Editing Lagrange point (section)

==Spaceflight applications==
{{anchor|Spacecraft and missions}}{{anchor|Lagrangian spacecraft and missions}}<!-- Links that are apparently unused, added here just to be safe. So they don't need to be part of the headline. -->
{{Main|List of objects at Lagrange points}}

=== Sun–Earth ===
[[File:ACE at L1.png|thumb|The satellite [[Advanced Composition Explorer|ACE]] in an orbit around Sun–Earth {{L1|nolink=yes}}]]
[[File:The orbits of Gaia and Webb ESA23998736.png|thumb|The [[Gaia (spacecraft)|Gaia]] (yellow) and [[James Webb Space Telescope]] (blue) orbits around Sun–Earth {{L2|nolink=yes}}]]

Sun–Earth {{L1|nolink=yes}} is suited for making observations of the Sun–Earth system. Objects here are never shadowed by Earth or the Moon and, if observing Earth, always view the sunlit hemisphere. The first mission of this type was the 1978 [[International Cometary Explorer|International Sun Earth Explorer 3]] (ISEE-3) mission used as an interplanetary early warning storm monitor for solar disturbances.<ref name="nasa_sse">{{cite web |url=http://solarsystem.nasa.gov/missions/profile.cfm?MCode=ISEEICE |title=ISEE-3/ICE |work=Solar System Exploration |publisher=NASA |access-date=8 August 2015 |archive-url=https://web.archive.org/web/20150720021218/http://solarsystem.nasa.gov/missions/profile.cfm?MCode=ISEEICE |archive-date=20 July 2015 |url-status=dead }}</ref> Since June 2015, [[Deep Space Climate Observatory|DSCOVR]] has orbited the L<sub>1</sub> point. Conversely, it is also useful for space-based [[solar telescope]]s, because it provides an uninterrupted view of the Sun and any [[space weather]] (including the [[solar wind]] and [[coronal mass ejections]]) reaches L<sub>1</sub> up to an hour before Earth. Solar and heliospheric missions currently located around L<sub>1</sub> include the [[Solar and Heliospheric Observatory]], [[Wind (spacecraft)|Wind]], [[Aditya-L1|Aditya-L1 Mission]] and the [[Advanced Composition Explorer]]. Planned missions include the [[Interstellar Mapping and Acceleration Probe]](IMAP) and the [[NEO Surveyor]].

Sun–Earth {{L2|nolink=yes}} is a good spot for space-based observatories. Because an object around {{L2|nolink=yes}} will maintain the same relative position with respect to the Sun and Earth, shielding and calibration are much simpler. It is, however, slightly beyond the reach of Earth's [[Umbra, penumbra and antumbra|umbra]],<ref>Angular size of the Sun at 1 AU + 1.5 million kilometres: 31.6′, angular size of Earth at 1.5 million kilometres: 29.3′</ref> so solar radiation is not completely blocked at L<sub>2</sub>. Spacecraft generally orbit around L<sub>2</sub>, avoiding partial eclipses of the Sun to maintain a constant temperature. From locations near L<sub>2</sub>, the Sun, Earth and Moon are relatively close together in the sky; this means that a large sunshade with the telescope on the dark-side can allow the telescope to cool passively to around 50 K – this is especially helpful for [[infrared astronomy]] and observations of the [[cosmic microwave background]]. The [[James Webb Space Telescope]] was positioned in a halo orbit about L<sub>2</sub> on 24 January 2022.

Sun–Earth {{L1|nolink=yes}} and {{L2|nolink=yes}} are [[saddle point]]s and exponentially unstable with [[time constant]] of roughly 23 days. Satellites at these points will wander off in a few months unless course corrections are made.<ref name="cornish" /> 

