Analytical Design of Low-Thrust V-infinity Leveraging

V-infinity leveraging (VIL) is a well-established technique for designing highly efficient interplanetary trajectories. However, for its application to low-thrust propulsion systems, which are increasingly central to modern space missions, the analytical theory remains poorly understood. This work develops a comprehensive analytical framework to guide the design and optimization of continuous-thrust VIL maneuvers. A closed-form optimal steering law is first derived to locally maximize the rate of change of the hyperbolic excess velocity (ν_∞). Based on this law, a universal analytical efficiency metric is formulated, which is proven to depend solely on the spacecraft’s instantaneous radial distance and the ν_∞ magnitude. This metric facilitates the rigorous classification of optimal thrust programs and the analytical determination of switching conditions between thrust and coast arcs. Furthermore, a novel semi-analytical model is introduced to accurately propagate the secular trajectory evolution. The proposed framework is poised to significantly accelerate the preliminary design and trade-space exploration of complex low-thrust missions, ultimately enabling more ambitious scientific exploration of the solar system.