A contour plot of the effective potential (the Hill's Surfaces) of a two-body system (the Sun and Earth here), showing the five Lagrange points. The arrows indicate the slopes around the L points – downhill toward or away from them. Counterintuitively, the L₄ and L₅ points are maxima.

The Lagrangian points (pronounced [ləˈgɹɒn.dʒi.ən] or [laˈgʀɑ̃.ʒjɑ̃]); also Lagrange point, L-point, or libration point), are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the Earth and Moon). The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to rotate with them. They are analogous to geosynchronous orbits in that they allow an object to be in a "fixed" position in space rather than an orbit in which its relative position changes continuously. Image File history File links Lagrange_points. ... Image File history File links Lagrange_points. ... It has been suggested that this article or section be merged with Scalar potential. ... “Sol” redirects here. ... This article is about Earth as a planet. ... The largest and the smallest element of a set are called extreme values, or extreme records. ... The animation shows a set of simulated views of the Moon over one month. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... Gravity is a force of attraction that acts between bodies that have mass. ... An Earth observation satellite, ERS 2 For other uses, see Satellite (disambiguation). ... This article is about Earth as a planet. ... Apparent magnitude: up to -12. ... A centripetal force is a force pulling an object toward the center of a circular path as the object goes around the circle. ... It has been suggested that this article or section be merged with geostationary orbit. ...

A more precise but technical definition is that the Lagrangian points are the stationary solutions of the circular restricted three-body problem. For example, given two massive bodies in circular orbits around their common center of mass, there are five positions in space where a third body, of comparatively negligible mass, could be placed which would then maintain its position relative to the two massive bodies. As seen in a rotating reference frame with the same period as the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the centrifugal force are in balance at the Lagrangian points, allowing the third body to be stationary with respect to the first two bodies. This article is about the n-body problem in classical mechanics. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it were concentrated. ... This article or section is in need of attention from an expert on the subject. ... A rotating frame of reference is a coordinate system that describes how physics appears when measured against a hypothetical network of rigid rulers extending from a rotating body. ... The gravitational field is a field (physics), generated by massive objects, that determines the magnitude and direction of gravitation experienced by other massive objects. ... Centrifugal force (from Latin centrum center and fugere to flee) is a term which may refer to two different forces which are related to rotation. ...

History and concepts

In 1772, the Italian-French mathematician Joseph-Louis Lagrange was working on the famous three-body problem when he discovered an interesting quirk in the results. Originally, he had set out to discover a way to easily calculate the gravitational interaction between arbitrary numbers of bodies in a system, because Newtonian mechanics conclude that such a system results in the bodies orbiting chaotically until there is a collision, or a body is thrown out of the system so that equilibrium can be achieved. The logic behind this conclusion is that a system with one body is trivial, as it is merely static relative to itself; a system with two bodies is very simple to solve for, as the bodies orbit around their common center of gravity. However, once more than two bodies are introduced, the mathematical calculations become very complicated. A situation arises where you would have to calculate every gravitational interaction between every pair of objects at every point along its trajectory. Year 1772 was a leap year starting on Wednesday (see link for calendar). ... Joseph Louis Lagrange (January 25, 1736 – April 10, 1813) was an Italian mathematician and astronomer who later lived in France and Prussia. ... The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i. ... It has been suggested that this article or section be merged with Classical mechanics. ... A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under specific conditions exhibit dynamics that are sensitive to initial conditions (popularly referred to as the butterfly effect). ... A standard definition of mechanical equilibrium is: A system is in mechanical equilibrium when the sum of the forces, and torque, on each particle of the system is zero. ...

Lagrange, however, wanted to make this simpler. He did so with a simple hypothesis: The trajectory of an object is determined by finding a path that minimizes the action over time. This is found by subtracting the potential energy from the kinetic energy. With this way of thinking, Lagrange re-formulated the classical Newtonian mechanics to give rise to Lagrangian mechanics. With his new system of calculations, Lagrange’s work led him to hypothesize how a third body of negligible mass would orbit around two larger bodies which were already in a near-circular orbit. In a frame of reference that rotates with the larger bodies, he found five specific fixed points where the third body experiences zero net force as it follows the circular orbit of its host bodies (planets).^[1] These points were named “Lagrangian points” in Lagrange's honor. It took over a hundred years before his mathematical theory was observed with the discovery of the Trojan asteroids in the 1900s at the Lagrange points of the Sun–Jupiter system. In physics, the action is an integral quantity that is used to determine the evolution of a physical system between two defined states using the calculus of variations. ... Potential energy is the energy available within a physical system due to an objects position in conjunction with a conservative force which acts upon it (such as the gravitational force or Coulomb force). ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Lagrangian mechanics is a re-formulation of classical mechanics introduced by Joseph Louis Lagrange in 1788. ... Look up Hypothesis in Wiktionary, the free dictionary. ... As originally defined, Trojan asteroids have a semi-major axis between 5. ...

In the more general case of elliptical orbits, there are no longer stationary points in the same sense: it becomes more of a Lagrangian “area”. The Lagrangian points constructed at each point in time, as in the circular case, form stationary elliptical orbits which are similar to the orbits of the massive bodies. This is due to Newton's second law (), where p = mv (p the momentum, m the mass, and v the velocity) is invariant if force and position are scaled by the same factor. A body at a Lagrangian point orbits with the same period as the two massive bodies in the circular case, implying that it has the same ratio of gravitational force to radial distance as they do. This fact is independent of the circularity of the orbits, and it implies that the elliptical orbits traced by the Lagrangian points are solutions of the equation of motion of the third body. Elliptical may refer to: Ellipse: a shape and mathematical construct Elliptical trainer: an exercise machine This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... Several equivalence relations in mathematics are called similarity. ... Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ... In classical mechanics, momentum (pl. ... In physics, invariants are usually quantities conserved (unchanged) by the symmetries of the physical system. ... It has been suggested that SUVAT equations be merged into this article or section. ...

The Lagrangian points

A diagram showing the five Lagrangian points in a two-body system with one body far more massive than the other (e.g. the Sun and the Earth). In such a system, L₃–L₅ will appear to share the secondary's orbit, although in fact they are situated slightly outside it.

