Ajay Kumar at 06:19, 2 September 2023

2023-09-02T06:19:50Z

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{{Short description|Periodic, three-dimensional orbit}}
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| image1 = Animation of Solar and Heliospheric Observatory trajectory - Polar view.gif
| caption1 = Polar view
| image2 = Animation of Solar and Heliospheric Observatory trajectory - Equatorial view.gif
| caption2 = Equatorial view
| footer = [[Solar and Heliospheric Observatory|SOHO]]{{'s}} trajectory, a halo orbit around the Sun-Earth L1 point {{legend2| RoyalBlue| Earth}}{{·}}{{legend2|Magenta| SOHO}}
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[[File:Lagrange points2.svg|thumb|right|270px|Polar view of the Sun-Earth [[Lagrange point|Lagrange points]]. Halo orbits orbit {{L1}}, {{L2}}, or {{L3}} (orbits not shown in diagram).]]
{{Astrodynamics}}
A '''halo orbit''' is a periodic, three-dimensional [[orbit]] near one of the L1, L2 or L3 [[Lagrange point]]s in the [[three-body problem]] of [[orbital mechanics]]. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by a [[Lissajous orbit]] or by a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and the [[Coriolis effect|Coriolis]] and [[centrifugal force]] on a spacecraft. Halo orbits exist in any three-body system, e.g., a [[Sun]]–[[Earth]]–orbiting satellite system or an Earth–[[Moon]]–orbiting satellite system. Continuous "families" of both northern and southern halo orbits exist at each Lagrange point. Because halo orbits tend to be unstable, [[Orbital station-keeping|station-keeping]] using thrusters may be required to keep a satellite on the orbit.

Most satellites in halo orbit serve scientific purposes, for example [[space telescope]]s.

==Definition and history==
[[Robert W. Farquhar]] first used the name "halo" in 1966 for orbits around L{{sub|2}} which were made periodic using thrusters.<ref>{{cite journal |last1=Robert Farquhar |title=Station-Keeping in the Vicinity of Collinear Libration Points with an Application to a Lunar Communications Problem |journal=AAS Science and Technology Series: Space Flight Mechanics Specialist Symposium |date=1966 |volume=11 |pages=519–535}}, see Farquhar, R.W.: [https://ntrs.nasa.gov/citations/19710000821 "The Control and Use of Libration-Point Satellites"], Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, California, 1968, pp. 103, 107–108.</ref> Farquhar advocated using spacecraft in such an orbit beyond the Moon (Earth–Moon {{L2|nolink=yes}}) as a communications relay station for an [[Apollo program|Apollo]] mission to the [[far side of the Moon]]. A spacecraft in such an orbit would be in continuous view of both the Earth and the far side of the Moon, whereas a Lissajous orbit would sometimes make the spacecraft go behind the Moon. In the end, no relay satellite was launched for Apollo, since all landings were on the near side of the Moon.<ref>{{cite web |last1=Schmid |first1=P. E. |date=June 1, 1968 |title=Lunar far-side communication satellites |url=https://ntrs.nasa.gov/citations/19680015886 |access-date=2008-07-16 |publisher=[[NASA]], [[Goddard Space Flight Center]]}}</ref>

In 1973 Farquhar and Ahmed Kamel found that when the in-plane amplitude of a Lissajous orbit was large enough there would be a corresponding out-of-plane amplitude that would have the same period, so the orbit ceased to be a Lissajous orbit and became approximately an ellipse. They used analytical expressions to represent these halo orbits; in 1984, [[Kathleen Howell]] showed that more precise trajectories could be computed numerically. Additionally, she found that for most values of the ratio between the masses of the two bodies (such as the Earth and the Moon) there was a range of stable orbits.<ref>{{cite journal |last1=Howell |first1=Kathleen C. |author-link1=Kathleen Howell |title=Three-Dimensional Periodic Halo Orbits |url=http://adsabs.harvard.edu/full/1984CeMec..32...53H |journal=[[Celestial Mechanics and Dynamical Astronomy|Celestial Mechanics]] |volume= 32 |issue=1 |pages=53–71 |year=1984|doi=10.1007/BF01358403 |bibcode=1984CeMec..32...53H |s2cid=189831091 }}</ref>

The first mission to use a halo orbit was [[International Cometary Explorer|ISEE-3]], a joint [[European Space Agency|ESA]] and [[NASA]] spacecraft launched in 1978. It traveled to the Sun–Earth {{L1|nolink=yes}} point and remained there for several years. The next mission to use a halo orbit was [[Solar and Heliospheric Observatory]] (SOHO), also a joint ESA/NASA mission to study the Sun, which arrived at Sun–Earth {{L1|nolink=yes}} in 1996. It used an orbit similar to ISEE-3.<ref>{{cite book |last1=Dunham |first1=D. W. |title=Libration Point Orbits and Applications |last2=Farquhar |first2=R. W. |year=2003 |isbn=978-981-238-363-1 |pages=45–73 |language=en-us |chapter=Libration Point Missions, 1978–2002 |doi=10.1142/9789812704849_0003}}</ref> Although several other missions since then have traveled to Lagrange points, they (eg. [[Gaia (spacecraft)|Gaia]] astrometric space observatory) typically have used the related non-periodic variations called [[Lissajous orbit]]s rather than an actual halo orbit.

