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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 a Lissaujous orbit at at Sun-Earth L₂. Also ESA's GAIA mission will use a Lissajous orbit at Sun-Earth L₂ in the future.

References

External links

Koon, W. S. (2006). Dynamical Systems, the Three-Body Problem, and Space Mission Design. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

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Revision as of 19:08, 14 May 2009 edit Abune (talk \| contribs) Extended confirmed users, Pending changes reviewers 31,759 edits mNo edit summary ← Previous edit		Revision as of 23:53, 14 May 2009 edit undo Abestrobi (talk \| contribs) 126 edits Added graphic Next edit →
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			[[Image:Lissajous_orbit_l2.jpg\|thumb\|300px\|Lissajous orbit around L2]]
	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 orbit]]s also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.		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 orbit]]s also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.