The five Lagrangian points are labeled and defined as follows: Image File history File links Lagrange_very_massive. ... Image File history File links Lagrange_very_massive. ...

L₁

The L₁ point lies on the line defined by the two large masses M₁ and M₂, and between them. It is the most intuitively understood of the Lagrangian points: the one where the gravitational attractions of the two other objects effectively cancel each other out.

Example: An object which orbits the Sun more closely than the Earth would normally have a shorter orbital period than the Earth, but that ignores the effect of the Earth's own gravitational pull. If the object is directly between the Earth and the Sun, then the effect of the Earth's gravity is to weaken the force pulling the object towards the Sun, and therefore increase the orbital period of the object. The closer to Earth the object is, the greater this effect is. At the L₁ point, the orbital period of the object becomes exactly equal to the Earth's orbital period.

The Sun–Earth L₁ is ideal for making observations of the Sun. Objects here are never shadowed by the Earth or the Moon. The Solar and Heliospheric Observatory (SOHO) is stationed in a Halo orbit at L₁, and the Advanced Composition Explorer (ACE) is in a Lissajous orbit, also at the L₁ point. The Earth–Moon L₁ allows easy access to lunar and earth orbits with minimal change in velocity, and would be ideal for a half-way manned space station intended to help transport cargo and personnel to the Moon and back. Two bodies with a slight difference in mass orbiting around a common barycenter. ... “Sol” redirects here. ... This article is about Earth as a planet. ... The Solar and Heliospheric Observatory (SOHO) is a spacecraft that was launched on an Atlas IIAS launch vehicle on 2 December 1995 to study the Sun, and began normal operations in May 1996. ... A halo orbit is an orbit around a Lagrange point between two larger bodies. ... Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition... In orbital mechanics, a Lissajous orbit is a quasi-periodic orbital trajectory an object can follow around a colinear libration point of a two-body system without requiring any propulsion. ...

L₂

A diagram showing the Sun–Earth L₂ point, which lies well beyond the Moon's orbit around the Earth.

The L₂ point lies on the line defined by the two large masses, beyond the smaller of the two. Here, the gravitational forces of the two large masses balance the centrifugal force on the smaller mass. Image File history File links Size of this preview: 719 × 600 pixelsFull resolution (2763 × 2305 pixel, file size: 381 KB, MIME type: image/jpeg) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Size of this preview: 719 × 600 pixelsFull resolution (2763 × 2305 pixel, file size: 381 KB, MIME type: image/jpeg) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

Example: On the side of the Earth away from the Sun, the orbital period of an object would normally be greater than that of the Earth. The extra pull of the Earth's gravity decreases the orbital period of the object, and at the L₂ point that orbital period becomes equal to the Earth's.

The Sun–Earth L₂ is a good spot for space-based observatories. Because an object around L₂ will maintain the same orientation with respect to the Sun and Earth, shielding and calibration are much simpler. The Wilkinson Microwave Anisotropy Probe is already in orbit around the Sun–Earth L₂. The future Herschel Space Observatory, Gaia probe, and James Webb Space Telescope will be placed at the Sun–Earth L₂. Earth–Moon L₂ would be a good location for a communications satellite covering the Moon's far side. Artist depiction of the WMAP satellite at the L2 point The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA satellite whose mission is to survey the sky to measure the temperature of the radiant heat left over from the Big Bang. ... The Herschel Space Observatory is a mission of the European Space Agency. ... Gaia is an astrometry space mission, and a successor to the ESA Hipparcos mission. ... The James Webb Space Telescope (JWST) is a planned space infrared observatory, intended to be a significant improvement on the aging Hubble Space Telescope. ... U.S. military MILSTAR communications satellite A communications satellite (sometimes abbreviated to comsat) is an artificial satellite stationed in space for the purposes of telecommunications. ...

If the mass of the smaller object (M₂) is much smaller than the mass of the larger object (M₁) then L₁ and L₂ are at approximately equal distances r from the smaller object, equal to the radius of the Hill sphere, given by: A Hill sphere approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from another heavier body around which it orbits. ...

where R is the distance between the two bodies.

This distance can be described as being such that the orbital period, corresponding to a circular orbit with this distance as radius around M₂ in the absence of M₁, is that of M₂ around M₁, divided by . The orbital period is the time it takes a planet (or another object) to make one full orbit. ...

Examples:

• Sun and Earth: 1,500,000 km from the Earth
• Earth and Moon: 61,500 km from the Moon

“Sol” redirects here. ... This article is about Earth as a planet. ... Apparent magnitude: up to -12. ...

L₃

The L₃ point lies on the line defined by the two large masses, beyond the larger of the two.

Example: L₃ in the Sun–Earth system exists on the opposite side of the Sun, a little outside the Earth's orbit but slightly closer to the Sun than the Earth is.^[2] Here, the combined pull of the Earth and Sun again causes the object to orbit with the same period as the Earth. The Sun–Earth L₃ point was a popular place to put a "Counter-Earth" in pulp science fiction and comic books – though of course, once space based observation was possible via satellites and probes, it was shown to hold no such object. In actual fact, Sun–Earth L₃ is highly unstable, because the gravitational forces of the other planets outweigh that of the Earth (Venus, for example, comes within 0.3 AU of L₃ every 20 months).

Counter-Earth is an Earth-like hypothetical planet, usually sharing an orbit with Earth but on the opposite side of the Sun. ... Science fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals. ... A comic book is a magazine or book containing the art form of comics. ... Adjectives: Venusian or (rarely) Cytherean Atmosphere Surface pressure: 9. ... The astronomical unit (AU or au or a. ...

L₄ and L₅

Gravitational accelerations at L₄.

The L₄ and L₅ points lie at the third corners of the two equilateral triangles in the plane of orbit whose common base is the line between the centres of the two masses, such that the point lies behind (L₅) or ahead of (L₄) the smaller mass with regard to its orbit around the larger mass. Image File history File links L4_diagram. ... Image File history File links L4_diagram. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...

