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Quasi-periodic orbital trajectory
trajectory In orbital mechanics, a Lissajous orbit (pronounced [li.sa.ʒu]), named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that
Lissajous_orbit
Periodic, three-dimensional orbit
space, its peculiar characteristic is that it can be orbited by a Lissajous orbit or by a halo orbit. These space curves can be thought of as resulting
Halo_orbit
Mathematical curve outputted from a specific pair of parametric equations
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
Lissajous_curve
Equilibrium points near two orbiting bodies
launched Euclid, also occupy orbits around L2. Gaia keeps a tighter Lissajous orbit around L2, while Euclid follows a halo orbit similar to JWST. Each of
Lagrange_point
French physicist
resulting in a Lissajous figure. This led to the invention of other apparatus such as the harmonograph. Lissajous curve Lissajous orbit O'Connor, John
Jules_Antoine_Lissajous
Topics referred to by the same term
showing a type of harmonic motion Lissajous knot, in knot theory Lissajous orbit, an orbital trajectory resembling a Lissajous curve This disambiguation page
Lissajous
Type of co-orbital motion of a small orbiting body relative to a larger orbiting body
objects Halo orbit – Periodic, three-dimensional orbit Interplanetary Transport Network – Low-energy trajectories in the Solar System Lissajous orbit – Quasi-periodic
Horseshoe_orbit
Transfer manoeuvre between two orbits
transfer Delta-v budget Geostationary transfer orbit Halo orbit Lissajous orbit List of orbits Orbital mechanics Walter Hohmann, The Attainability of
Hohmann_transfer_orbit
Objects intentionally placed into orbit
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 Lissajous orbit). Earth observation
Satellite
ESA space telescope in service 2009–2013
SOHO, Cluster II, XMM-Newton and Rosetta. The observatory was carried into orbit by an Ariane 5 in May 2009, reaching the second Lagrangian point (L2) of
Herschel_Space_Observatory
Maintenance of a particular orbit
operated there in a Lissajous orbit during 2009–2013, at which time it ran out of coolant for the space telescope. Small station-keeping orbital maneuvers were
Orbital_station-keeping
European space observatory for astrometry (2013–2025)
flying from Kourou in French Guiana. The spacecraft operated in a Lissajous orbit around the Sun–Earth L2 Lagrangian point. The science observation officially
Gaia_(spacecraft)
Space observatory
inject Planck into its final orbit around L2 was successfully completed on 3 July 2009, when it entered a Lissajous orbit with a 400,000 km (250,000 mi)
Planck_(spacecraft)
co-orbit with the planet. See asteroids 3753 Cruithne and 2002 AA29. Libration point orbits such as halo orbits and Lissajous orbits: These are orbits around
List_of_orbits
Time an astronomical object takes to complete one orbit around another object
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy
Orbital_period
Amount by which an orbit deviates from a perfect circle
value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic (escape orbit or capture orbit), and greater than 1 is
Orbital_eccentricity
Orbit with a fixed distance from the barycenter
A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle. In this case, not only the distance, but
Circular_orbit
2015 European Space Agency spacecraft
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
LISA_Pathfinder
Trajectory of Earth around the Sun
Earth orbits the Sun at an average distance of 149.60 million km (92.96 million mi), or 8.317 light-minutes, in a counterclockwise direction as viewed
Earth's_orbit
Angle between a reference plane and the plane of an orbit
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital
Orbital_inclination
NASA satellite of the Explorer program (2001-2010)
without looking to the Sun, the WMAP traced a path around L2 in a Lissajous orbit ca. 1.0° to 10°, with a 6-month period. The telescope rotated once
Wilkinson Microwave Anisotropy Probe
Wilkinson_Microwave_Anisotropy_Probe
NASA/ESA/CSA space telescope launched in 2021
telescope in a Lissajous orbit around the L2 Lagrange point. The telescope was launched with slightly less speed than needed to reach its final orbit, and slowed
James_Webb_Space_Telescope
The Moon's circuit around Earth
The orbit of the Moon is, while stable and known, highly complex, and as such still studied by lunar theory. Most models describe the Moon's orbit geocentrically
Orbit_of_the_Moon
Chinese lunar probe (2014–2020)
DFH-3A service module entered lunar orbit on 13 January 2015. This was initially a 200 x 5,300 km Lissajous orbit around Earth-Moon L2 with a period of
Chang'e_5-T1
American solar research spacecraft
