Thousands of space debris objects remain in space after decades of spaceflight without sustainability regulations. Some of these objects de-orbit naturally, but not objects in the geostationary region for which active debris removal is needed. This thesis presents the case of geostationary debris removal using solar sailing, a propulsion method where no propellant is consumed, which allows for repeatable debris removal. A focus is given to find minimum-time trajectories between the geostationary region and a so-called ‘graveyard orbit’ and back. Optimisation using numerical methods is time-consuming, as these trajectories include hundreds of orbit revolutions. This work utilises analytical control methods instead to determine solar-sail control, specifically the ’Accessibility-and-deficit blending method’ based on locally optimal steering laws. Resulting mission times are compared with literature for validation, and a catalogue of mission time is found for a wide range of mission parameters, including additional thrust from a solar-electric propulsion engine.

This thesis demonstrates the usability of differential dynamic programming (DDP) to obtain, for the first time, globally optimal Earth-centred solar-sail trajectories. To this end, DDP is combined with a global optimisation heuristic, monotonic basin hopping. The dynamical model is implemented as a two-body problem, augmented with an ideal solar-sail reflectance model and accounts for eclipses. The numerical performance of the optimisation algorithm is enhanced by integrating the sailcraft state in modified equinoctial elements and performing a Sundman transformation to change the independent variable from time to the true anomaly. The DDP algorithm is proven to be robust for trajectories extending up to 500 revolutions and, compared to known locally optimal steering laws, allows to obtain more or equally optimal solutions. The latter is demonstrated in this paper through a set of test cases that range from theoretical scenarios to realistic mission applications, including increasing the specific orbital energy of NASA’s upcoming ACS3 mission. Additionally, the algorithm's ability to cope with different optimisation settings, perturbing accelerations and constraints is demonstrated.