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(t_f)=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.