February 2015, and reached L1 on 8 June 2015, joining the list of objects orbiting at Lagrange points. NOAA operates DSCOVR from its Satellite and Product
Deep Space Climate Observatory
Deep_Space_Climate_Observatory
Process that leads to gradual decrease of the distance between two orbiting bodies
Orbital decay is a gradual decrease of the distance between two orbiting bodies at their closest approach (the periapsis) over many orbital periods. These
Orbital_decay
Field of classical mechanics concerned with the motion of spacecraft
Orbital mechanics , astrodynamics or space dynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft
Orbital_mechanics
Center of mass of multiple bodies orbiting each other
(kéntron) 'center') is the center of mass around which two or more bodies orbit. A barycenter is a dynamical point, not a physical object. It is an important
Barycenter_(astronomy)
NASA satellite of the Explorer program, at SE-L1 from 1997
ACE robotic spacecraft was launched on 25 August 1997, and entered a Lissajous orbit close to the L1 Lagrange point (which lies between the Sun and the
Advanced_Composition_Explorer
Circular orbit above Earth's Equator and following the direction of Earth's rotation
A geostationary orbit, also referred to as a GEO or GSO, is a circular geosynchronous orbit 35,786 km (22,236 mi) in altitude above Earth's equator, 42
Geostationary_orbit
Type of geocentric orbit
A Sun-synchronous orbit (SSO), also called a heliosynchronous orbit, is a nearly polar orbit around a planet, in which the satellite passes over any given
Sun-synchronous_orbit
Concept in gravitational orbital mechanics
the vis-viva equation is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical
Vis-viva_equation
Classical approach to the many-body problem of astronomy
geometrical terms. This is called a two-body problem, or an unperturbed Keplerian orbit. The differences between that and the actual motion of the body are perturbations
Perturbation_(astronomy)
Speed at which a body orbits around the barycenter of a system
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
Orbital_speed
Movement during spaceflight
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
Orbital_maneuver
Horizontal angle from north or other reference cardinal direction
Perturbations Sphere of influence N-body orbits Lagrangian points (Halo orbits) Lissajous orbits Lyapunov orbits Engineering and efficiency Preflight engineering
Azimuth
NASA sample return probe
cruised to the Earth-Sun L1 then performed a Lissajous orbit insertion maneuver, entering an elliptical orbit about L1 on November 16, 2001. Genesis exposed
Genesis_(spacecraft)
Orbit around Earth between 160 and 2000 km
A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less
Low_Earth_orbit
Chinese Moon orbiter
Lunar Exploration Program, and conducted research from a 100-km-high lunar orbit in preparation for the December 2013 soft landing by the Chang'e 3 lander
Chang'e_2
Kepler orbit with an eccentricity of less than one
elliptical orbit or eccentric orbit is an orbit with an eccentricity of less than 1;[citation needed] this includes the special case of a circular orbit, with
Elliptic_orbit
Quasiperiodic orbit around a Lagrange point
varieties of libration point orbits amenable to Lyapunov stability[clarification needed] are halo orbits and Lissajous orbits The James Webb Space Telescope
Libration_point_orbit
Laws describing planetary orbits
astronomy, Kepler's laws of planetary motion give good approximations for the orbits of planets around the Sun. They were published by Johannes Kepler from 1609
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
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
List_of_Solar_System_probes
Sun–Earth L2 point are in a Lissajous orbit until decommissioned, when they are sent into a heliocentric graveyard orbit.[citation needed] 2001 – 2010:
List of objects at Lagrange points
List_of_objects_at_Lagrange_points
Problem in physics and celestial mechanics
predict a planet's motion; i.e., to give its orbital properties: position, orbital diameter, period and orbital velocity. Having done so, he and others soon
N-body_problem
Type of high-latitude satellite orbit
A Molniya orbit (Russian: Молния, IPA: [ˈmoɫnʲɪjə] , "Lightning") is a type of satellite orbit designed to provide communications and remote sensing coverage
Molniya_orbit
Point where an orbit crosses a plane of reference to which it is inclined
An orbital node is either of the two points where an orbiting object intersects a plane of reference inclined with respect to the orbital plane. A non-inclined
Orbital_node
Orbit of an object around the Moon
spaceflight, a lunar orbit (also known as a selenocentric orbit) is an orbit by an object around Earth's Moon. In general these orbits are not circular.
