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==== Co-orbital asteroids ==== [[File:Lagrange Horseshoe Orbit.jpg|thumb|The five Lagrangian points relative to the Sun and Earth and possible orbits along gravitational contours]] Most NEAs have orbits that are significantly more [[Orbital eccentricity|eccentric]] than that of the Earth and the other major planets and their orbital planes can [[Orbital inclination|tilt]] several degrees relative to that of the Earth. NEAs which have orbits that do resemble the Earth's in eccentricity, inclination and semi-major axis are grouped as [[Arjuna asteroid]]s.<ref name="2023FY3_2024"/> Within this group are NEAs that have the same orbital period as the Earth, or a [[co-orbital configuration]], which corresponds to an [[orbital resonance]] at a ratio of 1:1. All co-orbital asteroids have special orbits that are relatively stable and, paradoxically, can prevent them from getting close to Earth: * ''[[Trojan (astronomy)|Trojans]]'': Near the orbit of a planet, there are five gravitational equilibrium points, the [[Lagrangian point]]s, in which an asteroid would orbit the Sun in fixed formation with the planet. Two of these, 60 degrees ahead and behind the planet along its orbit (designated L4 and L5 respectively) are stable; that is, an asteroid near these points would stay there for thousands or even millions of years in spite of light perturbations by other planets and by non-gravitational forces. Trojans circle around L4 or L5 on paths resembling a [[tadpole]].<ref name="Fuentes-horseshoe"/> {{As of|2023|10}}, Earth has two confirmed Trojans:<ref name="CastroCisneros2023"/> {{mpl|(706765) 2010 TK|7}} and {{mpl|(614689) 2020 XL|5}}, both circling Earth's L4 point.<ref name="WISE">{{cite press release |title=NASA's WISE mission finds first Trojan asteroid sharing Earth's orbit |date=July 27, 2011 |work=PR Newswire |publisher=[[NASA]] |url=https://www.prnewswire.com/news-releases/nasas-wise-mission-finds-first-trojan-asteroid-sharing-earths-orbit-126277963.html |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20240127131203/https://www.prnewswire.com/news-releases/nasas-wise-mission-finds-first-trojan-asteroid-sharing-earths-orbit-126277963.html |archive-date=January 27, 2024}}</ref><ref name="Trojan2">{{cite news |first=Chelsea |last=Gohd |title=Earth has an extra companion, a Trojan asteroid that will hang around for 4,000 years |date=February 1, 2022 |work=Space.com |url=https://www.space.com/earth-extra-moon-trojan-asteroid-2020-xl5-discovery |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20241208100907/https://www.space.com/earth-extra-moon-trojan-asteroid-2020-xl5-discovery |archive-date=December 8, 2024}}</ref> * ''[[Horseshoe orbit|Horseshoe librators]]'': The region of stability around L4 and L5 also includes orbits for co-orbital asteroids that run around both L4 and L5. Relative to the Earth and Sun, the orbit can resemble the circumference of a horseshoe, or may consist of annual loops that wander back and forth ([[Libration|librate]]) in a horseshoe-shaped area. In both cases, the Sun is at the horseshoe's center of gravity, Earth is in the gap of the horseshoe, and L4 and L5 are inside the ends of the horseshoe. Among Earth's known co-orbitals, those with the most stable orbits as well as those with the least stable orbits are horseshoe librators.<ref name="Fuentes-horseshoe">{{cite journal |last1=de la Fuente Marcos |first1=C. |last2=de la Fuente Marcos |first2=R. |title=A trio of horseshoes: Past, present, and future dynamical evolution of Earth co-orbital asteroids {{mp|2015 XX|169}}, {{mp|2015 YA}} and {{mp|2015 YQ|1}} |journal=[[Astrophysics and Space Science]] |volume=361 |issue=4 |pages=121–133 |date=April 2016 |doi=10.1007/s10509-016-2711-6 |arxiv=1603.02415 |bibcode=2016Ap&SS.361..121D |s2cid=119222384}}</ref> {{As of|2023|10}}, at least 13 horseshoe librators of Earth have been discovered.