The reason these points are in balance is that, at L₄ and L₅, the distances to the two masses are equal. Accordingly, the gravitational forces from the two massive bodies are in the same ratio as the masses of the two bodies, and so the resultant force acts through the barycentre of the system; additionally, the geometry of the triangle ensures that the resultant acceleration is to the distance from the barycentre in the same ratio as for the two massive bodies. The barycentre being both the centre of mass and centre of rotation of the system, this resultant force is exactly that required to keep a body at the Lagrange point in orbital equilibrium with the rest of the system. (Indeed, the third body need not have negligible mass; the general triangular configuration was discovered by Lagrange in work on the 3-body problem.) The barycenter (from the Greek βαρύκεντρον) is the center of mass of two or more bodies which are orbiting each other, and is the point around which both of them orbit. ... For the technique in organ building, see Resultant (organ). ... A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another. ... The center of mass or center of inertia of an object is a point at which the objects mass can be assumed, for many purposes, to be concentrated. ... A dynamic equilibrium occurs when two reversible processes occur at the same rate. ... The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i. ...

L₄ and L₅ are sometimes called triangular Lagrange points or Trojan points. The name Trojan points comes from the Trojan asteroids at the Sun–Jupiter L₄ and L₅ points, which themselves are named after characters from Homer's Iliad (the legendary siege of Troy). Asteroids at the L₄ point, which leads Jupiter, are referred to as the 'Greek camp', while at the L₅ point they are referred to as the 'Trojan camp'. These asteroids are (largely) named after characters from the respective sides of the war. As originally defined, Trojan asteroids have a semi-major axis between 5. ... Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... Homer (Greek: , ) was an early Greek poet and aoidos (rhapsode) traditionally credited with the composition of the Iliad and the Odyssey. ... title page of the Rihel edition of ca. ... Troy or Ilion, see Troy (disambiguation) and Ilion (disambiguation). ... This is a list of Trojan asteroids - asteroids that lie in elongated, curved regions around the two Lagrangian points 60° ahead and behind of Jupiter. ... This is a list of Trojan asteroids - asteroids that lie in elongated, curved regions around the two Lagrangian points 60° ahead and behind of Jupiter. ...

Examples:

• The Sun–Earth L₄ and L₅ points lie 60° ahead of and 60° behind the Earth as it orbits the Sun. They contain interplanetary dust.
• The Earth–Moon L₄ and L₅ points lie 60° ahead of and 60° behind the Moon as it orbits the Earth. They also contain interplanetary dust in what is called Kordylewski cloud.
• The Sun–Jupiter L₄ and L₅ points are occupied by the Trojan asteroids.
• Neptune has Trojan Kuiper Belt Objects at its L₄ and L₅ points.
• Saturn's moon Tethys has two much smaller satellites at its L₄ and L₅ points named Telesto and Calypso, respectively.
• Saturn's moon Dione has smaller moons Helene and Polydeuces at its L₄ and L₅ points, respectively.
• The giant impact hypothesis suggests that an object named Theia formed at L₄ or L₅ and crashed into the Earth after its orbit destabilized, forming the moon.

Kordylewski clouds are large concentrations of dust that may exist at the L4 and L5 Lagrangian points of the Earth-Moon system. ... Image of the Trojan asteroids in front of and behind Jupiter along its orbital path. ... NEPTUNE is an acronym for North-East Pacific Time-series Undersea Networked Experiments. ... The Kuiper belt (KYE per) is an area of the solar system extending from within the orbit of Neptune (at 30 AU) to 50 AU from the sun, at inclinations consistent with the ecliptic. ... Adjectives: Saturnian Atmosphere Surface pressure: 140 kPa Composition: >93% hydrogen >5% helium 0. ... Atmosphere none Tethys (tee-thəs or teth-əs, IPA , Greek Τηθύς) is a moon of Saturn that was discovered by Giovanni Domenico Cassini in 1684. ... Atmosphere none Telesto IPA: , Greek Τελεστώ) is a moon of Saturn. ... Atmosphere none Calypso (ka-lip-soe, Greek Καλυψώ) is a moon of Saturn. ... Atmosphere none Dione (dye-oe-nee, Greek Διώνη) is a moon of Saturn discovered by Giovanni Cassini in 1684. ... Helene (hel-e-nee, Greek ‘Ελένη) is a moon of Saturn. ... Saturns moon Polydeuces Atmosphere none Polydeuces (pol-ee-dew-seez, IPA: , Greek Πολυδεύκης) is a very small natural satellite of Saturn that is co-orbital with Dione and librates around the trailing Lagrangian point (L5). ... The Big Splash. ... Theia (THAY-uh) is the hypothetical planet that, according to the giant impact theory of the Moons formation, collided with Earth over four billion years ago. ...

Stability

The first three Lagrangian points are technically stable only in the plane perpendicular to the line between the two bodies. This can be seen most easily by considering the L₁ point. A test mass displaced perpendicularly from the central line would feel a force pulling it back towards the equilibrium point. This is because the lateral components of the two masses' gravity would add to produce this force, whereas the components along the axis between them would balance out. However, if an object located at the L₁ point drifted closer to one of the masses, the gravitational attraction it felt from that mass would be greater, and it would be pulled closer. (The pattern is very similar to that of tidal forces.) Fig. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ...

