing one orbit". New Scientist. 24 February 2011.
  4. ^ 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". The Astrophysical Journal. 814 (2): 147. arXiv:1511.01068. Bibcode:2015ApJ...814..147P. doi:10.1088/0004-637X/814/2/147. S2CID 118366565.
  5. ^ "The Extrasolar Planet Encyclopaedia — GJ 3470 d". Extrasolar Planets Encyclopaedia. Retrieved 2023-04-28.
  6. ^ "The Extrasolar Planet Encyclopaedia — GJ 3470 e". Extrasolar Planets Encyclopaedia. Retrieved 2023-04-28.
  7. ^ 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". Astronomy & Astrophysics. 675: A172. arXiv:2307.12811. Bibcode:2023A&A...675A.172B. doi:10.1051/0004-6361/202346493. S2CID 259684169.
  8. ^ "Does this exoplanet have a sibling sharing the same orbit?". ESO. 19 July 2023. Retrieved 19 July 2023.
  9. ^ Dvorak, R.; Pilat-Lohinger, E.; Schwarz, R.; Freistetter, F. (2004). "Extrasolar Trojan planets close to habitable zones". Astronomy & Astrophysics. 426 (2): L37–L40. arXiv:astro-ph/0408079. Bibcode:2004A&A...426L..37D. doi:10.1051/0004-6361:200400075. S2CID 15637771.
  10. ^ Dobrovolskis, Anthony R.; Lissauer, Jack J. (2022). "Do tides destabilize Trojan exoplanets?". Icarus. 385: 115087. arXiv:2206.07097. Bibcode:2022Icar..38515087D. doi:10.1016/j.icarus.2022.115087. S2CID 248979920.
  11. ^ Christou, A. A.; Asher, D. J. (2011). "A long-lived horseshoe companion to the Earth". Monthly Notices of the Royal Astronomical Society. 414 (4): 2965. arXiv:1104.0036. Bibcode:2011MNRAS.414.2965C. doi:10.1111/j.1365-2966.2011.18595.x. S2CID 13832179.
  12. ^ Galiazzo, M. A.; Schwarz, R. (2014). "The Hungaria region as a possible source of Trojans and satellites in the inner Solar system". Monthly Notices of the Royal Astronomical Society. 445 (4): 3999. arXiv:1612.00275. Bibcode:2014MNRAS.445.3999G. doi:10.1093/mnras/stu2016.
  13. ^ de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl (2014). "Asteroid 2014 OL339: yet another Earth quasi-satellite". Monthly Notices of the Royal Astronomical Society. 445 (3): 2985–2994. arXiv:1409.5588. Bibcode:2014MNRAS.445.2961D. doi:10.1093/mnras/stu1978.
  14. ^ Agle, DC; Brown, Dwayne; Cantillo, Laurie (15 June 2016). "Small Asteroid Is Earth's Constant Companion". NASA. Retrieved 15 June 2016.
  15. ^ de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl (2016). "Asteroid (469219) 2016 HO3, the smallest and closest Earth quasi-satellite". Monthly Notices of the Royal Astronomical Society. 462 (4): 3441–3456. arXiv:1608.01518. Bibcode:2016MNRAS.462.3441D. doi:10.1093/mnras/stw1972.
  16. ^ Funk, B. (2010). "Exchange orbits: a possible application to extrasolar planetary systems?". Monthly Notices of the Royal Astronomical Society. 410 (1): 455–460. Bibcode:2011MNRAS.410..455F. doi:10.1111/j.1365-2966.2010.17453.x.
  • Eric B. Ford and Matthew J. Holman (2007). "Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets". The Astrophysical Journal Letters. 664 (1): L51–L54. arXiv:0705.0356. Bibcode:2007ApJ...664L..51F. doi:10.1086/520579. S2CID 14285948.

External links edit

 
Wikimedia Commons has media related to Co-orbital objects.