Lunar_orbit
transfer Delta-v budget Geostationary transfer orbit Halo orbit Lissajous orbit List of orbits Orbital mechanics Grodzovskiy, G. L.; Ivanov, Yu. N.; Tokarev
Low thrust relative orbital transfer
Low_thrust_relative_orbital_transfer
Objects sharing the orbit of a larger one
Lissajous orbit – Quasi-periodic orbital trajectory List of objects at Lagrange points Tadpole orbit – Type of co-orbital motion of a small orbiting body
Trojan_(celestial_body)
NASA satellite of the Explorer program
Earth flyby, and approached insertion into a Lissajous orbit around a lunar Lagrange point. Lunar orbit insertion was targeted for April 2011. ARTEMIS-P2
THEMIS
Parameters that define a specific orbit
Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes are commonly used in astronomy and orbital mechanics
Orbital_elements
Earth-centered orbit above low Earth orbit and below geostationary orbit
A medium Earth orbit (MEO) is an Earth-centered orbit with an altitude above a low Earth orbit (LEO) and below a high Earth orbit (HEO) – between 2,000
Medium_Earth_orbit
Hemisphere of the Moon that always faces away from Earth
on the existing TIROS satellites to be launched into a Farquhar–Lissajous halo orbit around the L2 point so as to maintain line-of-sight contact with
Far_side_of_the_Moon
Orbit around the barycenter of the Sun
heliocentric orbit (also called circumsolar orbit) is an orbit around the Sun. The inner planets are mainly influenced by the Sun's gravity, and orbit points
Heliocentric_orbit
Type of orbit
mechanics a parabolic trajectory is a Kepler orbit with the eccentricity (e) equal to 1 and is an unbound orbit that is exactly on the border between elliptical
Parabolic_trajectory
Mathematical equation describing the motion of a rocket
applied to orbital maneuvers in order to determine how much propellant is needed to change to a particular new orbit, or to find the new orbit as the result
Tsiolkovsky_rocket_equation
Branch of engineering
enter orbit around the Moon, with two, Neil Armstrong and Buzz Aldrin, visiting the lunar surface. The third astronaut, Michael Collins, stayed in orbit to
Aerospace_engineering
Orbit keeping the satellite at a fixed longitude above the equator
A geosynchronous orbit (sometimes abbreviated GEO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours
Geosynchronous_orbit
Parameter of Keplerian orbits
parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position
True_anomaly
Term in geometry; longest and shortest semidiameters of an ellipse
eccentricity of the orbit. In astronomy, the semi-major axis is one of the most important orbital elements of an orbit, along with its orbital period. For Solar
Semi-major and semi-minor axes
Semi-major_and_semi-minor_axes
Curved path of an object around a point
mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Alternatively, it is known as an orbital revolution
Orbit
Concept in celestial mechanics
is the minimum speed needed for an object to escape from contact with or orbit of a primary body, assuming: Ballistic trajectory – no other forces are
Escape_velocity
Property of a dynamical system where solutions near an equilibrium point remain so
principle Lyapunov–Malkin theorem Markus–Yamabe conjecture Libration point orbit Hartman–Grobman theorem Perturbation theory Stability theory Lyapunov, A
Lyapunov_stability
Type of spacecraft maneuver
a spacecraft to burn its fuel is at the lowest possible orbital periapsis, when its orbital velocity (and so, its kinetic energy) is greatest. In some
Oberth_effect
Either of two extreme points in a celestial object's orbit
nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting
Apsis
Complex type of orbit