<ref name="CastroCisneros2023"/> The most-studied and, at about {{convert|5|km|mi|abbr=on}}, largest is [[3753 Cruithne]], which travels along bean-shaped annual loops and completes its horseshoe libration cycle every 770–780 years.<ref>{{cite journal |title=An asteroidal companion to the Earth |type=letter |last1=Wiegert |first1=Paul A. |last2=Innanen |first2=Kimmo A. |last3=Mikkola |first3=Seppo |journal=Nature |date=June 12, 1997 |volume=387 |issue=6634 |pages=685–686 |doi=10.1038/42662 |bibcode=1997Natur.387..685W |s2cid=4305272 |url=http://www.astro.uwo.ca/~pwiegert/papers/1997Nature.387.685.pdf |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20241203022402/https://physics.uwo.ca/~pwiegert/papers/1997Nature.387.685.pdf |archive-date=December 3, 2024}}</ref><ref>{{cite web |first=Brad |last=Snowder |title=Cruithne |publisher=Western Washington University Planetarium |url=https://astro101.wwu.edu/a101_cruithne.html |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20240101150817/https://astro101.wwu.edu/a101_cruithne.html |archive-date=January 1, 2024}}</ref> {{mpl|419624|2010 SO|16}} is an asteroid on a relatively stable circumference-of-a-horseshoe orbit, with a horseshoe [[libration]] period of about 350 years.<ref>{{cite journal |last1=Christou |first1=A.A. |last2=Asher |first2=D.J. |title=A long-lived horseshoe companion to the Earth |date=July 11, 2011 |journal=Monthly Notices of the Royal Astronomical Society |volume=414 |issue=4 |pages=2965–2969 |doi=10.1111/j.1365-2966.2011.18595.x |doi-access=free |arxiv=1104.0036 |bibcode=2011MNRAS.414.2965C |s2cid=13832179}}</ref> * ''[[Quasi-satellite]]s'': Quasi-satellites are co-orbital asteroids on a normal elliptic orbit with a higher eccentricity than Earth's, which they travel in a way synchronised with Earth's motion. Since the asteroid orbits the Sun slower than Earth when further away and faster than Earth when closer to the Sun, when observed in a rotating frame of reference fixed to the Sun and the Earth, the quasi-satellite appears to orbit Earth in a [[retrograde motion|retrograde]] direction in one year, even though it is not bound gravitationally. {{As of|2023|10}}, six asteroids were known to be a quasi-satellite of Earth.<ref name="CastroCisneros2023"/> [[469219 Kamoʻoalewa]] is Earth's closest quasi-satellite, in an orbit that has been stable for almost a century.<ref name="Fuentes-2016HO3">{{cite journal |last1=de la Fuente Marcos |first1=C. |last2=de la Fuente Marcos |first2=R. |title=Asteroid {{mp|469219|2016 HO|3}}, the smallest and closest Earth quasi-satellite |journal=Monthly Notices of the Royal Astronomical Society |volume=462 |issue=4 |pages=3441–3456 |date=November 11, 2016 |doi=10.1093/mnras/stw1972 |doi-access=free |arxiv=1608.01518 |bibcode=2016MNRAS.462.3441D |s2cid=118580771}}</ref> This asteroid is thought to be a piece of the Moon ejected during an impact.