Libration Points

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Libration Points

 

(1) Points at which a body of small mass can be in a state of relative equilibrium with respect to two other celestial bodies (the restricted three-body problem). For a system of two bodies (considered as attracting mass points), there exist three collinear libration points lying on a straight line passing through these bodies and two triangular libration points located such that the two bodies and the libration points form equilateral triangles. In the case of collinear libration points, the bodies are in unstable equilibrium. The libration points of the earth-moon and the sun-earth systems are of particular importance in astrodynamics.

(2) The positions of relative equilibrium in the problem of celestial mechanics of the motion of a body of small mass in a force field that is independent of time in a rotating coordinate system.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The libration points are of great interest for applications and so their stability was a subject of many papers during the past two hundred years.
Obviously, the particle [P.sub.2] may be situated in any of the five equilibrium positions of the corresponding three-body problem which coincide with the libration points [L.sub.1], ..., [L.sub.5] in case of [m.sub.2] =0.
To complete the study of the equilibrium positions in the restricted fourbody problem one needs to consider the case when particle [P.sub.2] is situated in one of the collinear libration points [L.sub.1], [L.sub.2], [L.sub.3] and, therefore, the massive particles [P.sub.0], [P.sub.1], [P.sub.2] are located on the same straight line.
The deployment of spacecraft formation in libration points orbit can be achieved for long baseline interferometry, which is of great significance to the study of the origin of the universe.
According to these parameters we can obtain simulation curves through control method of keeping flight formation by using SDRE on the sun-earth libration points.
In 2005, Hill suggested placing navigation constellation on the periodic orbits in the vicinity of libration points of the Earth-Moon system to support deep space navigation [6].
Liu, "On motions around the collinear libration points in the elliptic restricted three-body problem," Monthly Notices of the Royal Astronomical Society, vol.
There are the hyperbolic equilibria which have stable, unstable, and centre manifolds for hyperbolic Hamiltonian system, just like the collinear libration points [L.sub.1], [L.sub.2], and [L.sub.3] in CR3BP [1], of which the unstable manifolds may cause instability in the Lyapunov sense.
For a hyperbolic Hamiltonian system, there exist hyperbolic equilibria that have stable, unstable, and center manifolds [1], which are similar to the collinear libration points [L.sub.1], [L.sub.2], and [L.sub.3] in CR3BP.
NASA is considering missions beyond low Earth orbit such as libration points, which are gravitationally stable spots in space.
The existence of the libration points and their stability in the radiational elliptical restricted three-body problem has been investigated [14].
Tkhai, "Instability of libration points and resonance phenomena in the photogravitational elliptic restricted three-body problem," Solar System Research, vol.