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	Lagrangian points
		Lagrangian points are named after the Italian-born French mathematician and astronomer Joseph Louis de Lagrange who first showed their existence.
		There are five Lagrangian points in all, three of which are unstable because the slightest disturbance to any object located at one of them causes the object to drift away permanently.
		The remaining two Lagrangian points, L4 and L5, lie at the vertices of equilateral triangles formed with the two main gravitating masses and in their orbital plane.
	www.daviddarling.info /encyclopedia/L/Lagpoint.html (417 words)

	Lagrangian point - Wikipedia, the free encyclopedia
		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.
		points lie at the third point of an equilateral triangle whose base is the line between the two masses, such that the point is ahead of, or behind, the smaller mass in its orbit around the larger mass.
		When a body at these points is perturbed, it moves away from the point, but the Coriolis effect then acts, and bends the object's path into a stable, kidney bean‐shaped orbit around the point (as seen in the rotating frame of reference).
	en.wikipedia.org /wiki/Lagrangian_point (2255 words)

	RedOrbit - Reference Library (Site not responding. Last check: 2007-10-17)
		Lagrangian Point -- In Lagrangian mechanics, a Lagrangian point (or L-point) is one of five positions in space where the gravitational fields of two bodies of substantial but differing mass combine to form a point at which a third body of negligible mass would be stationary relative to the two bodies.
		Example: A third Lagrangian point, L3, exists on the opposite side of the Sun, a little further away from the Sun than the Earth is, where the combined pull of the Earth and Sun again causes the object to orbit with the same period as the Earth.
		At the third point of an equilateral triangle with the base of the line defined by the two masses, such that the point is ahead of the smaller mass in its orbit around the larger mass.
	www.redorbit.com /education/reference_library?article_id=283 (815 words)

	ESA - Space Science - L1, the first Lagrangian Point
		The L1 point is perhaps the most immediately significant of the Lagrangian points, which were discovered by mathematician Joseph Louis Lagrange.
		Lagrangian points are where all the gravitational forces acting between two objects cancel each other out and therefore can be used by spacecraft to ‘hover’.
		He discovered that there are five points, dotted around the two larger masses, in which all the forces acting on the small one would cancel out.
	www.esa.int /esaSC/SEMC4QS1VED_index_0.html (354 words)

	Dictionary of Technical Terms for Aerospace Use - L
		A parallel of latitude is a circle (or approximation of a circle) of the earth, parallel to the equator, and connecting points of equal latitude; or a circle of the celestial sphere, parallel to the ecliptic.
		The line connecting the two points of an orbit that are nearest and farthest from the center of attraction, as the perigee and apogee of the moon or the perihelion and aphelion of a planet; the major axis of any elliptical orbit and extending indefinitely in both directions.
		The straight line connecting the two points of intersection of the orbit or a planet, planetoid, or comet and the ecliptic, or the line of intersection of the planes of the orbits of a satellite and its primary.
	roland.grc.nasa.gov /~dglover/dictionary/l.html (7224 words)

	Lagrangian - Wikipedia, the free encyclopedia
		The same principle, and the Lagrange formalism, are tied closely to Noether's Theorem, which relates physical conserved quantities to continuous symmetries of a physical system; and Lagrangian mechanics and Noether's Theorem together yield a natural formalism for first quantization by including commutators between certain terms of the Lagrangian equations of motion for a physical system.
		The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics known as Lagrangian mechanics.
		In this context, the Lagrangian is usually taken to be the kinetic energy of a mechanical system minus its potential energy.
	en.wikipedia.org /wiki/Lagrangian (944 words)

	[No title]
		It goes like this: Lagrangian points (named after the 18th Century mathematical [i]Grande Fromage[/i] Lagrange) are orbit positions that balance the gravitational and angular momentum forces of [i]both[/i] a major body and minor body, such that a ship at that position in orbit remains in the same position relative to both major and minor bodies.
		Lagrangian points exist for systems where the minor's mass is less than roughly 1/24th of its major.
		To illustrate the mathematical beauty of the Lagrangian points, let me re-tell with a story: In A.C Clarke's 2010, a recovery mission goes to investigate the death and disappearance of the crew of the Discovery, and if possible to rehabilitate the onboard computer and return the ship to earth.
	www.orbitersim.com /Forum/default.aspx?g=posts&t=338 (1058 words)

