Lissajous orbit

Last updated
Animation of WMAP 's trajectory
Animation of Wilkinson Microwave Anisotropy Probe trajectory.gif
Oblique view
Animation of Wilkinson Microwave Anisotropy Probe trajectory - Viewd from Earth.gif
Viewed from Earth
   Earth ·   WMAP

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.

Contents

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 planets. [4]

Spacecraft using Lissajous orbits

Several missions have used Lissajous orbits: ACE at Sun–Earth L1, [5] SOHO at Sun–Earth L1, DSCOVR at Sun–Earth L1, [6] WMAP at Sun–Earth L2, [7] and also the Genesis mission collecting solar particles at L1. [8] On 14 May 2009, the European Space Agency (ESA) launched into space the Herschel and Planck observatories, both of which use Lissajous orbits at Sun–Earth L2. [9] ESA's current Gaia mission also uses a Lissajous orbit at Sun–Earth L2. [10] In 2011, NASA transferred two of its THEMIS spacecraft from Earth orbit to Lunar orbit by way of Earth–Moon L1 and L2 Lissajous orbits. [11] In June 2018, Queqiao, the relay satellite for China's Chang'e 4 lunar lander mission, entered orbit around Earth-Moon L2. [12] [lower-alpha 1]

Fictional appearances

In the 2005 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 storm. The shield is described to have been in a Lissajous orbit at L1. In the story a group of wealthy and powerful people shelter opposite the shield at L2 so as to be protected from the solar storm by the shield, the Earth and the Moon.

In the 2017 science fiction novel Artemis by Andy Weir, a Lissajous orbit is used as a transfer point for routine travel to and from the moon.

Notes

  1. ↑ Possibly a halo orbit. Sources disagree.

See also

Related Research Articles

<span class="mw-page-title-main">Lagrange point</span> Equilibrium points near two orbiting bodies

In celestial mechanics, the Lagrange points are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of the restricted three-body problem.

<span class="mw-page-title-main">Trans-lunar injection</span> Propulsive maneuver used to arrive at the Moon

A trans-lunar injection (TLI) is a propulsive maneuver used to set a spacecraft on a trajectory that will cause it to arrive at the Moon.

<span class="mw-page-title-main">Interplanetary Transport Network</span> Low-energy trajectories in the Solar System

The Interplanetary Transport Network (ITN) is a collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations where trajectories through space can be redirected using little or no energy. These points have the peculiar property of allowing objects to orbit around them, despite lacking an object to orbit. While it would use little energy, transport along the network would take a long time.

<span class="mw-page-title-main">SMART-1</span> European Space Agency satellite that orbited around the Moon

SMART-1 was a Swedish-designed European Space Agency satellite that orbited around the Moon. It was launched on 27 September 2003 at 23:14 UTC from the Guiana Space Centre in Kourou, French Guiana. "SMART-1" stands for Small Missions for Advanced Research in Technology-1. On 3 September 2006, SMART-1 was deliberately crashed into the Moon's surface, ending its mission.

Delta-<i>v</i> budget

In astrodynamics and aerospace, a delta-v budget is an estimate of the total change in velocity (delta-v) required for a space mission. It is calculated as the sum of the delta-v required to perform each propulsive maneuver needed during the mission. As input to the Tsiolkovsky rocket equation, it determines how much propellant is required for a vehicle of given empty mass and propulsion system.

<span class="mw-page-title-main">Deep Space Climate Observatory</span> American solar research spacecraft

Deep Space Climate Observatory is a National Oceanic and Atmospheric Administration (NOAA) space weather, space climate, and Earth observation satellite. It was launched by SpaceX on a Falcon 9 v1.1 launch vehicle on 11 February 2015, from Cape Canaveral. This is NOAA's first operational deep space satellite and became its primary system of warning Earth in the event of solar magnetic storms.

In astrodynamics, orbital station-keeping is keeping a spacecraft at a fixed distance from another spacecraft or celestial body. It requires a series of orbital maneuvers made with thruster burns to keep the active craft in the same orbit as its target. For many low Earth orbit satellites, the effects of non-Keplerian forces, i.e. the deviations of the gravitational force of the Earth from that of a homogeneous sphere, gravitational forces from Sun/Moon, solar radiation pressure and air drag, must be counteracted.

<span class="mw-page-title-main">Far side of the Moon</span> Hemisphere of the Moon that always faces away from Earth

The far side of the Moon is the lunar hemisphere that always faces away from Earth, opposite to the near side, because of synchronous rotation in the Moon's orbit. Compared to the near side, the far side's terrain is rugged, with a multitude of impact craters and relatively few flat and dark lunar maria ("seas"), giving it an appearance closer to other barren places in the Solar System such as Mercury and Callisto. It has one of the largest craters in the Solar System, the South Pole–Aitken basin. The hemisphere is sometimes called the "dark side of the Moon", where "dark" means "unknown" instead of "lacking sunlight" – each side of the Moon experiences two weeks of sunlight while the opposite side experiences two weeks of night.

