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 It might be outdated or ideologically biased.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.

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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.

Numerical-Symbolic Methods for Searching Relative Equilibria in the Restricted Problem of Four Bodies

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.

Research on 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.

Autonomous Orbit Determination for Lagrangian Navigation Satellite Based on Neural Network Based State Observer

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.

The Hamiltonian structure-preserving control and some applications to nonlinear astrodynamics

NASA is considering missions beyond low Earth orbit such as libration points, which are gravitationally stable spots in space.

Aerospace News - Asia / Pacific

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.

Existence of resonance stability of triangular equilibrium points in circular case of the planar elliptical restricted three-body problem under the oblate and radiating primaries around the binary system