	Lagrangian Point - Slackerpedia Galactica
		Lagrangian points, also called Lagrange points, are like Switzerlands in the gravity between two objects (like a planet orbiting a star).
		L2 is the point on the far side of the Earth from the Sun.
		L3 is the point on the far side of the Sun from the Earth.
	www.slackerastronomy.org /slackerpedia/index.php/Lagrangian_Point (248 words)

	Highbeam Encyclopedia - Search Results for Lagrangian
		Lagrangian points One of the five points at which a celestial body can remain in a position of equilibrium with respect to two much more massive bodies orbiting each other.
		Lagrangian points are named after the French astronomer Comte...
		one of five points in the plane of orbit of one body around another (e.g., the moon around the earth) at which a small third body can remain stationary.
	www.encyclopedia.com /SearchResults.aspx?Q=Lagrangian (1138 words)

	Lagrangian Points and Nasa's Plan to Explore Space \| Baby Developments
		Nasa is relying on its ability to determine the Lagrangian points between every set of planets, moons, asteroids, etcetera it intends to explore in order to implement its plan of successful interplanetary space exploration.
		A Lagrangian point between two bodies exerting competing forces on a body therefore is a point at which the forces are equal and opposite.
		Therefore, in this case of a mass under the influence of two competing gravitational forces, the Lagrangian points are the orbits in which the mass in question will have the greatest ability to withstand the biggest change in net force upon it that would disturb it into an unstable orbit.
	www.baby-developments.com /articles/lagrangian-points-and-nasas-plan-to-explore-space.html (428 words)

	Lagrangian Points and Nasa's Plan to Explore Space - Science
		A Lagrangian point needle two bodies exerting competing forces on a body is therefore a point at which the forces are equal and opposite.
		This point represents the point at which the maximum energy, the energy from the fenland of the bowl to the top, must be supplied to kick the body out of the bowl in order to prevent the body from rolling back down to the undermost of the bowl and returning to its energy minimum.
		Therefore, the point at the minimum of the bowl represents the point of maximum stability in terms of preventing the influence of a net imbalance in the forces of the two gravitational forces on it from disturbing it.
	www.mps-science.com /article/lagrangian-points-and-nasas-plan-47672.html (773 words)

	Lake County Astronomical Society NightTimes
		These are points where the pull of gravity of two large bodies acting on a smaller body, plus centrifugal force, is so equal that the small body is able to remain in a reasonably stable orbit, unless disturbed by another large body.
		Lagrangian Point L1 is the most stable such point in a direct line between the Earth and the sun.
		At this point, the gravity of the Sun on a small body is offset by the gravity of the Earth.
	www.bpccs.com /lcas/Articles/lagrange.htm (595 words)

	CSD ICARTT Analysis Products
		During the forward simulation of the North American CO tracer (plots of the results can be produced with the interactive tool) all particle positions were stored every 2 hours during the period of the Lagrangian experiment, i.e., from 11 July to 4 August.
		Therefore, the cases identified are certainly not all really Lagrangian (because of model errors and also because of the mismatches tolerated) and their Lagrangian nature must be confirmed using the chemistry measurement data.
		It is recommended to search data points in the vicinity of the times specified for upwind and downwind measurements to find the best match (or reject the Lagrangian case if no match can be found).
	esrl.noaa.gov /csd/ICARTT/analysis/LAGRANGIAN_CASES/lagrangian_description.html (1004 words)

	The Lagrangian Points for a Planetary Orbit
		A planet's orbit is determined by a balance between the gravitation attraction and the centrifugal force from its movement in an approximately circular orbit.
		For a particular planet there are five points that involve a balance involving the attraction of the Sun and the planet.
		There is a point between the Sun and Jupiter where a mass would be equally attracted to the Sun and Jupiter and therefore in balance.
	www.applet-magic.com /lagrangepoints.htm (555 words)

	Genesis : Search for Origins \| JPL \| NASA
		The points of equilibrium are called the Lagrange points.
		L4 and L5 are at the apex of equilateral triangles with the massive bodies at the vertices (Figure 1.) L4 usually is usually associated with the leading triangle, L5 the trailing.
		The forces due to gravity of the two massive bodies in the system dwarf outside perturbations, but objects at Lagrange points are in a delicate balance between those forces.
	genesismission.jpl.nasa.gov /mission/lagrangepoints.html (446 words)

