To match the trans-lunar injection with high accuracy, a near-optimal orbit control method for phasing loops is proposed. Sensitivity analysis was performed based on Gauss’s variational equations, and a near-optimal orbit control strategy was developed. A sequential shooting method was proposed to reduce the dimensions of each shooting problem and improve convergence. To satisfy the accessibility requirements of ground facilities, a maneuvering location adjustment strategy is proposed. The advantage of the delta-V saving of the near-optimal method was verified by comparing with the differential correction method. The robustness of the practical method was verified using Monte Carlo simulations with high-fidelity dynamics. The results of this study can be applied to midcourse correction of phasing loops before the trans-lunar injection of a lunar probe.

The 2∶1 resonant distant retrograde orbit (DRO), owing to its long-term stability and extensive global accessibility in the Earth-Moon space, holds strategic significance in contemporary space exploration missions. Investigations of quasi-periodic orbits near two distinct configurations of the 2∶1 DRO were carried out in the bicircular restricted four-body problem (BCR4BP) in order to better understand the phase space structure near the 2∶1 DRO and offer more parking orbit alternatives. Firstly, addressing the complexity in the numerical continuation of quasi-periodic orbits, an adaptive continuation scheme was proposed. This approach ensures the overstep of the resonance region while maintaining torus accuracy by automatically adjusting the continuation step size and the number of discrete nodes representing the torus. Based on this scheme, we computed quasi-periodic families near the 2∶1 DRO for both configurations in the BCR4BP and conducted a comprehensive analysis of their stability characteristics. The simulation results demonstrate the efficacy of the proposed method in differentiating and handling issues related to insufficient sampling orders and resonance singularities, yielding a more complete set of orbit families.