Escape and interplanetary trajectory optimization from Earth-Moon L2

This thesis is about trajectory optimization by means of an indirect method, based on optimal control theory. Space exploration is constantly increasing and Lagrangian points proved to be strategic locations for either unmanned scientific missions or human outposts thanks to the natural stabilization created by the balance of gravitational and centripetal forces. The study of optimal trajectories from these particular locations is therefore becoming increasingly necessary. A medium-size spacecraft is considered in the present study, whose final objective is to maximize final mass of the spacecraft, thus reducing fuel consumption as much as possible. 4-body gravitational influence with solar radiation pressure as perturbation, is considered in the dynamic model, using JPL ephemeris to track celestial body positions. The spacecraft is seen as a variable mass point. EME2000 is the adopted reference frame. Optimization code exploits Pontryagin's Maximum Principle (PMP) and basically solve a boundary values problem (BVP): a solution compliant with external constraints is sought perturbing the initial solution and adjusting values after error evaluation. The method results to be very sensitive to the trial solution used, enough to compromise convergence if not scrupulously chosen. Escape trajectories from Earth-Moon L2 and Interplanetary trajectories towards Near Earth Asteroid (NEA) are investigated in the study. Considering one-week apart starting times, during one Moon synodic period around Earth, and alternately imposing final time or final energy as constraints, an optimum value is manually detected. Escapes are initially sought as 2-phase (single burn), but 4-phase (2 burn) approach is also used when needed in order to maximize final mass. The results show that departure date, thus initial position of the spacecraft with respect to the Sun, has an influence on fuel consumption whether Sun perturbation acts in a positive or negative way. As far as interplanetary trajectories are concerned, one asteroid has been selected from a short-list, being in an early phase of the analysis. For target considered, a local optimum appeared among the initial times considered.