> That was me trying to have a small particle making an 8-shaped path around two bigger ones that would be sufficiently far apart to not interact too strongly w

> That was me trying to have a small particle making an 8-shaped path around two bigger ones that would be sufficiently far apart to not interact too strongly with each other. This kind of path is called a free return trajectory and was used in the Apollo program lunar missions. The trajectory is not periodic, ie. it doesn't repeat more than once. The trajectory around the earth takes less time than lunar period ("month") so when the craft goes back up, the moon has moved on. You might be able to construct a planet-moon system with an m:n resonance in the orbital periods of the moon and the craft so that the tracjetory is periodic. Free return trajectories are used in manned space flight to guarantee that the craft and crew return to earth if a failure prevents from entering lunar orbit.