<span class="mw-page-title-main">THEMIS</span> NASA satellite of the Explorer program

Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission began in February 2007 as a constellation of five NASA satellites to study energy releases from Earth's magnetosphere known as substorms, magnetic phenomena that intensify auroras near Earth's poles. The name of the mission is an acronym alluding to the Titan Themis.

<span class="mw-page-title-main">Low-energy transfer</span> Fuel-efficient orbital maneuver

A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional transfers. These routes work in the Earth–Moon system and also in other systems, such as between the moons of Jupiter. The drawback of such trajectories is that they take longer to complete than higher-energy (more-fuel) transfers, such as Hohmann transfer orbits.

<span class="mw-page-title-main">Halo orbit</span> Periodic, three-dimensional orbit

A halo orbit is a periodic, three-dimensional orbit near one of the L1, L2 or L3 Lagrange points in the three-body problem 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 or a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and the Coriolis and centrifugal force on a spacecraft. Halo orbits exist in any three-body system, e.g., a Sun–Earth–orbiting satellite system or an Earth–Moon–orbiting satellite system. Continuous "families" of both northern and southern halo orbits exist at each Lagrange point. Because halo orbits tend to be unstable, stationkeeping may be required to keep a satellite on the orbit.

A distant retrograde orbit (DRO), as most commonly conceived, is a spacecraft orbit around a moon that is highly stable because of its interactions with two Lagrange points (L1 and L2) of the planet–moon system.

EQUULEUS is a nanosatellite of the 6U CubeSat format that will measure the distribution of plasma that surrounds the Earth (plasmasphere) to help scientists understand the radiation environment in that region. It will also demonstrate low-thrust trajectory control techniques, such as multiple lunar flybys, within the Earth-Moon region using water steam as propellant. The spacecraft was designed and developed jointly by the Japan Aerospace Exploration Agency (JAXA) and the University of Tokyo.

The Comet Interceptor is a robotic spacecraft mission led by the European Space Agency (ESA) planned for launch in 2029. The spacecraft will be "parked" at the Sun-Earth L2 point and wait for up to three years for a long-period comet to fly by at a reachable trajectory and speed.

<span class="mw-page-title-main">CAPSTONE</span> NASA satellite to test the Lunar Gateway orbit

CAPSTONE is a lunar orbiter that will test and verify the calculated orbital stability planned for the Lunar Gateway space station. The spacecraft is a 12-unit CubeSat that will also test a navigation system that will measure its position relative to NASA's Lunar Reconnaissance Orbiter (LRO) without relying on ground stations. It was launched on 28 June 2022, arrived in lunar orbit on 14 November 2022, and is scheduled to orbit for six months.

<span class="mw-page-title-main">Queqiao relay satellite</span> Chinese satellite

Queqiao relay satellite (Chinese: 鹊桥号中继卫星; pinyin: Quèqiáo hào zhōngjì wèixīng; lit. 'Magpie Bridge relay satellite'), also known as the Chang'e 4 Relay, is a communications relay and radio astronomy satellite for the Chang'e 4 lunar farside mission. As part of the Chinese Lunar Exploration Program, the China National Space Administration (CNSA) launched the Queqiao relay satellite on 20 May 2018 to a halo orbit around the Earth–Moon L2 Lagrangian point Queqiao is the first ever communication relay and radio astronomy satellite at this location.

References

  1. ↑ "ESA Science & Technology: Orbit/Navigation". European Space Agency. 14 June 2009. Retrieved 2009-06-12.
  2. ↑ "A230242 - Decimal expansion of (25+3*sqrt(69))/2". OEIS . Retrieved 7 January 2019.
  3. ↑ Vallado, David A. (2007). Fundamentals of Astrodynamics and Applications (3rd ed.). Springer New York. ISBN   978-1-881883-14-2. (paperback), (hardback).
  4. ↑ 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.
  5. ↑ Advanced Composition Explorer (ACE) Mission Overview, Caltech, retrieved 2014-09-06.
  6. ↑ SpaceX Falcon 9 successfully launches the DSCOVR spacecraft, NASA, retrieved 2015-08-05.
  7. ↑ WMAP Trajectory and Orbit, NASA, retrieved 2014-09-06.
  8. ↑ Genesis: Lissajous Orbit Insertion, NASA, retrieved 2014-09-06.
  9. ↑ "Herschel: Orbit/Navigation". ESA . Retrieved 2006-05-15.
  10. ↑ "Gaia's Lissajous Type Orbit". ESA. Archived from the original on 2017-03-18. Retrieved 2006-05-15.
  11. ↑ ARTEMIS: The First Mission to the Lunar Libration Orbits
  12. ↑ Jones, Andrew (14 June 2018). "Chang'e-4 relay satellite enters halo orbit around Earth-Moon L2, microsatellite in lunar orbit". SpaceNews. Retrieved 6 January 2019.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.