Halo orbit
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Ahalo orbitis a periodic, three-dimensionalorbitassociated with one of the L1,L2or L3Lagrange pointsin thethree-body problemoforbital mechanics.Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by aLissajous orbitor by a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and theCoriolisandcentrifugal forceon a spacecraft. Halo orbits exist in any three-body system, e.g., aSun–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,station-keepingusing thrusters may be required to keep a satellite on the orbit.
Most satellites in halo orbit serve scientific purposes, for examplespace telescopes.
Definition and history[edit]
Robert W. Farquharfirst used the name "halo" in 1966 for orbits around L2which were made periodic using thrusters.[1]Farquhar advocated using spacecraft in such an orbit beyond the Moon (Earth–Moon L2) as a communications relay station for anApollomission to thefar 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.[2]
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,[3]so the orbit ceased to be a Lissajous orbit and became approximately an ellipse.[citation needed]They used analytical expressions to represent these halo orbits; in 1984,Kathleen Howellshowed 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.[4]
The first mission to use a halo orbit wasISEE-3,a jointESAandNASAspacecraft launched in 1978. It traveled to the Sun–Earth L1point and remained there for several years. The next mission to use a halo orbit wasSolar and Heliospheric Observatory(SOHO), also a joint ESA/NASA mission to study the Sun, which arrived at Sun–Earth L1in 1996. It used an orbit similar to ISEE-3.[5]Although several other missions since then have traveled to Lagrange points, they (eg.Gaiaastrometric space observatory) typically have used the related non-periodic variations calledLissajous orbitsrather than an actual halo orbit.
Although halo orbits were well known in the RTBP (Restricted Three Body Problem), it was difficult to obtain Halo orbits for the real Earth-Moon system. Translunar halo orbits were first computed in 1998 by M.A. Andreu, who introduced a new model for the motion of a spacecraft in the Earth-Moon-Sun system, which was called Quasi-Bicircular Problem (QBCP).[6]
In May 2018, Farquhar's original idea was finally realized when China placed the first communications relay satellite,Queqiao,into a halo orbit around the Earth-Moon L2point.[7]On 3 January 2019, theChang'e 4spacecraft landed in theVon Kármán crateron the far side of the Moon, using the Queqiao relay satellite to communicate with the Earth.[8][9]
TheJames Webb Space Telescopeentered a halo orbit around the Sun-Earth L2point on 24 January 2022.[10]Euclidentered a similar orbit around this point in August 2023.
India's space agencyISROlaunchedAditya-L1to study the sun from a halo orbit around L1point.[11]On 6 January 2024,Aditya-L1spacecraft, India's first solar mission, has successfully entered its final orbit with a period of approximately 180 days around the first Sun-EarthLagrangian point(L1), approximately 1.5 million kilometers fromEarth.[12]
See also[edit]
- 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[edit]
- ^Robert Farquhar (1966). "Station-Keeping in the Vicinity of Collinear Libration Points with an Application to a Lunar Communications Problem".AAS Science and Technology Series: Space Flight Mechanics Specialist Symposium.11:519–535.,see Farquhar, R.W.:"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.
- ^Schmid, P. E. (1 June 1968)."Lunar far-side communication satellites".NASA,Goddard Space Flight Center.Retrieved16 July2008.
- ^Farquhar, R. W.; Kamel, A. A. (June 1973)."Quasi-Periodic Orbits about the Translunar Libration Point".Springer.
- ^Howell, Kathleen C.(1984)."Three-Dimensional Periodic Halo Orbits".Celestial Mechanics.32(1): 53–71.Bibcode:1984CeMec..32...53H.doi:10.1007/BF01358403.S2CID189831091.
- ^Dunham, D. W.; Farquhar, R. W. (2003). "Libration Point Missions, 1978–2002".Libration Point Orbits and Applications.pp. 45–73.doi:10.1142/9789812704849_0003.ISBN978-981-238-363-1.
- ^Andreu, M.A. (1998).The Quasi-bicircular problem.Ph. D. Thesis, Dept. Matemática Aplicada i Anàlisi, Universitat de Barcelona. Publicacions Universitat de Barcelona.ISBN84-475-2319-5.
- ^Xu, Luyuan (15 June 2018)."How China's lunar relay satellite arrived in its final orbit".The Planetary Society.
This is the first-ever lunar relay satellite at this location.
- ^Jones, Andrew (5 December 2018)."China to launch Chang'e-4 lunar far side landing mission on December 7".gbtimes.Archived fromthe originalon 15 April 2019.
- ^Jones, Andrew (3 January 2019)."Chang'e-4 returns first images from lunar farside following historic landing".SpaceNews.Retrieved8 January2019.
- ^Roulette, Joey (24 January 2022)."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".The New York Times.Archivedfrom the original on 24 January 2022.Retrieved24 January2022.
- ^"After Chandrayaan-3, ISRO getting ready for Sun mission ADITYA-L1. Key things to know".The Economic Times.24 July 2023.Retrieved24 July2023.
- ^"Halo-Orbit Insertion of Aditya-L1 Successfully Accomplished".isro.gov.in.Retrieved6 January2024.
External links[edit]
- SOHO – The Trip to the L1 Halo Orbit
- Low Energy Interplanetary Transfers Using Halo Orbit Hopping Method with STK/Astrogator
- Gaia's Lissajous Type Orbit– a Lissajous-type orbit,i.e.,a near-circular ellipse or "halo"
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