A Rosetta orbit is a complex type of orbit. In astronomy, a Rosetta orbit occurs when there is a periastron shift during each orbital cycle. A retrograde
Rosetta_orbit
Space navigation technique
gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement (e.g. orbit around the Sun) and gravity
Gravity_assist
In astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum. Two objects in a radial trajectory move directly
Radial_trajectory
Specifies the orbit of an object in space
argument of pericenter), symbolized as ω (omega), is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the body's ascending
Argument_of_periapsis
Elliptical orbit used to move a spacecraft from one circular orbit to another
In orbital mechanics, a transfer orbit is an intermediate elliptical orbit that is used to move a spacecraft in an orbital maneuver from one circular
Transfer_orbit
Spaceflight operation
In spaceflight an orbit insertion is an orbital maneuver which adjusts a spacecraft’s trajectory, allowing entry into an orbit around a planet, moon, or
Orbit_insertion
Celestial orbit whose trajectory is a conic section in the orbital plane
In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) is the motion of one body relative to another
Kepler_orbit
Orbital mechanics term
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force. It was derived by Johannes
Kepler's_equation
Astronomy with terahertz (< 1 mm)-range light
infrared and submillimetre wavebands. Rather than an Earth orbit, Herschel entered into a Lissajous orbit around L2, the second Lagrangian point of the Earth-Sun
Submillimetre_astronomy
Measure of the efficiency of a rocket based on its propellant's mass
Perturbations Sphere of influence N-body orbits Lagrangian points (Halo orbits) Lissajous orbits Lyapunov orbits Engineering and efficiency Preflight engineering
Rocket_mass_ratio
Parameter in the gravitational two-body problem
two-body problem, the specific orbital energy ε {\displaystyle \varepsilon } (or specific vis-viva energy) of two orbiting bodies is the constant quotient
Specific_orbital_energy
Specifies the orbit of an object in space
the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which
Mean_anomaly
Type of orbit around an astronomical body
near-equatorial orbit is an orbit that lies close to the equatorial plane of the primary body orbited. Such an orbit has an inclination near 0°. Such orbits lie near
Near-equatorial_orbit
Range of low orbital altitudes
Very low Earth orbit (VLEO) is a range of geocentric orbits with lowest altitudes (at perigee) below 400 km (250 mi). It is of increasing commercial importance
Very_low_Earth_orbit
European Space Agency space weather mission
opportunity arose: ISRO had plans to start a new solar observatory in low earth orbit. ESA convinced ISRO to expand the mission to a larger satellite bus, more
Vigil_(space_mission)
Chinese lunar communications satellite
types of orbits near the equilibrium points, include Lyapunov orbits, halo orbits, Lissajous orbits, and quasi-halo orbits. Lyapunov orbits pass behind
Queqiao-1
Spacecraft end-of-life orbit
graveyard orbit, also called a junk orbit or disposal orbit, is an orbit that lies away from common operational orbits. One significant graveyard orbit is a
Graveyard_orbit
Type of orbital maneuver
aerospace engineering, the bi-elliptic transfer is an orbital maneuver that moves a spacecraft from one orbit to another and may, in certain situations, require
Bi-elliptic_transfer
Transfer orbit used to reach geosynchronous or geostationary orbit
transfer orbit (GTO) or geosynchronous transfer orbit is a highly elliptical type of geocentric orbit, usually with a perigee as low as low Earth orbit (LEO)
Geostationary_transfer_orbit
Solar system exploration program by NASA