Sun–Earth {{L3|nolink=yes}} was a popular place to put a "[[Counter-Earth]]" in [[Pulp magazine|pulp]] [[science fiction]] and [[comic book]]s, despite the fact that the existence of a planetary body in this location had been understood as an impossibility once orbital mechanics and the perturbations of planets upon each other's orbits came to be understood, long before the Space Age; the influence of an Earth-sized body on other planets would not have gone undetected, nor would the fact that the foci of Earth's orbital ellipse would not have been in their expected places, due to the mass of the counter-Earth. The Sun–Earth {{L3|nolink=yes}}, however, is a weak saddle point and exponentially unstable with time constant of roughly 150 years.<ref name="cornish" /> Moreover, it could not contain a natural object, large or small, for very long because the gravitational forces of the other planets are stronger than that of Earth (for example, [[Venus]] comes within 0.3&nbsp;[[Astronomical unit|AU]] of this {{L3|nolink=yes}} every 20&nbsp;months).<ref name=DUNCOMBE2>{{cite web|last=DUNCOMBE|first=R. L.|title=Appendix E. Report on Numerical Experiment on the Possible Existence of an "Anti-Earth"|url=http://files.ncas.org/condon/text/appndx-e.htm|work=1968|publisher=U.S. NAVAL OBSERVATORY|access-date=24 October 2013|quote=The separation of [a Counter-Earth] from the line joining the Earth and the Sun shows a variation with increasing amplitude in time, the effect being most pronounced for the largest assumed mass. During the 112 years covered by the integration the separation becomes large enough in all cases that Clarion should have been directly observed, particularly at times of morning or evening twilight and during total solar eclipses.}}</ref>

A spacecraft orbiting near Sun–Earth {{L3|nolink=yes}} would be able to closely monitor the evolution of active sunspot regions before they rotate into a geoeffective position, so that a seven-day early warning could be issued by the [[National Oceanic and Atmospheric Administration|NOAA]] [[Space Weather Prediction Center]]. Moreover, a satellite near Sun–Earth {{L3|nolink=yes}} would provide very important observations not only for Earth forecasts, but also for deep space support (Mars predictions and for crewed missions to [[Near-Earth object#Near-Earth asteroids|near-Earth asteroids]]). In 2010, spacecraft transfer trajectories to Sun–Earth {{L3|nolink=yes}} were studied and several designs were considered.<ref name="transferslibthree">{{Cite journal|title=Spacecraft trajectories to the {{L3|nolink=yes}} point of the Sun–Earth three-body problem |journal=Celestial Mechanics and Dynamical Astronomy |last1=Tantardini|first1=Marco |last2=Fantino|first2=Elena |first3=Yuan |last3=Ren |first4=Pierpaolo |last4=Pergola |first5=Gerard |last5=Gómez |first6=Josep J. |last6=Masdemont |date=2010 |doi=10.1007/s10569-010-9299-x |volume=108 |issue=3 |pages=215–232|bibcode = 2010CeMDA.108..215T |s2cid=121179935 |url=https://hal.archives-ouvertes.fr/hal-00568378/file/PEER_stage2_10.1007%252Fs10569-010-9299-x.pdf }}</ref>

===Earth–Moon===
Earth–Moon {{L1|nolink=yes}} allows comparatively easy access to lunar and Earth orbits with minimal change in velocity and this has as an advantage to position a habitable [[space station]] intended to help transport cargo and personnel to the Moon and back. The [[SMART-1]] mission <ref>[http://www.moontoday.net/news/viewsr.html?pid=14345 SMART-1: On Course for Lunar Capture | Moon Today – Your Daily Source of Moon News<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20051102120549/http://www.moontoday.net/news/viewsr.html?pid=14345 |date=2 November 2005 }}</ref> passed through the L<sub>1</sub> Lagrangian Point on 11 November 2004 and passed into the area dominated by the Moon's [[gravity|gravitational]] influence.

