The Three-Body Problem: Moon — Earth — Sun

Abstract

The problem of three interacting point-like masses continues to be at the center of physics. The latest version consists of three quarks making up a proton or a neutron; but there are also two hydrogens and one oxygen as the constituents of a water molecule, or an atom of helium built with one alpha particle and two electrons. Behind these modern examples are all the famous instances from celestial mechanics, particularly the most obvious as well as the most difficult of them all, the motion of the Moon in the combined gravitational field of the Earth and the Sun. Since chaos made its first though hardly recognized appearance in this context, and the case is far from closed, an abbreviated discussion of this special problem seems both instructive and topical.