board the European Space Agency's Mars Express orbiter. Launched on 2 June 2003, it has been orbiting Mars since 30 December 2003. The Principal Investigator
Discovery_Program
Region of space gravitationally dominated by a given body
particular celestial body exerts the main gravitational influence on an orbiting object. As such it is the dominating part of a gravitational field. It
Sphere of influence (astrodynamics)
Sphere_of_influence_(astrodynamics)
Region in which an astronomical body dominates the attraction of satellites
planet by a star, a moon by a planet—the less massive body must have an orbit that lies within the gravitational potential represented by the more massive
Hill_sphere
Spaceflight where spacecraft orbits an astronomical body
An orbital spaceflight (or orbital flight) is a spaceflight in which a spacecraft is placed on a trajectory where it could remain in space for at least
Orbital_spaceflight
Orbit around Earth
A geocentric orbit, Earth-centered orbit, or Earth orbit involves any object orbiting Earth, such as the Moon or artificial satellites. In 1997, NASA estimated
Geocentric_orbit
Branch of astronomy
produce ephemeris data. The computation of the motion of the bodies through orbital mechanics can be simplified by using an appropriate inertial frame of reference
Celestial_mechanics
Astrodynamic equation
In astrodynamics, an orbit equation defines the path of orbiting body m 2 {\displaystyle m_{2}\,\!} around central body m 1 {\displaystyle m_{1}\,\!}
Orbit_equation
Concept in astrodynamics
astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit (from Newtonian theory: hyperbola shape) is the trajectory of any object
Hyperbolic_trajectory
Motion problem in classical mechanics
used to calculate and predict the motion of two massive bodies that are orbiting each other in space. The problem assumes that the two bodies are perfect
Two-body_problem
Type of gravitational orbit seen in triaxial systems
(3): 1177–1189, arXiv:astro-ph/9903452, Bibcode:1999AJ....118.1177M, doi:10.1086/301012, S2CID 14621588 Horseshoe orbit Lissajous curve List of orbits
Box_orbit
NASA heliophysics mission
on-board propulsion to insert into an +/−9.5° ×+/-3.9° Lissajous orbit around L1, very similar to the orbit of Advanced Composition Explorer (ACE). The baseline
Interstellar Mapping and Acceleration Probe
Interstellar_Mapping_and_Acceleration_Probe
Geocentric orbit with an altitude entirely above that of a geosynchronous orbit
A high Earth orbit is a geocentric orbit with an apogee farther than that of the geosynchronous orbit, which is 35,786 km (22,236 mi) away from Earth.
High_Earth_orbit
Satellite orbit with high inclination
A polar orbit is one in which a satellite passes above or nearly above both poles of the body being orbited (usually a planet such as the Earth, but possibly
Polar_orbit
Concept in celestial mechanics
The central body in an orbital system can be defined as the one whose mass (M) is much larger than the mass of the orbiting body (m), or M ≫ m. This
Standard gravitational parameter
Standard_gravitational_parameter
Measure of aircraft/spacecraft efficiency
considerably higher useful load fractions, on the order of 45–55%. For orbital rockets the payload fraction is between 1% and 5%, while the useful load
Payload_fraction
LISSAJOUS ORBIT
LISSAJOUS ORBIT
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Circumference of the Orbit; Limit; Realm
Boy/Male
Indian
Orbit, Eye socket, Argument
Boy/Male
Muslim
Orbit, Eye socket, Argument
Boy/Male
Arabic, Hindu, Indian, Muslim, Sindhi
One who Argues a Lot; Orbit; Eye Socket; Orgument; Debate
Boy/Male
Muslim/Islamic
Orbit eye socket, Orgument, debate
LISSAJOUS ORBIT
LISSAJOUS ORBIT
LISSAJOUS ORBIT
LISSAJOUS ORBIT
LISSAJOUS ORBIT
LISSAJOUS ORBIT
LISSAJOUS ORBIT