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In orbital mechanics, a Lissajous orbit (), named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system without requiring any propulsion. Lyapunov orbits around a Lagrangian point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve. Halo orbits also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not. In practice, any orbits around Lagrangian points , , or are dynamically unstable, meaning small departures from equilibrium grow over time. As a result, spacecraft in Langrangian point orbits must use their propulsion systems to perform orbital station-keeping. In the absence of other influences, orbits about Lagrangian points and are dynamically stable so long as the ratio of the masses of the two main objects is greater than about 25, meaning the natural dynamics (without the use of a spacecraft's propulsion system) keep the spacecraft in the vicinity of the Lagrangian point even when slightly perturbed from equilibrium. These orbits can however be destabilized by other heavy nearby objects. It has been found for example that the and points in the Earth–Moon system would be stable for billions of years, even with perturbations from the sun, but because of smaller perturbations by the planets, orbits around these points can only last a few million years.〔("Solar and planetary destabilization of the Earth–Moon triangular Lagrangian points" ) by Jack Lissauer and John Chambers, ''Icarus'', vol. 195, issue 1, May 2008, pp. 16-27.〕 ==Spacecraft using Lissajous orbits== Several missions have used Lissajous orbits: ACE at Sun–Earth ,〔(Advanced Composition Explorer (ACE) Mission Overview ), CalTech, retrieved 2014-09-06.〕 DSCOVR at Sun–Earth ,〔(SpaceX Falcon 9 successfully launches the DSCOVR spacecraft, NASA, retrieved 2015-08-05. )〕 WMAP at Sun–Earth ,〔(WMAP Trajectory and Orbit ), NASA, retrieved 2014-09-06.〕 and also the Genesis mission collecting solar particles at .〔(Genesis: Lissajous Orbit Insertion ), NASA, retrieved 2014-09-06.〕 On 14 May 2009, the European Space Agency (ESA) launched into space the Herschel and Planck observatories, both of which use Lissajous orbits at Sun–Earth .〔 (【引用サイトリンク】 url = http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=34699 )〕 ESA's current Gaia mission also uses a Lissajous orbit at Sun–Earth .〔(【引用サイトリンク】 url = http://sci2.esa.int/interactive/media/flashes/5_5_1.htm )〕 In 2011, NASA transferred two of its THEMIS spacecraft from Earth orbit to Lunar orbit by way of Earth-Moon and Lissajous orbits.〔(ARTEMIS: The First Mission to the Lunar Libration Orbits )〕 China's lunar orbiter Chang'e 2 left lunar orbit on June 8, 2011 and flew to .〔http://scitech.people.com.cn/GB/14041406.html〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「lissajous orbit」の詳細全文を読む スポンサード リンク
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