Out-of-plane equilibrium points in the restricted three-body problem with oblateness

The equations of motion of the three-dimensional restricted three-body problem with oblateness are found to allow the existence of out-of-plane equilibrium points. These points lie in the $(x-z)$ plane almost directly above and below the center of each oblate primary. Their positions can be determined numerically and are approximated by series expansions. The effects of their existence on the topology of the zero–velocity curves are considered and their stability is explored numerically.