Analysis of the effects of orbital parameters and phase angle on missions to near-Earth asteroids

In this thesis will be analysed a strategy of optimization of trajectories for missions to near-Earth asteroids. Near-Earth Asteroids, also known as NEA, are a class of asteroids of sizes ranging from meters to tens of kilometres that orbit the Sun and whose orbits come close to that of Earth's, and this aspect makes them interesting, firstly in order to monitor their positions and predict eventual potential impacts with Earth. In addition, NEAs are interesting both from the perspective of studying the genesis of the Solar System and the life on our planet, and with the aim of a space economy also based on the extraction of the minerals they contain. With the continuous discovery of new NEAs through sky observations, employing electrical propulsion becomes advantageous. Unlike chemical propulsion, it significantly reduces propellant consumption, leading to a substantial savings in missions. The mission analysed in this thesis is scheduled to start at the beginning of 2028. A technique known as optimal control theory, with indirect methods of resolution of the fundamental equations, which are characterized by a significant numeric precision, with a low number of parameters and limited time of calculation, is used to optimise trajectories: through the definition of additional equations to be aggregated to the system of differential equations governing the problem, it is possible to minimise a cost function representing the parameter to be optimised, in this case the mass at the end of the journey. Using a list of asteroids with a close passage to Earth in the next few years, they were first ranked by scores and then trajectories were optimised to find the optimal launch window to maximise the final mass. Furthermore, it was analysed how the variation of orbital parameters and phase angle impact trajectory optimization, highlighting which asteroids may be easier to reach in terms of cost. The objective was to optimize the trajectory in a way that required the least amount of propellant, showcasing the practical application of the research findings.