Euler’s three‐body problem

The simplest three‐body problem that attracts physical interest is the one first studied by Euler. In Euler’s problem, a primary and secondary mass are fixed in space, a given distance apart, and a test mass is allowed to move unrestricted in their superimposed gravitational fields. The equations of motion are derived and solved via a simple numerical procedure. The algorithm is adaptable to a small programmable calculator and should help to stimulate interest in the classroom. Several examples of motion are discussed and graphically presented.