Although the L₁, L₂, and L₃ points are nominally unstable, it turns out that it is possible to find stable periodic orbits around these points, at least in the restricted three-body problem. These perfectly periodic orbits, referred to as "halo" orbits, do not exist in a full n-body dynamical system such as the solar system. However, quasi-periodic (i.e. bounded but not precisely repeating) orbits following Lissajous curve trajectories do exist in the n-body system. These quasi-periodic Lissajous orbits are what all Lagrangian point missions to date have used. Although they are not perfectly stable, a relatively modest effort at station keeping can allow a spacecraft to stay in a desired Lissajous orbit for an extended period of time. It also turns out that, at least in the case of Sun–Earth L₁ missions, it is actually preferable to place the spacecraft in a large amplitude (100,000–200,000 km) Lissajous orbit, instead of having it sit at the Lagrangian point, because this keeps the spacecraft off the direct Sun–Earth line, thereby reducing the impact of solar interference on the Earth–spacecraft communications links. Another interesting and useful property of the collinear Lagrangian points and their associated Lissajous orbits is that they serve as "gateways" to control the chaotic trajectories of the Interplanetary Transport Network. Major features of the Solar System (not to scale; from left to right): Pluto, Neptune, Uranus, Saturn, Jupiter, the asteroid belt, the Sun, Mercury, Venus, Earth and its Moon, and Mars. ... Lissajous figure on an oscilloscope- the shape of the ABC logo Lissajous figure in three dimensions In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion. ... In orbital mechanics, a Lissajous orbit is a quasi-periodic orbital trajectory an object can follow around a colinear libration point of a two-body system without requiring any propulsion. ... In astrodynamics orbital stationkeeping is a term used to describe a particular set of orbital maneuvers used to keep a spacecraft in assigned orbit, either low earth orbit (LEO), or geostationary orbit (GEO). ... Artists concept of the Interplanetary Transport Network. ...

In contrast to the collinear Lagrangian points, the triangular points (L₄ and L₅) are stable equilibria (cf. attractor), provided that the ratio of M₁/M₂ is greater than 24.96^[3][4]. This is the case for the Sun–Earth and, by a smaller margin, the Earth–Moon systems. When a body at these points is perturbed, it moves away from the point, but the Coriolis effect bends the object's path into a stable, kidney bean‐shaped orbit around the point (as seen in the rotating frame of reference). However, in the Earth–Moon case, the problem of stability is greatly complicated by the appreciable solar gravitational influence.^[5] In dynamical systems, an attractor is a set to which the system evolves after a long enough time. ... In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. ... Dry kidney beans The kidney bean is a medium-sized variety of the common bean (Phaseolus vulgaris) with dark red skin. ...

Intuitive explanation

This section non-mathematically (intuitively^[6]) explains the five Lagrangian points using the Earth–Moon system.

Lagrangian points L₂ through L₅ only exist in rotating systems, as in the monthly orbiting of the Moon about the Earth. At these points, an outward (fictitious, as explained below) centrifugal force is balanced by the two radially attractive gravitational forces of the Moon and Earth. The expression centrifugal force is used to express that if an object is being swung around on a string the object seems to be pulling on the string. ...

Imagine using your hand to spin a weight at the end of a string. Your hand will feel an outward radial force in the direction of the weight. However, if you release the string, the weight does not travel radially outward in the direction of the sensed force. Instead, the weight travels tangent to the circle, in the direction of spin at the time the string was released. This is why this force is called "fictitious". This same outward force is present in the Earth–Moon system, where the role of the string is played by the summed (or net) effect of the two attractive gravities, and the weight is an asteroid or science satellite. The Earth–Moon system rotates about a barycenter. Because the Earth is much heavier, this barycenter is located about a thousand miles below the Earth's surface, in the direction of the Moon (three thousand miles above the Earth's center, see Earth, Moon, and barycenter). Any object gravitationally held by the rotating Earth–Moon system will sense this (fictitious but calculably real) outward radial force away from the barycenter, in the same way your hand feels the outward pull of the string. In mathematics, the word tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry. ... Circle illustration This article is about the shape and mathematical concept of circle. ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it was concentrated. ... This article is about Earth as a planet. ... Apparent magnitude: up to -12. ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it was concentrated. ...

Unlike the other Lagrangian points, L₁ would exist even in a non-rotating (static or inertial) system. Rotation slightly pushes L₁ away from the (heavier) Earth towards the (lighter) Moon. L₁ is slightly unstable (see stability above) because drifting towards the Moon or Earth increases one gravitational attraction while decreasing the other, causing more drift. In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...

At Lagrangian points L₂, L₃, L₄, and L₅, a satellite feels an outward centrifugal force, away from the barycenter, that exactly balances the attractive gravity of the Earth and Moon. L₂ and L₃ are slightly unstable because small changes in satellite position more strongly affect gravity than the balancing centrifugal force. Stability at L₄ and L₅ depends crucially on the satellite being pulled in three different directions, namely the outward centrifugal force away from the barycenter, balancing the inward gravitational forces towards the Earth and Moon.

Lagrangian point missions

The Lagrangian point orbits have unique characteristics that have made them a good choice for performing some kinds of missions. NASA has operated a number of spacecraft in orbit around the Sun–Earth L₁ and L₂ points, including The National Aeronautics and Space Administration (NASA) is an agency of the United States federal government, responsible for the nations public space program. ...

The Planck satellite in 2008 and the James Webb Space Telescope are also planned to be placed in orbit around L₂. [1] Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition Explorer Advanced Composition... In its collecting configuration, the Genesis spacecraft exposed collecting wafers to the solar wind. ... The International Cometary Explorer (ICE) spacecraft was originally known as International Sun/Earth Explorer 3 (ISEE-3) satellite, launched August 12, 1978. ... The Solar and Heliospheric Observatory (SOHO) is a spacecraft that was launched on an Atlas IIAS launch vehicle on 2 December 1995 to study the Sun, and began normal operations in May 1996. ... Artist depiction of the WMAP satellite at the L2 point The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA satellite whose mission is to survey the sky to measure the temperature of the radiant heat left over from the Big Bang. ... WMAP image, unrelated to Planck The Planck Surveyor is the third Medium-Sized Mission (M3) of ESAs Horizon 2000 Scientific Programme. ... The James Webb Space Telescope (JWST) is a planned space infrared observatory, intended to be a significant improvement on the aging Hubble Space Telescope. ...

The L5 Society was a precursor of the National Space Society, and promoted the possibility of establishing a colony and manufacturing facility in orbit around the L₄ or L₅ points in the Earth–Moon system (see Space colonization). The original L5 Society logo, currently located at the L5 News archive on the World Wide Web The L5 Society was founded in 1975 by Carolyn and Keith Henson to promote the space colony ideas of Dr. Gerard K. ONeill. ... National Space Society logo The National Space Society (NSS) is an international nonprofit 501(c)(3), educational, and scientific organization specializing in space advocacy. ... Artists conception of a space habitat called the Stanford torus, by Don Davis Space colonization (also called space settlement, space humanization, space habitation, etc. ...

