Optimal Ascent Trajectories to Sun-Synchronous Orbits via Indirect Methods

This research aims to optimize ascent trajectories for satellite launches into Sun-Synchronous Orbits (SSO) while minimizing propellant usage during launch to maximize payload capacity. The study evaluates various launch sites and directions, incorporating the multi-stage dynamics of the launch vehicle to accurately model the ascent trajectories and different mission launch times to evaluate performance in regard to the final local time of the ascending node (LTAN) that the insertion orbit should have. The optimization technique employs an indirect method rooted in optimal control principles and Pontryagin's Maximum Principle, aiming to identify a trajectory that maximizes the Hamiltonian, thereby minimizing propellant use. Considering the vehicle's proximity to Earth during launch and orbital insertion, the dynamical model incorporates Earth's gravitational effects and uses the Harris-Priester Atmospheric Density Model to accurately account for atmospheric drag under aerothermodynamic constraints. A tailored scenario was created to simulate the ascent of a launch vehicle aimed for insertion into a Low Earth SSO. This simulation was structured to determine the necessary co-states for deriving optimal control solutions. Results indicate that variations in launch site significantly influence propellant use, thereby impacting the payload capacity deliverable to orbit. Furthermore, although the optimal ascent trajectory exhibits consistent characteristics, it is significantly affected by the chosen atmospheric drag model and the specific local time of ascending node (LTAN) settings.