Low Thrust Trajectory Design Using A Semi-Analytic Approach

Space missions that use low-thrust propulsion technology are becoming increasingly popular since they utilize propellant more efficiently and thus reduce mission costs. However, optimizing continuous-thrust trajectories is complex, time-consuming, and extremely sensitive to initial guesses. Hence, generating approximate trajectories that can be used as reliable initial guesses in trajectory generators is essential. This paper presents a semi-analytic approach for designing planar and three-dimensional trajectories using Hills equations. The spacecraft is assumed to be acted upon by a constant thrust acceleration magnitude. The proposed equations are employed in a Nonlinear Programming Problem (NLP) solver to obtain the thrust directions. Their applicability is tested for various design scenarios like orbit raising, orbit insertion, and rendezvous. The trajectory solutions are then validated as initial guesses in high-fidelity optimal control tools. The usefulness of this method lies in the preliminary stages of low-thrust mission design, where speed and reliability are key.