In orbital mechanics, a Lissajous orbit (pronounced[li.sa.ʒu]), 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 with minimal 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 usually not.
In practice, any orbits around Lagrangian points L1, L2, or L3 are dynamically unstable, meaning small departures from equilibrium grow over time.[1] As a result, spacecraft in these Lagrangian point orbits must use their propulsion systems to perform orbital station-keeping. Although they are not perfectly stable, a modest effort of station keeping keeps a spacecraft in a desired Lissajous orbit for a long time.
In the absence of other influences, orbits about Lagrangian points L4 and L5 are dynamically stable so long as the ratio of the masses of the two main objects is greater than about 25.[2] The natural dynamics keep the spacecraft (or natural celestial body) in the vicinity of the Lagrangian point without use of a propulsion system, even when slightly perturbed from equilibrium.[3] These orbits can however be destabilized by other nearby massive objects. For example, orbits around the L4 and L5 points in the Earth–Moon system can last only a few million years instead of billions because of perturbations by the other planets in the Solar System.[4]
^"ESA Science & Technology: Orbit/Navigation". European Space Agency. 14 June 2009. Retrieved 2009-06-12.
^"A230242 – Decimal expansion of (25+3*sqrt(69))/2". OEIS. Retrieved 7 January 2019.
^Vallado, David A. (2007). Fundamentals of Astrodynamics and Applications (3rd ed.). Springer New York. ISBN 978-1-881883-14-2. (paperback), (hardback).
^Lissauer, Jack J.; Chambers, John E. (2008). "Solar and planetary destabilization of the Earth–Moon triangular Lagrangian points". Icarus. 195 (1): 16–27. Bibcode:2008Icar..195...16L. doi:10.1016/j.icarus.2007.12.024.
trajectory In orbital mechanics, a Lissajousorbit (pronounced [li.sa.ʒu]), named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that...
of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by a Lissajous orbit...
showing a type of harmonic motion Lissajous knot, in knot theory Lissajousorbit, an orbital trajectory resembling a Lissajous curve This disambiguation page...
A Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations x = A sin...
launched Euclid, also occupy orbits around L2. Gaia keeps a tighter Lissajousorbit around L2, while Euclid follows a halo orbit similar to JWST. Each of...
co-orbit with the planet. See asteroids 3753 Cruithne and 2002 AA29. Libration point orbits such as halo orbits and Lissajousorbits: These are orbits around...
parking orbit. From there it executed a short burn each time perigee was passed, slowly raising the apogee closer to the intended halo orbit around the...
elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity...
Orbital decay is a gradual decrease of the distance between two orbiting bodies at their closest approach (the periapsis) over many orbital periods. These...
ACE robotic spacecraft was launched on 25 August 1997, and entered a Lissajousorbit close to the L1 Lagrange point (which lies between the Sun and the...
the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around...
satellites orbit other bodies (such as the Moon, Mars, and the Sun) or many bodies at once (two for a halo orbit, three for a Lissajousorbit). Earth observation...
resulting in a Lissajous figure. This led to the invention of other apparatus such as the harmonograph. Lissajous curve Lissajousorbit O'Connor, John...
In spaceflight, an orbital maneuver (otherwise known as a burn) is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far...
Earth flyby, and approached insertion into a Lissajousorbit around a lunar Lagrange point. Lunar orbit insertion was targeted for April 2011. ARTEMIS-P2...
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets...
mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical...
A geostationary orbit, also referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit 35,786 km (22,236 mi) in altitude...
varieties of libration point orbits amenable to Lyapunov stability[clarification needed] are halo orbits and Lissajousorbits The James Webb Space Telescope...
The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days (a tropical...
This is a list of space probes that have left Earth orbit (or were launched with that intention but failed), organized by their planned destination. It...
telescope in a Lissajousorbit around the L2 Lagrange point. The telescope was launched with slightly less speed than needed to reach its final orbit, and slowed...
An orbital node is either of the two points where an orbit intersects a plane of reference to which it is inclined. A non-inclined orbit, which is contained...
Global Information
