Trajectories Derived from Periodic Orbits around the Lagrangian Point L1 and Lunar Swing-Bys: Application in Transfers to Near-Earth Asteroids

To present a set of trajectories derived from the retrograde periodic orbits around the Lagrangian equilibrium point L-1, this paper considers the Circular Restricted Three-body Problem with Earth-Moon masses (CR3BP), the Restricted Bicircular, and Full Four-Body Sun-Earth-Moon-spacecraft Problems (BCR4BP and FR4BP, respectively). These periodic orbits are predicted by the dynamics of the CR3BP. To generate the trajectories of this set, first, slightly different increments of velocity ( increment Vs) from those needed to generate periodic orbits around L-1 are applied to a spacecraft in circular low Earth orbits in the same direction of their motion when the Earth, the spacecraft, and the Moon are aligned in this order. Thus, translunar trajectories derived from the periodic orbits are obtained and they will lead the spacecraft to the vicinity of the Moon. Depending on the values of the | increment Vs|, which are also functions of the relative positioning between the Sun, the Earth, and the Moon, three types of trajectories of interest are found: Collision with the Moon, escape, and geocentric orbits with large semi-major axes. For a well-defined interval of the | increment Vs|, the trajectories accomplish swing-bys with the Moon and obtain energy to escape from the Earth-Moon system and reach Near-Earth Asteroids (NEAs) between the orbits of Venus and Mars. This procedure reduces the costs of inserting spacecraft into transfer trajectories to a set of NEAs in terms of the required | increment V| by up to 5% when compared to Lambert's problem, for example. This work also presents analyses of examples of transfers to the NEAs 3361 Orpheus, 99942 Apophis, and 65803 Didymos, from 2025 on.