Any one of the five solutions to the three-body problem of gravitational attraction formulated by the 18th century mathematician Joseph-Louis Lagrange. Lagrange was searching for a stable configuration in which three bodies could mutually orbit each other and stay in the same position relative to each other. He found five such solutions, and they are called the five Lagrange points in honor of their discoverer.
In three of the solutions found by Lagrange, the bodies are in line; in the other two the bodies are at the points of equilateral triangles. The five lagrangian points for a binary system are as follows;
- First Lagrange Point (L1) is an orbit in line with and between the binary pair.
- Second Lagrange Point (L2) is an orbit in line with and outside the orbit of the smallest of the binary pair.
- Third Lagrange Point (L3) is an orbit identical in distance to the distance between the two bodies of the binary pair but in opposition to the orbital position of the smallest of the binary pair.
- Fourth Lagrange Point (L4) is in the same orbit as the smallest of the binary pair but 60° ahead of it position.
- Fifth Lagrange Point (L5) is in the same orbit as the smallest of the binary pair but trailing its position by 60°.