  • from Murray and Dermott
  • The Planetary Society
  • A Search for Trojan Planets Web page of group of astronomers searching for extrasolar trojan planets at Appalachian State University

January 01, 1970
orbital, configuration, astronomy, orbital, configuration, configuration, more, astronomical, objects, such, asteroids, moons, planets, orbiting, same, very, similar, distance, from, their, primary, they, mean, motion, resonance, orbiting, opposite, directions. In astronomy a co orbital configuration is a configuration of two or more astronomical objects such as asteroids moons or planets orbiting at the same or very similar distance from their primary i e they are in a 1 1 mean motion resonance or 1 1 if orbiting in opposite directions 1 There are several classes of co orbital objects depending on their point of libration The most common and best known class is the trojan which librates around one of the two stable Lagrangian points Trojan points L4 and L5 60 ahead of and behind the larger body respectively Another class is the horseshoe orbit in which objects librate around 180 from the larger body Objects librating around 0 are called quasi satellites 2 An exchange orbit occurs when two co orbital objects are of similar masses and thus exert a non negligible influence on each other The objects can exchange semi major axes or eccentricities when they approach each other Contents 1 Parameters 2 Trojans 2 1 Trojan minor planets 2 2 Trojan moons 2 3 Trojan planets 2 3 1 Formation of the Earth Moon system 3 Horseshoe orbits 3 1 Co orbital moons 3 2 Earth co orbital asteroids 4 Quasi satellite 5 Exchange orbits 6 See also 7 References 8 External linksParameters editOrbital parameters that are used to describe the relation of co orbital objects are the longitude of the periapsis difference and the mean longitude difference The longitude of the periapsis is the sum of the mean longitude and the mean anomaly l ϖ M displaystyle lambda varpi M nbsp and the mean longitude is the sum of the longitude of the ascending node and the argument of periapsis ϖ W w displaystyle varpi Omega omega nbsp Trojans edit nbsp Trojan points are the points labelled L4 and L5 highlighted in red on the orbital path of the secondary object blue around the primary object yellow Main article Trojan celestial body Trojan objects orbit 60 ahead of L4 or behind L5 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 Jupiter around the Sun Trojan objects do not orbit exactly at one of either Lagrangian points but do remain relatively close to it appearing to slowly orbit it In technical terms they librate around D l D ϖ displaystyle Delta lambda Delta varpi nbsp 60 60 The point around which they librate is the same irrespective of their mass or orbital eccentricity 2 Trojan minor planets edit There are several thousand known trojan minor planets orbiting the Sun Most of these orbit near Jupiter s Lagrangian points the traditional Jupiter trojans As of 2015 update there are also 13 Neptune trojans 7 Mars trojans 2 Uranus trojans 2011 QF99 and 2014 YX49 and 2 Earth trojans 2010 TK7 and 614689 2020 XL5 that are known to exist No Saturnian trojans have been observed Trojan moons edit The Saturnian system contains two sets of trojan moons Both Tethys and Dione have two trojan moons each Telesto and Calypso in Tethys s L4 and L5 respectively and Helene and Polydeuces in Dione s L4 and L5 respectively Polydeuces is noticeable for its wide libration it wanders as far as 30 from its Lagrangian point and 2 from its mean orbital radius along a tadpole orbit in 790 days 288 times its orbital period around Saturn the same as Dione s Trojan planets edit A pair of co orbital exoplanets was proposed to be orbiting the star Kepler 223 but this was later retracted 3 The possibility of a trojan planet to Kepler 91b was studied but the conclusion was that the transit signal was a false positive 4 In April 2023 a group of amateur astronomers reported two new exoplanet candidates co orbiting in a horseshoe exchange orbit close to the star GJ 3470 this star has been known to have a confirmed planet GJ 3470 b 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 5 6 In July 2023 the possible detection of a cloud of debris co orbital with the proto planet PDS 70 b was announced This debris cloud could be evidence of a Trojan planetary mass body or one in the process of forming 7 8 One possibility for the habitable zone is a trojan planet of a giant planet close to its star 9 The reason why no trojan planets have been definitively detected could be that tides destabilize their orbits 10 Formation of the Earth Moon system edit According to the giant impact hypothesis the Moon formed after a collision between two co orbital objects Theia thought to have had about 10 of the mass of Earth about as massive as Mars and the proto Earth Their orbits were perturbed by other planets bringing Theia out of its trojan position and causing the collision Horseshoe orbits edit nbsp Rotating frame depiction of the horseshoe exchange orbits of Janus and Epimetheus nbsp Animation of Epimetheus s orbit Rotating reference frame Saturn Janus Epimetheus Main article