Minimum-propellant low-thrust trajectory optimization for orbit lowering in LEO via indirect methods

The growing interest in low-altitude operations for scientific and commercial applications has strengthened the relevance of orbit-lowering campaigns in Low Earth Orbit (LEO). Operating in this environment offers substantial advantages, including enhanced spatial resolution for Earth observation and natural compliance with space debris mitigation guidelines. However, the significant atmospheric drag and strong coupling between orbital and aerodynamic dynamics make trajectory optimization a complex task. This work addresses the problem of optimizing a low-thrust orbital descent using an indirect approach based on Optimal Control Theory (OCT). The governing equations are formulated as a Two-Point Boundary Value Problem (TPBVP), derived from the necessary conditions of optimality given by Pontryagin’s Maximum Principle. The resulting nonlinear system is solved iteratively through a Differential Correction (DC) procedure, which updates the initial conditions until the prescribed terminal constraints are satisfied. The dynamical model is based on a medium-fidelity Two-Body Problem (2BP) including atmospheric drag effects computed through the NRLMSISE-00 empirical model. The numerical implementation has been developed in Python with particular attention to convergence stability and sensitivity to initial conditions. The results confirm that the indirect optimization framework effectively identifies minimum-propellant trajectories for controlled orbit lowering under low-thrust propulsion. The methodology developed in this thesis provides a robust foundation for future studies focused on guidance, control, and end-of-life operations in LEO and Very Low Earth Orbit (VLEO) regimes.