Libration Point

Author: Tianjiang Says
Website: https://cislunarspace.cn

Definition

A libration point (also called equilibrium point or Lagrange point) is a point in the Circular Restricted Three-Body Problem (CR3BP) where the gravitational forces of two primary bodies and the centrifugal force in the rotating reference frame are in equilibrium. At these points, the third body can maintain a stationary position relative to the two primary bodies.

Classification

There are five libration points in the CR3BP, divided into two categories:

Point	Location	Stability
L1	Between the two primary bodies	Unstable
L2	Beyond the smaller primary body	Unstable
L3	Beyond the larger primary body	Unstable
L4	60° ahead of the smaller primary body	Conditionally stable
L5	60° behind the smaller primary body	Conditionally stable

L1, L2, and L3 are collinear libration points (on the line connecting the two primary bodies), while L4 and L5 are triangular libration points (forming equilateral triangles with the two primary bodies).

Calculation

In the Earth-Moon system, the positions of libration points can be determined by solving the equilibrium equations in the rotating reference frame. The collinear libration points require solving a quintic equation, while L4 and L5 form equilateral triangles with the two primary bodies.

Significance

Libration points serve as natural "gateways" in cislunar space:

L1: Connects Earth and Moon regions, suitable for lunar relay communications
L2: Gateway to deep space, suitable for space telescopes and deep space exploration
L4/L5: Stable equilibrium points, potential locations for space stations and resource depots

Orbits around libration points (Halo orbits, Lissajous orbits) are important mission orbits for cislunar space operations.

References

Chen Yuju. DRO Orbit Design and Control Research for Cislunar Space Situation Awareness[D]. 2024.