# 16: Equivalent Potential and the Restricted Three-Body Problem

- Page ID
- 6895

- 16.1: Introduction
- The collinear lagrangian points any points on the line passing through the two masses where a third body of negligible mass could orbit around C with the same period as the other two masses; i.e. it would remain on the line joining the two main masses? The collinear points were discussed by Euler before Lagrange, but Lagrange took the problem further and discovered an additional two points not collinear with the masses, and the five points today are generally all known as the lagrangian points.

- 16.2: Motion Under a Central Force
- There is no general analytical solution in terms of simple algebraic functions for the problem of three gravitating bodies of comparable masses. Except in a few very specific cases the problem has to be solved numerically. However in the restricted three-body problem, we imagine that there are two bodies of comparable masses revolving around their common center of mass, and a third body of negligible mass moves in the field of the other two.

*Thumbnail: Configuration of the Sitnikov three-body problem. Image used with permission (CC BY-SA 2.5; Moneo).*