The Circular-Restricted Three-Body Problem

Compute and plot characteristics of the circular-restricted three-body problem.

This document describes several MATLAB scripts that can be used to analyze and display orbits in the circular-restricted three-body problem (CRTBP). This is a special case of the general three-body problem where the primary and secondary bodies move in circular orbits about the common center of mass, and the effect of the gravitational attraction of the smallest body and any other perturbations such as solar radiation pressure are ignored.

Several of the applications described here are for orbital problems in the Earth-Moon-satellite system. However, the equations and algorithms are valid for any circular-restricted three-body system for which the mass ratio of the primary and secondary is between 0 and 1/2.

The classic textbook for this problem is Theory of Orbits by Victor Szebehely, Academic Press, New York, 1967. An excellent discussion about this problem can also be found in Chapter 8 of An Introduction to Celestial Mechanics by Forest Ray Moulton, Dover Publications, 1970.