# Lissajous orbit: Wikis

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# Encyclopedia

Lissajous orbit around L2

In orbital mechanics, a Lissajous orbit 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 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.[1]

In practice, any orbit around Lagrangian points L1, L2, or L3 is dynamically unstable, meaning small departures from equilibrium grow exponentially over time.[2] As a result, spacecraft in libration point orbits must use their propulsion systems to perform orbital station-keeping. Orbits about Lagrangian points L4 and L5 are dynamically stable in theory, 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.[3] In the case of the Earth Moon system the effect of the ellipticity of the Moon's orbit and the effect of solar perturbation cause these Lagrange points to be unstable as well.

Several missions have used Lissajous trajectories. ACE at Sun-Earth L1 and WMAP at Sun-Earth L2 and also the Genesis mission collecting solar particles and the Solar and Heliospheric Observatory at L1. On May 14, 2009, the European Space Agency (ESA) launched into space the Herschel and Planck observatories, both of which use Lissajous orbits at Sun-Earth L2. [4] ESA's future Gaia mission will also use a Lissajous orbit at Sun-Earth L2.[5]

In the science fiction novel Sunstorm by Arthur C. Clarke and Stephen Baxter, a huge shield is constructed in space to protect the Earth from a deadly solar super storm which would have been in a Lissajous orbit as would a group of other wealthy and powerful people who sheltered opposite it at L2 - in line with both Earth and Moon as well as the L1 shield with a Lunar eclipse taking place at the time.

## References

1. ^ Koon, Wang Sang (2000). "Dynamical Systems, the Three-Body Problem, and Space Mission Design". International Conference on Differential Equations. Berlin: World Scientiﬁc. pp. 1167–1181.
2. ^ "ESA Science & Technology: Orbit/Navigation". European Space Agency. 14-Jun-2009. Retrieved 2009-06-12.
3. ^ Vallado, David A. (2007). Fundamentals of Astrodynamics and Applications (3 ed.). Space Technology Library (jointly with Microcosm Press). ISBN 978-1-881883-14-2 (paperback), 978-0-387-71831-6 (hardback).
4. ^ "Herschel: Orbit/Navigation". ESA. Retrieved 2006-05-15.
5. ^ "Gaia's Lissajous Type Orbit". ESA. Retrieved 2006-05-15.