Lissajous orbit: Difference between revisions

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	In ], a '''Lissajous orbit''' is a quasi-periodic orbital trajectory that an object can follow around a collinear ] (]) of a three-body system without requiring any propulsion. ] around a libration 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 ]. ]s also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.		In ], a '''Lissajous orbit''' is a quasi-periodic orbital trajectory that an object can follow around a collinear ] (]) of a three-body system without requiring any propulsion. ] around a libration 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 ]. ]s also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.<ref>{{cite conference
			\| last = Koon
			\| first = Wang Sang
			\| authorlink =
			\| title = Dynamical Systems, the Three-Body Problem, and Space Mission Design
			\| booktitle = International Conference on Diﬀerential Equations
			\| publisher = World Scientiﬁc
			\| url = http://www.gg.caltech.edu/~mwl/publications/papers/dynamicalThreeBody.pdf
			\| location = Berlin
			\| date = 2000
			\| pages = 1167-1181}}</ref>

	In practice, any orbit around a collinear libration point is dynamically unstable, meaning small departures from equilibrium grow exponentially over time. As a result, spacecraft in libration point orbits must use their propulsion systems to perform ].		In practice, any orbit around a collinear libration point is dynamically unstable, meaning small departures from equilibrium grow exponentially over time. As a result, spacecraft in libration point orbits must use their propulsion systems to perform ].

	Several missions have used Lissajous trajectories. ] at Sun-Earth L<sub>1</sub> and ] at Sun-Earth L<sub>2</sub>. On May 14, 2009, the ] (ESA) launched into space the ] and ] observatories, both of which will use Lissajous orbits at Sun-Earth L<sub>2</sub>. ~~ESA's future ] will also use a Lissajous orbit at Sun-Earth L~~<~~sub~~>~~2</sub>.~~		Several missions have used Lissajous trajectories. ] at Sun-Earth L<sub>1</sub> and ] at Sun-Earth L<sub>2</sub>. On May 14, 2009, the ] (ESA) launched into space the ] and ] observatories, both of which will use Lissajous orbits at Sun-Earth L<sub>2</sub>.<ref>{{cite web
			\| title = Herschel: Orbit/Navigation
		⚫	\| url = http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=34699
			\| accessdate = 2006-05-15}}</ref> ESA's future ] will also use a Lissajous orbit at Sun-Earth L<sub>2</sub>.<ref>{{cite web
			\| title = Gaia's Lissajous Type Orbit
		⚫	\| url = http://sci2.esa.int/interactive/media/flashes/5_5_1.htm
			\| accessdate = 2006-05-15}}</ref>

	== References ==		== References ==

	* http://sci.esa.int/science-e/www/area/index.cfm?fareaid=16
			{{Reflist}}
	* http://sci.esa.int/science-e/www/area/index.cfm?fareaid=17
⚫	* http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=34699
⚫	* http://sci2.esa.int/interactive/media/flashes/5_5_1.htm
	* {{cite book \|title=Dynamical Systems, the Three-Body Problem, and Space Mission Design \|last=Koon \|first=W. S. \|coauthors=M. W. Lo, J. E. Marsden, and S. D. Ross \|url=http://www.cds.caltech.edu/~marsden/books/Mission_Design.html \|date=2006}}

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Revision as of 17:49, 15 May 2009

In orbital mechanics, a Lissajous orbit is a quasi-periodic orbital trajectory that an object can follow around a collinear libration point (Lagrangian point) of a three-body system without requiring any propulsion. Lyapunov orbits around a libration 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 orbit around a collinear libration point is dynamically unstable, meaning small departures from equilibrium grow exponentially over time. As a result, spacecraft in libration point orbits must use their propulsion systems to perform orbital stationkeeping.

Several missions have used Lissajous trajectories. ACE at Sun-Earth L₁ and WMAP at Sun-Earth L₂. On May 14, 2009, the European Space Agency (ESA) launched into space the Herschel and Planck observatories, both of which will use Lissajous orbits at Sun-Earth L₂. ESA's future Gaia mission will also use a Lissajous orbit at Sun-Earth L₂.

References

Koon, Wang Sang (2000). "Dynamical Systems, the Three-Body Problem, and Space Mission Design" (PDF). International Conference on Diﬀerential Equations. Berlin: World Scientiﬁc. pp. 1167–1181. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help)
"Herschel: Orbit/Navigation". Retrieved 2006-05-15.
"Gaia's Lissajous Type Orbit". Retrieved 2006-05-15.

Gravitational orbits

Types

General	Box Capture Circular Elliptical / Highly elliptical Escape Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic trajectory Parking Prograde / Retrograde Synchronous semi sub Transfer orbit
Geocentric	Geosynchronous Geostationary Geostationary transfer Graveyard High Earth Low Earth Medium Earth Molniya Near-equatorial Orbit of the Moon Polar Sun-synchronous Transatmospheric Tundra Very low Earth
About other points	Mars Areocentric Areosynchronous Areostationary Lagrange points Distant retrograde Halo Lissajous Libration Lunar Sun Heliocentric Earth's orbit Mars cycler Heliosynchronous Other Lunar cycler

Parameters

Shape Size	e Eccentricity a Semi-major axis b Semi-minor axis Q, q Apsides
Orientation	i Inclination Ω Longitude of the ascending node ω Argument of periapsis ϖ Longitude of the periapsis
Position	M Mean anomaly ν, θ, f True anomaly E Eccentric anomaly L Mean longitude l True longitude
Variation	T Orbital period n Mean motion v Orbital speed t₀ Epoch

Maneuvers

Orbital
mechanics

List of orbits

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