In May 2018, Farquhar's original idea was finally realized when China placed the first communications relay satellite, [[Queqiao relay satellite|Queqiao]], into a halo orbit around the Earth-Moon {{L2|nolink=yes}} point.<ref>{{cite news |last1=Xu |first1=Luyuan |title=How China's lunar relay satellite arrived in its final orbit |url=http://www.planetary.org/blogs/guest-blogs/2018/20180615-queqiao-orbit-explainer.html |work=The Planetary Society |date=2018-06-15 |language=en |quote=This is the first-ever lunar relay satellite at this location.}}</ref> On 3 January 2019, the [[Chang'e 4]] spacecraft landed in the [[Von Kármán (lunar crater)|Von Kármán crater]] on the far side of the Moon, using the Queqiao relay satellite to communicate with the Earth.<ref>{{cite news|url=https://gbtimes.com/china-to-launch-change-4-lunar-far-side-landing-mission-on-december-7 |date=December 5, 2018 |first=Andrew |last=Jones |archive-url=https://web.archive.org/web/20190415075917/https://gbtimes.com/china-to-launch-change-4-lunar-far-side-landing-mission-on-december-7 |title=China to launch Chang'e-4 lunar far side landing mission on December 7 |url-status=dead |archive-date=2019-04-15|work=gbtimes.com}}</ref><ref>{{Cite web |first=Andrew |last=Jones |url=https://spacenews.com/change-4-makes-historic-first-landing-on-the-far-side-of-the-moon/ |title=Chang'e-4 returns first images from lunar farside following historic landing |date=2019-01-03 |website=SpaceNews.com |language=en-US |access-date=2019-01-08}}</ref>

The [[James Webb Space Telescope]] entered a halo orbit around the Sun-Earth {{L2|nolink=yes}} point on 24 January 2022.<ref>{{cite news |last=Roulette |first=Joey |date=24 January 2022 |title=After Million-Mile Journey, James Webb Telescope Reaches Destination – The telescope's safe arrival is a relief to scientists who plan to spend the next 10 or more years using it to study ancient galaxies. |newspaper=[[The New York Times]] |url=https://www.nytimes.com/2022/01/24/science/james-webb-telescope-arrival.html |url-status=live |url-access=subscription |access-date=24 January 2022 |archive-url=https://web.archive.org/web/20220124191053/https://www.nytimes.com/2022/01/24/science/james-webb-telescope-arrival.html |archive-date=2022-01-24}}</ref> [[Euclid (spacecraft)|Euclid]] will enter a similar orbit around this point in August 2023.

India's space agency [[ISRO]] plans to launch [[Aditya-L1]] to study the sun from a halo orbit around L{{sub|1}}.<ref>{{Cite news
|url=https://m.economictimes.com/news/india/after-chandrayaan-3-isro-getting-ready-for-sun-mission-aditya-l1-key-things-to-know/articleshow/102074355.cms |title=After Chandrayaan-3, ISRO getting ready for Sun mission ADITYA-L1. Key things to know |date=2023-07-24 |newspaper=[[The Economic Times]] |language=en |access-date=2023-07-24}}</ref>

==See also==
* [[Interplanetary Transport Network]]
* [[Interplanetary spaceflight]]
* [[Lissajous orbit]], another Lagrangian-point orbit which generalizes halo orbits.
* [[Near-rectilinear halo orbit]]
* [[:Category:Spacecraft using halo orbits]]
* [[Libration point orbit]]

==References==
{{Reflist}}

==External links==
* [http://www.esa.int/esapub/bulletin/bullet88/vande88.htm SOHO – The Trip to the L1 Halo Orbit]
* [https://web.archive.org/web/20110716144221/http://www.stk.com/downloads/corporate/partners/edu/SFMpaper.pdf Low Energy Interplanetary Transfers Using Halo Orbit Hopping Method with STK/Astrogator]
* [https://web.archive.org/web/20170318200526/http://sci2.esa.int/interactive/media/flashes/5_5_1.htm Gaia's Lissajous Type Orbit] – a Lissajous-type orbit, ''i.e.'', a near-circular ellipse or "halo"

{{Orbits|state=expanded}}
{{Authority control}}

{{DEFAULTSORT:Halo Orbit}}
[[Category:Three-body orbits]]
[[Category:Trojans (astronomy)]]
[[Category:Lagrangian mechanics]]

Halo orbit - Revision history

Ajay Kumar at 06:19, 2 September 2023