The Earth–Moon L₂ point has been proposed as a location for a communication satellite covering the far side of the Moon. NASA TN_D-4059

Natural examples

In the Sun–Jupiter system several thousand asteroids, collectively referred to as Trojan asteroids, are in orbits around the Sun–Jupiter L₄ and L₅ points. Other bodies can be found in the Sun–Saturn, Sun–Mars, Sun–Neptune, Jupiter–Jovian satellite, and Saturn–Saturnian satellite systems. There are no known large bodies in the Sun–Earth system's Trojan points, but clouds of dust surrounding the L₄ and L₅ points were discovered in the 1950s. Clouds of dust, called Kordylewski clouds, even fainter than the notoriously weak gegenschein, are also present in the L₄ and L₅ of the Earth–Moon system. Atmospheric characteristics Atmospheric pressure 70 kPa Hydrogen ~86% Helium ~14% Methane 0. ... 253 Mathilde, a C-type asteroid. ... Image of the Trojan asteroids in front of and behind Jupiter along its orbital path. ... Atmospheric characteristics Atmospheric pressure 140 kPa Hydrogen >93% Helium >5% Methane 0. ... Mars is the fourth planet from the Sun in the solar system, named after the Roman god of war (the counterpart of the Greek Ares), on account of its blood red color as viewed in the night sky. ... Atmospheric characteristics Surface pressure ≫100 MPa Hydrogen - H2 80% ±3. ... An Earth observation satellite, ERS 2 For other uses, see Satellite (disambiguation). ... This does not cite any references or sources. ... Kordylewski clouds are large concentrations of dust that may exist at the L4 and L5 Lagrangian points of the Earth-Moon system. ... Gegenschein (German for counterglow) is a faint brightening of the night sky in the region of the ecliptic directly opposite the Sun. ... Apparent magnitude: up to -12. ...

The Saturnian moon Tethys has two smaller moons in its L₄ and L₅ points, Telesto and Calypso. The Saturnian moon Dione also has two Lagrangian co-orbitals, Helene at its L₄ point and Polydeuces at L₅. The moons wander azimuthally about the Lagrangian points, with Polydeuces describing the largest deviations, moving up to 32 degrees away from the Saturn–Dione L₅ point. Tethys and Dione are hundreds of times more massive than their "escorts" (see the moons' articles for exact diameter figures; masses are not known in several cases), and Saturn is far more massive still, which makes the overall system stable. Atmosphere none Tethys (tee-thÉ™s or teth-É™s, IPA , Greek Τηθύς) is a moon of Saturn that was discovered by Giovanni Domenico Cassini in 1684. ... Atmosphere none Telesto IPA: , Greek Τελεστώ) is a moon of Saturn. ... Atmosphere none Calypso (ka-lip-soe, Greek Καλυψώ) is a moon of Saturn. ... Atmosphere none Dione (dye-oe-nee, Greek Διώνη) is a moon of Saturn discovered by Giovanni Cassini in 1684. ... Helene (hel-e-nee, Greek ‘Ελένη) is a moon of Saturn. ... Saturns moon Polydeuces Atmosphere none Polydeuces (pol-ee-dew-seez, IPA: , Greek Πολυδεύκης) is a very small natural satellite of Saturn that is co-orbital with Dione and librates around the trailing Lagrangian point (L5). ... Azimuth is the horizontal component of a direction (compass direction), measured around the horizon, from the north toward the east (i. ...

Other co-orbitals

The Earth's companion object 3753 Cruithne is in a relationship with the Earth which is somewhat Trojan-like, but different from a true Trojan. This asteroid occupies one of two regular solar orbits, one of them slightly smaller and faster than the Earth's orbit, and the other slightly larger and slower. The asteroid periodically alternates between these two orbits due to close encounters with Earth. When the asteroid is in the smaller, faster orbit and approaches the Earth, it loses orbital energy to the Earth and moves into the larger, slower orbit. It then falls farther and farther behind the Earth, and eventually Earth approaches it from the other direction. Then the asteroid gains orbital energy from the Earth, and the asteroid moves back into the smaller orbit, thus beginning the cycle anew. The cycle has no noticeable impact on the length of the year, because Earth's mass is over 20 billion (2 × 10¹⁰) times more than 3753 Cruithne. 3753 Cruithne (pronounced ) is an asteroid in orbit around the Sun. ... One thousand million (1,000,000,000) is the natural number following 999,999,999 and preceding 1,000,000,001. ...

Epimetheus and Janus, satellites of Saturn, have a similar relationship, though they are of similar masses and so actually exchange orbits with each other periodically. (Janus is roughly 4 times more massive, but still light enough for its orbit to be altered.) Another similar configuration is known as orbital resonance, in which orbiting bodies tend to have periods of a simple integer ratio, due to their interaction. Epimetheus (ep-i-mee-thee-us, Greek Επιμηθεύς) is a moon of Saturn. ... Janus (jay-nus, Greek Ιανός) is a moon of Saturn. ... In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other. ... A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another. ...

In fiction

The Lagrange points are mentioned in science fiction from time to time (most often hard science fiction), but, due to the general lack of public familiarity with them, they are rarely used as a plot device or reference. Science fiction is a form of speculative fiction principally dealing with the impact of imagined science and technology, or both, upon society and persons as individuals. ... Hard science fiction is a category of science fiction characterized by an emphasis on scientific or technical detail, or on scientific accuracy, or on both. ...

L5

• L5 is arguably the best known of the Lagrangian points.

• The L5 Lagrange point is mentioned in L5: First City in Space, an early IMAX 3D movie.

• In William Gibson's novel Neuromancer, much of the action takes place in the L5 "archipelago", the location of many space stations.

