A new model for the analysis of low-thrust trajectory design in the Earth–Moon system

This study presents a new model for designing low-thrust transfer trajectories in the Earth–Moon Circular Restricted Three-Body Problem (CRTBP) incorporating a continuation fractional potential to model Earth’s non-spherical gravitational field. The proposed formulation extends the classical CRTBP by introducing a modified potential function that enhances numerical stability and expands the convergence domain for trajectory optimization. The optimal control framework is established using Pontryagin’s Minimum Principle for minimum-time transfers. Simulation results for transfers from Geostationary Orbit (GEO) to the L4 planar Lyapunov orbit demonstrate that the continuation fractional potential significantly improves trajectory performance compared to the spherical Earth model. For instance, with a thrust magnitude of 0.66 N, the proposed model achieves a 12.6% reduction in transfer time, a 48.7% decrease in computational time, and a 12.4% reduction in fuel consumption, while completely eliminating trajectory divergence. Enforcing the terminal Hamiltonian constraint H(tf)=0 yields optimal trajectories with minimum transfer time (7.5–13.7 days for thrust levels of 1.98–1.02 N), whereas relaxing this constraint accelerates computation by 28% but increases transfer duration and fuel use. Overall, the integration of the continuation fractional potential within the CRTBP framework offers a robust and computationally efficient method for low-thrust trajectory design, particularly beneficial for long-duration cislunar missions and rapid preliminary mission analysis.