Horseshoe orbit Objects in a horseshoe orbit librate around 180 from the primary Their orbits encompass both equilateral Lagrangian points i e L4 and L5 2 Co orbital moons edit See also Epimetheus moon Orbit The Saturnian moons Janus and Epimetheus 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 will slowly catch 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 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 Earth co orbital asteroids edit A small number of asteroids have been found which are co orbital with Earth The first of these to be discovered asteroid 3753 Cruithne 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 11 More resonant near Earth objects NEOs have since been discovered These include 54509 YORP 85770 1998 UP1 2002 AA29 2010 SO16 2009 BD and 2015 SO2 which exist in resonant orbits similar to Cruithne s 2010 TK7 and 2020 XL5 are the only two identified Earth trojans Hungaria asteroids were found to be one of the possible sources for co orbital objects of the Earth with a lifetime up to 58 kyrs 12 Quasi satellite editMain article Quasi satellite 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 2 From a co rotating perspective the quasi satellite appears to orbit the primary like a retrograde satellite although at distances so large that it is not gravitationally bound to it 2 Two examples of quasi satellites of the Earth are 2014 OL339 13 and 469219 Kamoʻoalewa 14 15 Exchange orbits editIn 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 16 See also edit nbsp Astronomy portal Double planet Kordylewski cloud Chinese Space Station TelescopeReferences edit Morais M H M F Namouni 2013 Asteroids in retrograde resonance with Jupiter and Saturn Monthly Notices of the Royal Astronomical Society Letters 436 L30 L34 arXiv 1308 0216 Bibcode 2013MNRAS 436L 30M doi 10 1093 mnrasl slt106 a b c d e Dynamics of two planets in co orbital motion Two planets found sharing one orbit New Scientist 24 February 2011 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 The Astrophysical Journal 814 2 147 arXiv 1511 01068 Bibcode 2015ApJ 814 147P doi 10 1088 0004 637X 814 2 147 S2CID 118366565 The Extrasolar Planet Encyclopaedia GJ 3470 d Extrasolar Planets Encyclopaedia Retrieved 2023 04 28 The Extrasolar Planet Encyclopaedia GJ 3470 e Extrasolar Planets Encyclopaedia Retrieved 2023 04 28 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 Astronomy amp Astrophysics 675 A172 arXiv 2307 12811 Bibcode 2023A amp A 675A 172B doi 10 1051 0004 6361 202346493 S2CID 259684169 Does this exoplanet have a sibling sharing the same orbit ESO 19 July 2023 Retrieved 19 July 2023 Dvorak R Pilat Lohinger E Schwarz R Freistetter F 2004 Extrasolar Trojan planets close to habitable zones Astronomy amp Astrophysics 426 2 L37 L40 arXiv astro ph 0408079 Bibcode 2004A amp A 426L 37D doi 10 1051 0004 6361 200400075 S2CID 15637771 Dobrovolskis Anthony R Lissauer Jack J 2022 Do tides destabilize Trojan exoplanets Icarus 385 115087 arXiv 2206 07097 Bibcode 2022Icar 38515087D doi 10 1016 j icarus 2022 115087 S2CID 248979920 Christou A A Asher D J 2011 A long lived horseshoe companion to the Earth Monthly Notices of the Royal Astronomical Society 414 4 2965 arXiv 1104 0036 Bibcode 2011MNRAS 414 2965C doi 10 1111 j 1365 2966 2011 18595 x S2CID 13832179 Galiazzo M A Schwarz R 2014 The Hungaria region as a possible source of Trojans and satellites in the inner Solar system Monthly Notices of the Royal Astronomical Society 445 4 3999 arXiv 1612 00275 Bibcode 2014MNRAS 445 3999G doi 10 1093 mnras stu2016 de la Fuente Marcos Carlos de la Fuente Marcos Raul 2014 Asteroid 2014 OL339 yet another Earth quasi satellite Monthly Notices of the Royal Astronomical Society 445 3 2985 2994 arXiv 1409 5588 Bibcode 2014MNRAS 445 2961D doi 10 1093 mnras stu1978 Agle DC Brown Dwayne Cantillo Laurie 15 June 2016 Small Asteroid Is Earth s Constant Companion NASA Retrieved 15 June 2016 de la Fuente Marcos Carlos de la Fuente Marcos Raul 2016 Asteroid 469219 2016 HO3 the smallest and closest Earth quasi satellite Monthly Notices of the Royal Astronomical Society 462 4 3441 3456 arXiv 1608 01518 Bibcode 2016MNRAS 462 3441D doi 10 1093 mnras stw1972 Funk B 2010 Exchange orbits a possible application to extrasolar planetary systems Monthly Notices of the Royal Astronomical Society 410 1 455 460 Bibcode 2011MNRAS 410 455F doi 10 1111 j 1365 2966 2010 17453 x Eric B Ford and Matthew J Holman 2007 Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets The Astrophysical Journal Letters 664 1 L51 L54 arXiv 0705 0356 Bibcode 2007ApJ 664L 51F doi 10 1086 520579 S2CID 14285948 External links edit nbsp Wikimedia Commons has media related to Co orbital objects QuickTime animation of co orbital motion from Murray and Dermott Cassini Observes the Orbital Dance of Epimetheus and Janus The Planetary Society A Search for Trojan Planets Web page of group of astronomers searching for extrasolar trojan planets at Appalachian State University Retrieved from https en wikipedia org w index php title Co orbital configuration amp oldid 1215776858, wikipedia, wiki, book, books, library,

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