• The planet Troas in the stories "Sucker Bait" by Isaac Asimov and "Question and Answer" by Poul Anderson was located in the L₅ point of a fictional binary star system.

• The space station Babylon 5 is described to be located "at the L-5 point in a binary star system between a moon and a barren, lifeless planet." [2]

• In Hideo Kojima's video game Policenauts, the setting of the game, an O'Neill model space colony, is located at the L5 Lagrange point.

• The genetically engineered humans or "Coordinators" of Mobile Suit Gundam Seed settle in L5 living in hour glass shaped colonies known as PLANTs

IMAX theatre at the Melbourne Museum complex, Australia BFI London IMAX by night IMAX dome in Guayaquil, Ecuador IMAX (short for Image Maximum) is a film format created by Canadas IMAX Corporation that has the capacity to display images of far greater size and resolution than conventional film display... For the 1988 video game, see Neuromancer (video game). ... Troas is a fictional planet that serves as the setting for the science fiction novellas Sucker Bait by Isaac Asimov and Question and Answer by Poul Anderson as part of a proposed Twain Triplet. ... Sucker Bait is a science fiction novella by Isaac Asimov. ... Isaac Asimov (January 2?, 1920?[1] – April 6, 1992), IPA: , originally Исаак Озимов but now transcribed into Russian as Айзек Азимов) was a Russian-born American Jewish author and professor of biochemistry, a highly successful and exceptionally prolific writer best known for his works of science fiction and for his popular science books. ... Question and Answer is a science fiction novella by Poul Anderson that originally appeared in the June and July 1954 issues of Astounding Science Fiction. ... Poul William Anderson (November 25, 1926–July 31, 2001) was an American science fiction author of the genres Golden Age. ... Artists impression of a binary system consisting of a black hole, with an accretion disc around it, and a main sequence star. ... Babylon 5 is an epic American science fiction television series created, produced, and largely written by J. Michael Straczynski. ... Hideo Kojima , born August 24, 1963) is a Japanese video game designer at Konami. ... Policenauts ) is a Japanese adventure game written and directed by Hideo Kojima and developed and published by Konami. ... A pair of ONeill cylinders The ONeill cylinder is a space habitat design proposed by physicist Gerard K. ONeill in his book, The High Frontier. ... This article or section should be merged with Cosmic Era glossary In the Cosmic Era timeline of the fictional anime Gundam Seed, Coordinators are genetically-enhanced humans who inhabit space colonies called PLANTs. ... Mobile Suit Gundam SEED ), shortened to Gundam SEED, is an anime television series by Sunrise and Bandai Visual. ... Divisions Green algae Chlorophyta Charophyta Land plants (embryophytes) Non-vascular plants (bryophytes) Marchantiophyta—liverworts Anthocerotophyta—hornworts Bryophyta—mosses Vascular plants (tracheophytes) †Rhyniophyta—rhyniophytes †Zosterophyllophyta—zosterophylls Lycopodiophyta—clubmosses †Trimerophytophyta—trimerophytes Pteridophyta—ferns and horsetails Seed plants (spermatophytes) †Pteridospermatophyta—seed ferns Pinophyta—conifers Cycadophyta—cycads Ginkgophyta—ginkgo Gnetophyta—gnetae Magnoliophyta—flowering plants...

L4

• In Larry Niven's novels The Integral Trees and The Smoke Ring, the L4 and L5 points of the Smoke Ring (a ring of breathable air and plant life orbiting a neutron star) have become gathering places for masses of water, living things, and human settlers.

• The eponymous interplanetary relay station in George O. Smith's "Venus Equilateral" stories was located in the L₄ point of the Sun–Venus system.

Laurence van Cott Niven (born April 30, 1938 Los Angeles, California) is a US science fiction author. ... The Integral Trees is a 1984 science fiction novel by Larry Niven (first published as a serial in Analog in 1983). ... The Smoke Ring (ISBN 0345302575), published in 1987, is the sequel to the novel The Integral Trees by Larry Niven. ... A neutron star is one of the few possible endpoints of stellar evolution. ... Microwave radio relay is a technology for transmitting digital and analog signals, such as long distance telephone calls and the relay of television programs to transmitters, between two locations on a line of sight radio path. ... George Oliver Smith (April 9, 1911 - May 27, 1981) (also known as Wesley Long) was an American science fiction author. ... The Venus Equilateral series is a set of 13 science fiction short stories by George O. Smith, concerning the Venus Equilateral Relay Station, an interplanetary communications hub located at the L4 Lagrangian point of the Sun-Venus system. ...

L3

• In Peter F Hamilton's Night's Dawn Trilogy, a ZTT jump drive cannot be used in a strong gravitational field. In the first book of the trilogy, The Reality Dysfunction, the main characters cannot escape from a gas giant's gravity well before their pursuers catch up with them. Instead, they race to the Lagrange point between the gas giant and one of its moons in order to activate their drive. Successful execution of this untried and reckless maneuver gains captain Joshua Calvert the nickname "LaGrange" Calvert. In the second book The Neutronium Alchemist, a visit is paid to the supposed home planet of the Kiint, Jobis, which features three moons orbiting the Lagrange One point, rotating around a common centre.
• In the third season of the TV series Lexx, the planets Fire and Water are found to reside in Earth's L3 point.

• John Norman's Gor series takes place on a counter earth.

Peter F. Hamilton (born 1960, Rutland, England), is a British science fiction author. ... British author Peter F. Hamiltons The Nights Dawn Trilogy consists of three epic science fiction novels: The Reality Dysfunction (1996), The Neutronium Alchemist (1997), and The Naked God (1999). ... The Reality Dysfunction is a science fiction novel by Peter F. Hamilton; the first book in his The Nights Dawn Trilogy. ... The Neutronium Alchemist is a science fiction novel by Peter F. Hamilton and is the second book in The Nights Dawn Trilogy. ... Lexx is a science fantasy TV series that follows the adventures of a group of mismatched individuals aboard the Lexx, the most powerful destructive force in the two universes from which the show takes its name. ... In the sci-fi television series LEXX, the fictional planet Fire is the afterlife for all evil souls, and the location for much of Season 3. ... In the television series LEXX, the fictional planet Water is the afterlife for all good souls, and the location for much of Season 3. ... John Norman, pen name of John Frederick Lange, Jr. ... Gor, the Counter-Earth, is the alternate-world setting for John Normans Chronicles of Gor, a series of 26 novels that combine philosophy, erotica and science fiction. ...