	3-1.html
		The point(s) where the gradient of the Lagrangian vanishes (i.e., is equal to 0) are points where the least and greatest distances must occur, if they do occur.
		Although we have not proven so directly, it is safe to conclude that (1,1,0) and (-1,-1,0) are the points on the hyperboloid that are closest to the origin.
		A sphere of radius 1 centered at (3,4,0) is subjected to a gravitational potential field whose source is a point mass located at the origin.
	faculty.etsu.edu /knisleyj/multicalc/Chap3/Chap3-1/3-15.html (358 words)

	Neil deGrasse Tyson : The Five Points of Lagrange
		But unlike the first three Lagrangian points, which enjoy only unstable equilibrium, the equilibria at L4 and L5 are stable; no matter which direction you lean, no matter which direction you drift, the forces prevent you from leaning farther, as though you were in a valley surrounded by hills.
		For each of the Lagrangian points, if your object is not located exactly where all forces cancel, then its position will oscillate around the point of balance in paths called librations.
		From the Sun-Earth Lagrangian points you are half way to Mars; not in distance or time but in the all-important category of fuel consumption.
	research.amnh.org /~tyson/18magazines_five.php (2170 words)

	Lagrange Points
		The L1 point of the Earth-Sun system affords an uninterrupted view of the sun and is currently home to the Solar and Heliospheric Observatory Satellite SOHO.
		The L2 point of the Earth-Sun system will soon be home to the MAP Satellite and (perhaps) the Next Generation Space Telescope.
		The L1 and L2 points are unstable on a time scale of approximately 23 days, which requiress satellites parked at these positions to undergo regular course and attitude corrections.
	www.physics.montana.edu /faculty/cornish/lagrange.html (761 words)

	Lagrangian point
		Lagrangian point is a point in space at which a small body, under the gravitational influence of two large ones, will remain approximately at rest relative to them.
		The existence of such points was deduced by the French mathematician and astronomer Joseph-Louis Lagrange in 1772.
		Each stable point forms one tip of an equilateral triangle having the two massive bodies at the other vertices.
	abyss.uoregon.edu /~js/glossary/lagrangian_point.html (122 words)

	ESA - Space Science - L2, the second Lagrangian Point
		The L2 point is rapidly establishing itself as a pre-eminent location for advanced spaceprobes and ESA has a number of missions that will make use of this orbital 'sweet-spot' in the coming years.
		L2 is one of the so-called Lagrangian points, discovered by mathematician Joseph Louis Lagrange, where all the gravitational forces acting between two objects cancel each other out and therefore can be used by spacecraft to 'hover'.
		Since Lagrangian points are produced by the 'balance' of two or more opposing forces, it is possible that 'artificial' Lagrangian points could be created by spacecraft if they could constantly produce a force to counteract the pull of gravity.
	www.esa.int /esaSC/SEMO4QS1VED_index_0.html (381 words)

	Roche Model
		As the distance from the point mass increases, the shape of the equipotential surface elongates in the direction of the center of gravity, until the two surfaces ``touch'' in a roughly ``hour-glass'' form (refer to Fig.
		The intersection point between the two masses (the neck of the ``hour glass'') is labeled the inner Lagrangian point, or the L1 point.
		Figure 1.1 displays the positions of the Lagrangian points in the binary system, KU Cygni, as well as the critical Roche lobes around each stellar component and other multiple equipotential surfaces.
	mintaka.sdsu.edu /faculty/quyen/node10.html (835 words)

	Lagrangian Points
		The sister-site From Stargazers to Starships discusses Lagrangian points in more detail than is done here, among other things deriving the distance of L1 (the derivation of L2 is almost identical) and also the equilibrium points L4 and L5.
		The L1 point is a very good position for monitoring the solar wind, which reaches it about one hour before reaching Earth.
		The L2 point has been chosen by NASA as the future site of a large infra-red observatory, the "Next Generation Space Telescope", renamed in honor of a late NASA director The James Webb Observatory.
	www-spof.gsfc.nasa.gov /Education/wlagran.html (901 words)

	CPAC: The Lagrangian Points
		We are finally in a position to explain what the Lagrangian points are and, more importantly, why they exist.
		Imagine that the asteroid is now placed in such a position that the result of the two forces, from the Earth and the Moon, is to make the asteroid move towards B, the centre of mass of the Earth and Moon.
		L1, L2 and L3 are simply points on the line joining the Earth and Moon at which their combined pull allows a potential asteroid to orbit around B, just as before.
	www.cpac.freeserve.co.uk /docs/lagrange.htm (1364 words)

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