Optimization of trajectories to Near-Earth asteroids

The study of Near-Earth asteroids (NEAs) and potential interplanetary transfers to them is crucial for exploration, the extraction of resources useful to humanity and planetary defence. Indeed, their proximity to Earth, in addition to making them accessible via relatively simple trajectories, turning them into a potential resource for humanity, can also pose a threat due to potential collisions with the planet. Regarding this latter aspect, asteroid 2024 YR4, discovered in December 2024, has attracted particular interest in recent months due to its orbit and initial probability of collision with Earth. To date, the possibility of an impact between the planet and the asteroid has been ruled out, although a minimal possibility of collision with the Moon remains. The purpose of this thesis is to research and analyse trajectories toward asteroid 2024 YR4 using indirect methods, with the goal of identifying solutions that allow for a transfer with minimal propellant consumption. The spacecraft under consideration has an initial mass of 1000 kg and is equipped with a low-thrust electric propulsion system. Specifically, the thesis focuses on the study of both direct trajectories and those involving Earth flyby. As the results show, flyby solutions are those that allow for the greatest fuel savings, since they effectively exploit the Earth's gravitational field. Among the solutions analysed, which envisage a mission duration of between 3 and 4.5 years, those with an arrival date prior to the possible impact with the Moon on December 22, 2032, are of particular interest. The optimization was performed using a Fortran code provided by the Polytechnic of Turin. After introducing the basic concepts related to asteroids, orbital mechanics and space propulsion, the thesis presents the optimal control theory and the mathematical model adopted. In the final part, the solutions obtained are illustrated, analysed and compared in detail.