L2

• See also: Lilith (hypothetical moon)

• In the TV series Quatermass II, the hostile aliens live on a small asteroid "no more than half a mile across" at a "theoretical point of equilibrium" on the dark side of the earth, although neither L2 or Lagrange are mentioned by name (the term "Bieber Variation" is used instead).

• In the Star Trek: The Next Generation episode, "The Survivors", the Enterprise is surprised by an enemy ship that had been hiding in a Lagrange point.

• In the manga series Battle Angel Alita: Last Order, the ex-colony ship turned space station Leviathan 1 is at the L2 point in the Earth/Moon system.

To meet Wikipedias quality standards, this article may require cleanup. ... The opening title sequence of Quatermass II. Quatermass II is a British television science-fiction serial, the second in the popular and influential Quatermass series written by Nigel Kneale. ... The title as it appeared in most episodes opening credits. ... The Survivors is a third season episode of Star Trek: The Next Generation first broadcast on October 9, 1989. ... The USS Enterprise (NCC-1701-D) (or Enterprise-D, to distinguish it from prior starships with the same name) is a 24th century starship in the Star Trek fictional universe and the principal setting of the Star Trek: The Next Generation television series. ...

L1

• In Arthur Clarke and Stephen Baxter's novel Sunstorm, the L1 point plays a crucial role in the building of a shield that has the purpose of saving Earth from a storm of energy from the Sun.

• In the Xbox video game Halo: Combat Evolved (2001) and sequel Halo 2 (2004), Halo Megastructures play key locations throughout the games. In Halo: CE and Halo 2, the Halo structures are in L1 Lagrange points between the Gas Giants (and a moon) Threshold and Substance, respectively.

• In the Hugo Award-winning novel A Deepness in the Sky by Vernor Vinge, a temporary human habitat is built at the L1 point between the planet Arachna and its primary star, a highly variable dwarf called the On/Off Star.

Arthur C. Clarke, considered by many to be a grand master of science fiction and communication satellites Sir Arthur Charles Clarke (born December 16, 1917) is a British author and inventor, probably most famous for his science fiction novel 2001: A Space Odyssey. ... Stephen Baxter at the Science-Fiction-Tage NRW in Dortmund, Germany, March 1997 Stephen Baxter (born in Liverpool, 13 November 1957) is a British hard science fiction author. ... Sunstorm is a science fiction novel by Arthur C. Clarke. ... The Xbox is a sixth generation era video game console produced by Microsoft Corporation. ... Namcos Pac-Man was a hit, and became a universal phenomenon. ... Halo: Combat Evolved, or simply Halo, is a video game in the first-person shooter (FPS) genre, created by the Microsoft-owned Bungie Studios. ... Year 2001 (MMI) was a common year starting on Monday (link displays the 2001 Gregorian calendar). ... This article is about the video game. ... shelby was here 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... Halos are fictional megastructures in the Halo video game series. ... Halo: Combat Evolved, or simply Halo, is a video game in the first-person shooter (FPS) genre, created by the Microsoft-owned Bungie Studios. ... This article is about the video game. ... Threshold is the planet to which a blind jump was made in Halo: Combat Evolved. ... In 1999 Vernor Vinge published his science fiction novel, A Deepness in the Sky, a loose prequel (set 30,000 years earlier) to his novel A Fire Upon the Deep (1992). ... Vernor Steffen Vinge (IPA: ) (born February 10, 1944) is a mathematician, computer scientist and science fiction author who is best known for his Hugo award-winning novels A Fire Upon the Deep and A Deepness in the Sky, as well as for his 1993 essay The Technological Singularity, in which... Most stars are of almost constant luminosity. ... Hertzsprung-Russell diagram The main sequence of the Hertzsprung-Russell diagram is the curve where the majority of stars are located in this diagram. ...

Unspecified Lagrange points

• Lagrange points are mentioned most famously in the science fiction film 2010: The Year We Make Contact, where the Discovery spacecraft is located on a Lagrange point. The movie expands on this, claiming that Discovery is located at a point between Io and Jupiter, which would place it in the L₁ point of the Jupiter–Io system.

• The Lagrange points are mentioned in the anime saga Mobile Suit Gundam, where clusters of space colonies (called "Sides") are located at the five Lagrange points of Earth, in addition to resource satellites and space fortresses. Lagrange Points have been mentioned in several other Gundam series as well.

• Lagrange points also play a role in the Larry Niven/Jerry Pournelle classic The Mote in God's Eye.

• In Robert Forward's Rocheworld the locations for Lagrange points around a binary planet are discussed in contrast to typical system.

• In Iain M. Banks' The Algebraist Lagrange points and their alternate forms are central to the plot, as possible locations for wormholes.

• In the Independence War computer games, Lagrange points L₄ and L₅ are used as the only locations for jump-points.

• In the Battletech game series, a star's Nadir and Zenith are the standard hyperspace jump points for most interstellar spacecraft. Lagrange points (usually the L₄ and L₅ points) are sometimes used to enter a system closer to planets, almost always for small-scale military or pirate operations due to the risk of catastrophic misjumps.

• In the Halo novels the Lagrange points are the only places where a human ship can safely make a slipspace jump.

• In the PC video game Star Wars: X-Wing, Lagrange points are mentioned in the briefings of some missions that revolve around attacking objects placed at them.

• In the Robert A. Heinlein novel The Number of the Beast, two of the main characters engage in a discussion of adding planets to the solar system at Lagrange points.

• In the sci-fi series Stargate Atlantis there was a defensive satellite located at a Lagrangian point in the solar system in which Atlantis was located.[3]

• In 1991, Konami released a science fiction RPG for the NES in Japan called Lagrange Point.

