2008MNRAS.384..548N

An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based on calculations known from classical mechanics, but with the addition of certain terms necessary to give a reasonably good approximation. The results are compared with simulations. The derived simple set of analytical expressions gives periodic orbits on the discs of binary systems without the need to solve the equations of motion by numerical integration.