# Lagrangian points

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## Lagrangian points

(lă-grayn -jee-ăn) Five locations in space where a small body can maintain a stable orbit despite the gravitational influence of two much more massive bodies, orbiting about a common center of mass. They are named after the French mathematician J.L. Lagrange who first suggested their existence in 1772. A Lagrangian point 60° ahead of Jupiter in its orbit around the Sun, and another 60° behind Jupiter, are the average locations of members of the Trojan group of asteroids; these points are denoted L4 and L5. The three other Lagrangian points in the Sun–Jupiter gravitational field do not permit stable asteroid orbits owing to the perturbing influence of the other planets. In any system these three points lie on the line joining the centers of mass of the two massive bodies and are denoted L1 (the inner Lagrangian point) and L2 and L3 (the outer Lagrangian points); small bodies here would be in unstable equilibrium (see equipotential surfaces).

## Lagrangian points

[lə′grän·jē·ən ‚poins]
(astronomy)
Five points in the orbital plane of two massive objects orbiting about a common center of gravity at which a third object of negligible mass can remain in equilibrium; three points of instable equilibrium are located on the line passing through the centers of mass of the two bodies, and two points of stable equilibrium are located in the orbit of the less massive body, 60° ahead of or behind it.
References in periodicals archive ?
After the first time step, the Lagrangian points representing the filament boundary move from their initial positions in the flow direction.
Ramesh Kumar, "Effects of photogravitational and oblantensss on the triangular Lagrangian points in the elliptical restricted three body problem," International Journal of Pure and Applied Mathematics, vol.
Particles displaced slightly from the first three Lagrangian points will continue to move away and hence these locations are unstable.
It arrived at what is called a Lagrangian point, where it will stay till the end of next year to conduct scientific observations and test deep space tracking and control capability for future possible explorations of Jupiter and the poles of the Sun.
The Lagrangian Points, discovered by the French mathematician, Louis Lagrange are locations in space where gravitational forces and the orbital motion of a body balance each other.
For private Martian settlement programs, this may require development of low-cost space vehicles and the establishment of commercial space industries where nearer destinations (the Moon, Lagrangian points, and near-Earth asteroids) are visited first in a step-by-step fashion.
"His find is the result of many years of searching, based upon the idea that the most likely locations for additional satellites are the Lagrangian points of the Earth-Moon system."
My nerdy high school gang wore "L5 in 95" T-shirts, imagining we would help create permanent colonies at the Lagrangian points of Earth's orbit.
Free-space venues like the Earth-Moon or Earth-Sun Lagrangian points and the use of simple solar shields offer thermal stability and freedom from dust and debris, unlike low Earth orbits or the lunar surface.
Of the 100-plus entries I read, only two hit me over the head with obvious errors: "centrifugal pseudo-forces work against gravity" at all five Lagrangian points, not just the stable L4 and L5 ones; and "HETE" stands for High Energy Transient Explorer, not High Energy Solar Spectroscopic Imager.
The generally excellent Oxford Dictionary, for its part, best defined and illustrated Lagrangian points and spherical aberration.

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