Example of a first kind periodic orbit with C_j = 7.337 × 10⁻³ km² s⁻² and the period of the periodic orbit in the rotating frame is T = 11.5 h. The point at the centre of the islands in red, shown in the Poincaré surface of section of Fig. 2 (first plot), corresponds to this periodic orbit. The trajectory in the rotating frame is shown in the top plot, while the trajectory in the inertial frame is in the middle plot. The temporal evolution of the orbital radius is shown in the bottom plot. The numbers in the top and middle plots show the locations equally spaced in time, indicating the time evolution of the trajectory.