{'fraction_non_alphanumeric': 0.01316872427983539, 'fraction_numerical': 0.0032921810699588477, 'mean_word_length': 4.931707317073171, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Analysis of capture trajectories into periodic orbits about libration points

Spacecraft capture trajectories to Lyapunov/Halo periodic orbits of the L1 and L2 points in the restricted Hill three-body problem are analyzed. The specific focus is on transfer to these orbits from interplanetary trajectories. This application is motivated by future proposals to place "deep space ports" at the Earth and Mars L1 or L2 points. We use stable manifolds for capture trajectories to periodic orbits around the libration points. Numerical results show that the stable and unstable manifolds from periodic orbits around the libration points can intersect the surface of any of the planets of the solar system by changing the size of periodic orbits. Applying this to Earth-Mars transfers, the cost of capture into a periodic orbit is reduced compared with direct capture into a parabolic orbit. Moreover, if a spaceport is built on a periodic orbit in the vicinity of a sun-Mars libration point and propellant can be supplied there to the spacecraft, the required A V for entry into a circular orbit about Mars from an interplanetary trajectory can be considerably reduced compared with a direct entry into a circular orbit.