Earth–Moon {{L2|nolink=yes}} has been used for a [[communications satellite]] covering the Moon's far side, for example, [[Queqiao relay satellite|Queqiao]], launched in 2018,<ref name="magpie-earth-moon-l2">{{cite magazine |last=Jones |first=Andrew |title=Chang'e-4 relay satellite enters halo orbit around Earth-Moon L2, microsatellite in lunar orbit |url=https://spacenews.com/change-4-relay-satellite-enters-halo-orbit-around-earth-moon-l2-microsatellite-in-lunar-orbit/ |magazine=SpaceNews |date=14 June 2018}}</ref> and would be "an ideal location" for a [[propellant depot]] as part of the proposed depot-based space transportation architecture.<ref name="aiaa20100902_p4">{{cite web |last1=Zegler |first1=Frank |title=Evolving to a Depot-Based Space Transportation Architecture |url=http://www.ulalaunch.com/uploads/docs/Published_Papers/Exploration/DepotBasedTransportationArchitecture2010.pdf |work=AIAA SPACE 2010 Conference & Exposition |publisher=AIAA |access-date=25 January 2011 |first2=Bernard |last2=Kutter |date=2 September 2010 |page=4 |quote=L<sub>2</sub> is in deep space far away from any planetary surface and hence the thermal, micrometeoroid, and atomic oxygen environments are vastly superior to those in LEO. Thermodynamic stasis and extended hardware life are far easier to obtain without these punishing conditions seen in LEO. L<sub>2</sub> is not just a great gateway—it is a great place to store propellants. ...&nbsp;L<sub>2</sub> is an ideal location to store propellants and cargos: it is close, high energy, and cold. More importantly, it allows the continuous onward movement of propellants from LEO depots, thus suppressing their size and effectively minimizing the near-Earth boiloff penalties. |archive-url=https://web.archive.org/web/20140624125633/http://www.ulalaunch.com/uploads/docs/Published_Papers/Exploration/DepotBasedTransportationArchitecture2010.pdf |archive-date=24 June 2014 |url-status=dead }}</ref>

Earth–Moon {{L4|nolink=yes}} and {{L5|nolink=yes}} are the locations for the [[Kordylewski cloud|Kordylewski dust clouds]].<ref name="kordylewski">{{cite magazine |last=Kordylewski |first=Kazimierz |author-link=Kazimierz Kordylewski |title=Photographische Untersuchungen des Librationspunktes L<sub>5</sub> im System Erde-Mond |url=https://adsabs.harvard.edu/full/1961AcA....11..165K |magazine=Acta Astronomica, Vol. 11, p.165 |date=1961|volume=11 |page=165 |bibcode=1961AcA....11..165K }}</ref> The [[L5 Society]]'s name comes from the L<sub>4</sub> and L<sub>5</sub> Lagrangian points in the Earth–Moon system proposed as locations for their huge rotating space habitats. Both positions are also proposed for communication satellites covering the Moon alike communication satellites in [[geosynchronous orbit]] cover the Earth.<ref name="TychoESAmoonlight">{{cite magazine |last=Hornig |first=Andreas |title=TYCHO: Supporting Permanently Crewed Lunar Exploration with High-Speed Optical Communication from Everywhere |url=https://ideas.esa.int/servlet/hype/IMT?userAction=Browse&templateName=&documentId=e3f5e00bb992b91a4378e46176b02376 |magazine=ESA |date=1 May 2022}}</ref><ref name="TychoVideo">{{cite magazine |last=Hornig |first=Andreas |title=TYCHO mission to Earth-Moon libration point EML-4 @ IAC 2013 |url=https://www.youtube.com/watch?v=7RJSLFP7yyA |magazine=IAC2013 |date=6 October 2013}}</ref>

===Sun–Venus===
Scientists at the [[B612 Foundation]] were<ref>{{Cite web |last=Foust |first=Jeff |date=20 June 2017 |url=https://spacenews.com/b612-studying-smallsat-missions-to-search-for-near-earth-objects/ |title=B612 studying smallsat missions to search for near Earth objects |website=SpaceNews.com |access-date=6 May 2025 }}</ref> planning to use [[Venus]]'s L<sub>3</sub> point to position their planned [[Sentinel (space telescope)|Sentinel telescope]], which aimed to look back towards Earth's orbit and compile a catalog of [[near-Earth object|near-Earth asteroids]].<ref>{{cite web|url=https://b612foundation.org/sentinel-mission/ |archive-url=https://web.archive.org/web/20120630034544/http://b612foundation.org/sentinel-mission/ |url-status=dead |archive-date=30 June 2012 |title=The Sentinel Mission |publisher=B612 Foundation |access-date=1 February 2014}}</ref>

===Sun–Mars===
In 2017, the idea of positioning a [[magnetic dipole]] shield at the Sun–Mars {{L1|nolink=yes}} point for use as an artificial magnetosphere for Mars was discussed at a NASA conference.<ref>{{Cite web|url=https://phys.org/news/2017-03-nasa-magnetic-shield-mars-atmosphere.html|title=NASA proposes a magnetic shield to protect Mars' atmosphere|website=phys.org}}</ref> The idea is that this would protect the planet's atmosphere from the Sun's radiation and solar winds.