An orbit insertion is one of the most critical operations in many missions. Its failure makes a spacecraft fly by the target body and may cause a prohibitively large amount of delta-v and/or a long time to reencounter it. To avert the doom of the orbit insertion failure, a variety of recovery options has been developed for missions such as SELENE, BepiColombo, MMX, and Artemis I, to name a few. In the light of the growing number of lunar missions, a trajectory design strategy that is robust against the lunar orbit insertion (LOI) failure would be in high demand.

Lunar transfer trajectories may be classified into two categories based on the orbital energy just before the LOI. High-energy transfer trajectories arrive at the sphere of influence of the Moon with hyperbolic excess velocity whereas low-energy transfer trajectories end up at the Moon with negative Keplerian energy. This work explores low-energy Earth-to-Moon transfer trajectories that are tolerant of a chemical LOI burn failure. Such trajectories are referred to as robust low-energy LOI trajectories. The robustness against the LOI failure would be significantly enhanced if a low-energy lunar approaching trajectory is naturally connected with a backup orbit that possesses multiple close perilune passages where a recovery burn can be performed. 

The peculiarity of the three-body dynamics in the Earth-Moon system may offer two distinct types of such backup orbits. One leverages the ballistic capture phenomenon, which allows a spacecraft to revolve around the Moon multiple times even after the complete LOI failure. Such a recovery strategy using a ballistically captured orbit has been proposed for the BepiColombo mission around Mercury, but the flight time until reencountering the Moon can be too short in the Earth-Moon system from the operational point of view. The other reencounters the Moon after the LOI failure via an orbit around Earth in mean motion resonance with the Moon. This option offers at least a one-month margin for checking the spacecraft’s status, performing orbit determination, and redesigning a trajectory that would be operationally advantageous.

This work adopts both backup scenarios and investigates the connectivity between the low-energy Earth-to-Moon transfer trajectories leveraging the solar tidal force and the ballistically captured orbits or resonant orbits experiencing multiple close encounters with the Moon. We start from propagating trajectories forward and backward in time from low-energy perilune conditions where a nominal LOI is supposed to take place. A successful forward leg has close perilune passages and a successful backward leg reaches the vicinity of Earth. The union of these legs is a robust low-energy LOI trajectory that can bring a spacecraft back to backup LOI points after the complete LOI failure. The optimization reveals that the extra delta-v cost of achieving some robust low-energy LOI trajectories is less than 20 [m/s] as compared with the minimum delta-v solutions with the same flight time. It has been found that the backup orbits that have many close perilune passages closely shadow Moon-grazing periodic orbits in a circular restricted three-body problem. From the near-periodic orbits, families of periodic orbits have been identified and the associated stable manifolds have been found to be useful in efficiently searching for robust low-energy LOI trajectories.

The general behavior of the robust low-energy LOI trajectories has been studied in simplified dynamical models of multi-body systems such as the circular restricted three-body problem and the bicircular restricted four-body problem. Not only the scenario of the complete LOI failure but also the scenario of the partial LOI failure is under consideration. When the partial LOI failure occurs for low-energy lunar transfer, the energy level after the LOI burn would likely be less than that of L1 libration point and escape from the vicinity of the Moon is no longer a big concern. Instead, the likelihood of avoiding impact with the Moon for various levels of the partial LOI failure would be an additional criterion for further screening the robust low-energy LOI trajectories. An efficient maneuver planning strategy for recovering from the partial LOI failure leveraging a precomputed database of perilune-to-perilune arcs will be also presented.