Missions towards NEAs with Departure from Lagrangian Points L4 and L5

The interest in space missions involving the equilateral Lagrangian points is expected to grow in the near future. In fact, these points represent a strategic location both for space observation and, as considered in this thesis, for the departure of missions towards Near-Earth Asteroids. Among these small bodies there is a huge number of Potentially Hazardous Objects —PHOs—, which may impact the Earth with serious consequences. The study of such objects is the first crucial step for the risk mitigation of such an undesired event. The rendezvous with a PHO is essential to study the properties of the body and to monitor its orbit characteristics. Only with the aforementioned inspections it is possible to evaluate the risk connected to the eventual impact of the object and to define the necessity for an active intervention to modify its orbit. It comes without saying that the optimization of trajectories towards Near-Earth Asteroids is of extreme importance, given the considerations highlighted. In this thesis the absolute importance of missions towards Near-Earth Asteroids has been combined with the trend of exploiting the advantageous location of the equilateral Lagrangian points. An indirect method, based on the Optimal Control Theory, is adopted to maximize the payload fraction, thus minimizing the propellant consumption. The analyzed missions use electrical propulsion and leverage an Earth gravity assist manoeuvre, to bring the satellite to the Near-Earth Asteroid orbit with the smallest propellant throughput. The reference mission considers CubeSats that could be left at the starting Lagrangian point as a piggyback of a larger primary spacecraft. Leveraging the advantageous starting position and its inherent stability, the satellites could wait for the optimal time to begin their mission. Firstly, an overview of the characteristics of Near-Earth Asteroids is carried out. In second place, the essential elements of orbital mechanics and space propulsion, necessary to fully understand the analyzed problem, are recalled. Then, the general characteristics of indirect methods of space trajectories optimization, exploiting the Optimal Control Theory, are described. Thus, it is possible to formulate the problem and how such theory can be applied to its solution. In the end, the results are reported.