• In the Robotech television series, an effect called an Orbital Warp Blast is created when a spaceship creates "a phenomenon known as the molecular vacuum" at a fictional "Lagrange Point 6, approximately 20,000 kilometers from Mars" (where one does not exist in the real world).

• In The Monkeys Thought 'Twas All In Fun by Orson Scott Card a structure called the Trojan Object appears at L₄ or L₅

• In the Star Trek novel The Abode of Life by Lee Corey, Captain Kirk states the the planet Mercan has no Lagrangian points.

• In a parody of the science fiction comic Freefall a character refers to a satellite bar located in "the Lagrange point" so that it's always Happy hour there. He then heads for said bar promising to be back before sunset (which of course never happens).

(Redirected from 2010: The Year We Make Contact) 2010: Odyssey Two, is a science fiction novel by Arthur C. Clarke (January 1982) and also a motion picture (1984) by Peter Hyams entitled simply 2010, or sometimes 2010: The Year We Make Contact. ... The main cast of the anime Cowboy Bebop (1998) (L to R: Spike Spiegel, Jet Black, Ed Tivrusky, Faye Valentine, and Ein the dog) For the oleo-resin, see Animé (oleo-resin). ... Mobile Suit Gundam ) is a televised anime series written and directed by Yoshiyuki Tomino and made up of 43 episodes aired in 1979. ... Cover of 1991-03-01 paperback edition The Mote in Gods Eye, by Larry Niven and Jerry Pournelle, was called possibly the finest science fiction novel I have ever read by Robert A. Heinlein. ... Robert Lull Forward commonly known as Robert L. Forward (August 15, 1932 - September 21, 2002) was a United States physicist and science fiction writer. ... Rocheworld Rocheworld (1990) AKA The Flight of the Dragonfly (1984) is a science fiction novel by Robert Forward. ... Iain Menzies Banks (born on February 16, 1954 in Dunfermline, Fife, Scotland) writes mainstream novels as Iain Banks and science fiction as Iain M. Banks. ... The Algebraist, a science fiction novel by Scottish writer Iain M. Banks, first appeared in print in 2004. ... A wormhole, also known as an Einstein-Rosen bridge, is a hypothetical topological feature of spacetime that is essentially a shortcut from one point in the universe to another point in the universe, allowing travel between them that is faster than it would take light to make the journey through... For other uses of the abbreviation I-War, see I-War I-War (known as Independence War after the North American release) is a space simulation computer game developed by English development house Particle Systems Ltd. ... Jump drive is a name given to a method of traveling faster than light in science fiction. ... BattleTech is a wargaming and science fiction franchise, launched by FASA Corporation and currently owned by WizKids. ... It has been suggested that Covenant Vehicles in Halo be merged into this article or section. ... The Altair 8800 was among the first microcomputers to be affordable by an individual, although it initially lacked peripherals and memory. ... Namcos Pac-Man was a hit, and became a universal phenomenon. ... Robert Anson Heinlein (July 7, 1907 – May 8, 1988) was one of the most popular, influential, and controversial authors of hard science fiction. ... The Number of the Beast is a science fiction novel by Robert A. Heinlein published in 1980. ... A planet (from the Greek πλανήτης, planetes or wanderers) is a body of considerable mass that orbits a star and that produces very little or no energy through nuclear fusion. ... Major features of the Solar System (not to scale; from left to right): Pluto, Neptune, Uranus, Saturn, Jupiter, the asteroid belt, the Sun, Mercury, Venus, Earth and its Moon, and Mars. ... Stargate Atlantis is a Canadian-American science fiction television program, part of the Stargate franchise. ... Lagrange Point is an RPG game by Konami, released only in Japan in 1991. ... Robotech science fiction and anime universe. ... The tone or style of this article or section may not be appropriate for Wikipedia. ... The current Star Trek franchise logo Star Trek is an American science fiction entertainment series and media franchise. ... G. Harry Stine (March 26, 1928 - November 2, 1997) is widely regarded as the father of model rocketry. ... Captain James T. Kirk James Tiberius Kirk, a fictional character in the Star Trek television series, was the captain of the starship Enterprise (NCC-1701 and NCC-1701-A). ... First impressions: Florence (left) meets Sam and Helix for the first time. ... Happy hour is a period of time, which is usually an hour or two in the late afternoons Monday through Thursday, and sometimes Friday (usually taking place between 4 pm and 7 pm) during which some restaurants and bars give discounts for drinks, especially alcoholic drinks. ...

Notes and references

Joseph Louis Lagrange (January 25, 1736 – April 10, 1813) was an Italian mathematician and astronomer who later lived in France and Prussia. ... The barycenter (from the Greek βαρύκεντρον) is the center of mass of two or more bodies which are orbiting each other, and is the point around which both of them orbit. ... Neil deGrasse Tyson (b. ... Simulated view of a black hole in front of the Milky Way. ...

See also

• List of objects at Lagrangian points
• Lunar space elevator
• Home on Lagrange (The L5 Song)
• L5 Society
• Colonization of the Sun (Lagrange Points)

This is a list of known objects which have been, are or are planned to occupy any of the five Lagrangian points of two-body systems in space. ... A lunar space elevator (also called a moonstalk) is a proposed cable running from the surface of the Moon into space. ... Home on Lagrange (The L5 Song) is a filk song, written in 1978 by William S. Higgins and Barry D. Gehm, intended to be sung to the tune of Home on the Range. ... The original L5 Society logo, currently located at the L5 News archive on the World Wide Web The L5 Society was founded in 1975 by Carolyn and Keith Henson to promote the space colony ideas of Dr. Gerard K. ONeill. ... Lagrange Point Colonization is the colonization of the five equilibrim points in the orbit of a planet or moon around its primary, called Lagrange points. ...

External links

• Explanation of Lagrange points – Prof. Neil J. Cornish
• A NASA explanation – also attributed to Neil J. Cornish
• Explanation of Lagrange points – Prof. John Baez
• Geometry and calculations of Lagrange points – Dr J R Stockton
• Locations of Lagrange points, with approximations – Dr. David P. Stern