Quasi-periodic orbits near 2∶1 resonant DRO in the four-body problem

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.