Solution set of circumlunar abort trajectory and its direct application to optimization design

Circumlunar abort trajectories constitute a vital contingency return strategy during the translunar phase of crewed lunar missions. This paper proposes a methodology for constructing the solution set of the circumlunar abort trajectory and leverages its advantageous properties to address the optimization design problem of abort trajectories. Initially, a solution set of all feasible abort trajectories, originating from an abort point on the nominal trajectory and complying with fundamental re-entry constraints, is formulated through the introduction of two novel design parameters. Subsequently, the geometric characteristics of the solution set, as well as the distributional properties of key iterative constraint responses, including flight time and velocity increment, are analyzed. Finally, the characteristics exhibited in the solution set are employed to directly identify the design parameters of the abort trajectories with minimum flight time and velocity increment, thereby providing solutions to two distinct types of optimization problems. The simulation results for a variety of nominal trajectories, encompassing the reconstruction and redesign of the Apollo13 abort trajectory, validate the proposed method, demonstrating its ability to directly generate optimal abort trajectories. The method proposed in this paper investigates feasible abort trajectories from a global perspective, providing both a framework and convenience for mission planning and iterative optimization in abort trajectory design.