The Three-Body Problem in Shape Space

The general three-body problem is considered in shape space. Solutions to the problem in such a space have a number of remarkable properties. The paper presents the equations of motion of the three-body problem in shape space, the integrals of the problem are investigated. As it turns out, Sundman’s inequality is a simple consequence of the energy integral in the shape space. The periodic solutions obtained of the three-body problem are considered in shape space, and their properties are studied.