<ref name="CastroCisneros2023">{{cite journal |first1=Jose Daniel |last1=Castro-Cisneros |first2=Renu |last2=Malhotra |first3=Aaron J. |last3=Rosengren |title=Lunar ejecta origin of near-Earth asteroid Kamo'oalewa is compatible with rare orbital pathways |date=October 23, 2023 |journal=[[Communications Earth & Environment]] |volume=4 |issue=1 |at=section 372 |doi=10.1038/s43247-023-01031-w |pmid=39524985 |pmc=11549049 |arxiv=2304.14136 |bibcode=2023ComEE...4..372C}}</ref><ref>{{cite news |first=Robert |last=Lea |title=Earth's weird 'quasi-moon' Kamo'oalewa is a fragment blasted out of big moon crater |date=April 23, 2024 |work=Space.com |url=https://www.space.com/quasi-moon-kamooalewa-giant-lunar-impact |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20241224181137/https://www.space.com/quasi-moon-kamooalewa-giant-lunar-impact |archive-date=December 24, 2024}}</ref> Orbit calculations show that almost all quasi-satellites and many horseshoe librators repeatedly transfer between horseshoe and quasi-satellite orbits.<ref name="Fuentes-2016HO3"/><ref name="DiRuzza2023">{{cite journal |first1=Sara |last1=Di Ruzza |first2=Alexandre |last2=Pousse |first3=Elisa Maria |last3=Alessi |title=On the co-orbital asteroids in the solar system: medium-term timescale analysis of the quasi-coplanar objects |date=January 15, 2023 |journal=Icarus |volume=390 |at=section 115330 |doi=10.1016/j.icarus.2022.115330 |arxiv=2209.05219 |bibcode=2023Icar..39015330D}}</ref> One of these objects, {{mpl|2003 YN|107}}, was observed during its transition from a quasi-satellite orbit to a horseshoe orbit in 2006; it is expected to transfer back to a quasi-satellite orbit sometime around year 2066.<ref>{{cite news |first=Tony |last=Phillips |title=Corkscrew asteroid |date=June 9, 2006 |work=Science@NASA |publisher=[[NASA]] |url=http://science.nasa.gov/headlines/y2006/09jun_moonlets.htm |access-date=November 13, 2017 |url-status=dead |archive-url=https://web.archive.org/web/20060929155325/http://science.nasa.gov/headlines/y2006/09jun_moonlets.htm |archive-date=September 29, 2006}}</ref> A quasi-satellite discovered in 2023 but then found in old photographs back to 2012, {{mpl|2023 FW|13}}, was found to have an orbit that is stable for about 4,000 years, from 100 BC to AD 3700.<ref>{{cite news |first=David L. |last=Chandler |title=Astronomers have discovered an asteroid that orbits the Sun with Earth, earning it the moniker "quasi-moon." |date=April 7, 2023 |work=Sky & Telescope |url=https://skyandtelescope.org/astronomy-news/does-earth-have-new-quasi-moon/ |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20240721235051/https://skyandtelescope.org/astronomy-news/does-earth-have-new-quasi-moon/ |archive-date=July 21, 2024}}</ref> * Asteroids on ''compound orbits'': orbital calculations show that some co-orbital asteroids transit between horseshoe and quasi-satellite orbits during every horseshoe resp. quasi-satellite cycle. Theoretically, similar continuous transitions between Trojan and horseshoe orbits are possible, too. {{As of|2023|1}}, at least 20 Earth co-orbital NEAs are thought to be in the horseshoe-like phase of compound orbits.<ref name="DiRuzza2023"/> [[File:Animation of 2020 CD3's orbit around Earth.gif|thumb|Animation of {{mpl|2020 CD|3}}'s orbit around Earth<br />{{legend2|Magenta|{{mp|2020 CD|3}}}}{{·}}{{legend2|DarkKhaki|Moon}}{{·}}{{legend2|RoyalBlue|Earth}}]] * ''[[Temporary satellite]]s'': NEAs can also transfer between solar orbits and distant Earth orbits, becoming gravitationally bound temporary satellites. According to simulations, temporary satellites are typically caught when they pass Earth's L1 or L2 Lagrangian points at the time Earth is either at the point in its orbit closest or farthest from the Sun, complete a couple of orbits around Earth, and then return to a heliocentric orbit due to perturbations from the Moon.