Low-Energy Round-Trip Trajectories to Near-Earth Objects using Solar Electric Propulsion

Near-Earth Objects (NEOs) represent valuable targets for space exploration, due to their accessibility, scientific significance, and potential for in-situ resource utilization. Recent advances in low-energy trajectory design have uncovered efficient routes to these bodies. However, the use of low-energy transfers for direct connections between Earth and NEOs remains largely unexplored, particularly when combined with low-thrust propulsion. This work aims to develop a systematic and streamlined methodology for designing low-energy trajectories to NEOs, encompassing both one-way and round-trip transfers. An effective and consolidated approach based on the combined use of the Sun-Earth-spacecraft circular restricted three-body problem (CR3BP) and the Sun-spacecraft two-body problem (2BP) is adopted. Within the CR3BP, invariant manifold trajectories (MTs) and associated transit orbits (TOs) traverse Earth’s vicinity, acquiring a phase difference relative to Earth. Beyond a certain distance from Earth, as the terrestrial gravitational influence becomes negligible, the Sun-spacecraft 2BP is used to approximate MTs and TOs. The 2BP simplifies the identification of spacecraft-NEO encounters, which are determined through intersection of the respective heliocentric elliptical orbits. Impulsive trajectories serve as the backbone of the analysis, and are subsequently replaced by low-thrust arcs, improving propellant efficiency. Because the axes of the Sun-Earth synodic frame rotate, the same MT or TO is approximated by infinitely many 2BP orbits, which differ only by their orientation in space, determined by the transition epoch. This property provides a degree of freedom that can be leveraged in the design of both the outbound (Earth-NEO) and inbound (NEO-Earth) branches of a round-trip trajectory, thus enabling the selection of the preferred solution according to custom design criteria such as mission duration and propellant budget. The solid foundation of the methodology at hand was demonstrated in a previous contribution, which successfully applied this strategy to identify low-energy solutions for NEO rendezvous missions, leveraging the departure epoch as a free parameter. This work extends the range of applicability of the method to planar round-trip trajectories by incorporating the arrival epoch as the additional design parameter associated with the inbound branch of the transfer.