<ref name="ST111230">{{cite news |first=Camille M. |last=Carlisle |title=Pseudo-moons orbit Earth |date=December 30, 2011 |work=Sky & Telescope |url=https://skyandtelescope.org/astronomy-news/pseudo-moons-orbit-earth/ |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20240530185354/https://skyandtelescope.org/astronomy-news/pseudo-moons-orbit-earth/ |archive-date=May 30, 2024}}</ref> Strictly speaking, temporary satellites aren't co-orbital asteroids, and they can have orbits of the broader Arjuna type before and after capture by Earth, but simulations show that they can be captured from, or transfer to, horseshoe orbits.<ref name="2023FY3_2024"/> The simulations also indicate that Earth typically has at least one temporary satellite {{convert|1|m|ft|abbr=on}} across at any given time, but they are too faint to be detected by current surveys.<ref name="ST111230"/> {{As of|2024|12}}, five temporary satellites have been observed:<ref name="2023FY3_2024"/> {{mpl|1991 VG|}},<ref name="Fuente-Marcos-2018">{{Cite journal |first1=Carlos |last1=de la Fuente Marcos |first2=Raúl |last2=de la Fuente Marcos |date= January 2018 |title=Dynamical evolution of near-Earth asteroid 1991 VG |journal=Monthly Notices of the Royal Astronomical Society |volume=473 |issue=3 |pages=2939–2948 |bibcode=2018MNRAS.473.2939D |doi=10.1093/mnras/stx2545 |doi-access=free |arxiv=1709.09533}}</ref> {{mpl|2006 RH|120}}, {{mpl|2020 CD|3}},<ref>{{cite news |first=Roger W. |last=Sinnott |title=Earth's "other moon" |date=April 17, 2007 |work=Sky & Telescope |url=https://skyandtelescope.org/astronomy-news/earths-other-moon/ |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20241130072820/https://skyandtelescope.org/astronomy-news/earths-other-moon/ |archive-date=November 30, 2024}}</ref><ref name="Naidu2020">{{cite news |first1=Shantanu |last1=Naidu |last2=Farnocchia |first2=Davide |title=Tiny Object Discovered in Distant Orbit Around the Earth |date=February 27, 2020 |publisher=NASA/JPL CNEOS |url=https://cneos.jpl.nasa.gov/news/news205.html |access-date=January 2, 2025 |url-status=live |archive-url=https://web.archive.org/web/20241219113203/https://cneos.jpl.nasa.gov/news/news205.html |archive-date=December 19, 2024}}</ref> {{mpl|2022 NX|1}}<ref name="2023FY3_2024"/> and {{mpl|2024 PT|5}}.<ref>{{cite news |first=Robert |last=Lea |title=Earth's mini-moon has finally departed. Will it ever return as a 'second moon?' |date=November 26, 2024 |work=Space.com |url=https://www.space.com/goodnight-second-moon-asteroid-2024PT5 |access-date=January 1, 2025 |url-status=live |archive-url=https://web.archive.org/web/20250101183548/https://www.space.com/goodnight-second-moon-asteroid-2024PT5 |archive-date=January 1, 2025}}</ref> Calculations for the {{convert|5|m|ft|abbr=on}} asteroid {{mpl|2023 FY|3}} showed repeated transitions into temporary satellite orbits both in the past and the future 10,000 years.<ref name="2023FY3_2024">{{cite journal |first1=R. |last1=de la Fuente Marcos |first2=C. |last2=de la Fuente Marcos |display-authors=etal |title=When the horseshoe fits: Characterizing {{mp|2023 FY|3}} with the 10.4 m Gran Telescopio Canarias and the Two-meter Twin Telescope |date=January 2024 |journal=Astronomy & Astrophysics |volume=681 |at=section A4 |doi=10.1051/0004-6361/202347663 |arxiv=2310.08724 |bibcode=2024A&A...681A...4D}}</ref> Near-Earth asteroids also include the co-orbitals of Venus. {{As of|2023|1}}, all known co-orbitals of Venus have orbits with high eccentricity, also crossing Earth's orbit.<ref name="DiRuzza2023"/><ref>{{cite journal |first1=Petr |last1=Pokorý |first2=Marc |last2=Kuchner |title=Threat from Within: Excitation of Venus's Co-orbital Asteroids to Earth-crossing Orbits |date=October 2021 |journal=The Planetary Science Journal |volume=2 |issue=5 |at=part 193 |doi=10.3847/PSJ/ac1e9b |doi-access=free |bibcode=2021PSJ.....2..193P}}</ref>
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