Escape maneuvers from Sun-Earth L2 Lagrangian Point with electric propulsion

In recent years interest in space exploration is growing fast. The synergistic commitment between many nations is allowing an impressing growth in terms of technology, which expands the boundaries of what humankind can achieve. With the ISS, humans have set a fundamental step for the understanding and study of how the human body reacts to low gravity and therefore has set an important step towards the possibility of long period mission in space. A new space run has begun to make space more accessible for all the people, thanks to the development of suborbital flights, but also less expensive, thanks to the progress in terms of rocket reusable first stage. Furthermore, with NASA’s mission Artemis, what seemed science fiction a few years ago is now becoming reality. A new human outpost will be settled on the Moon and a Lunar Orbital Platform-Gateway (LOP-G) will be placed on L2 of the Moon-Earth system. The interest in L2 has therefore increased again, not only in the Earth-Moon system but also in the Sun-Earth system. The second Lagrangian point is expected to be the most suitable point where to place the new Comet Interceptor mission. This mission is an ESA-JAXA collaboration, that aims to leave a spacecraft at L2 of Sun-Earth system, where it will wait for a suitable target. Once the target will be found, then the spacecraft will travel to the objective until the three modules, which composed the Comet Interceptor spacecraft, separate a few weeks prior to intercepting the comet. This mission is very ambitious and will help to explore how comet-like bodies form and evolve in other star systems. The study of evasion maneuvers from L2 became fundamental for future missions, L2 is also ideal for astronomy because a spacecraft is close enough to readily communicate with Earth; can keep Sun, Earth and Moon behind the spacecraft for solar power and provides a clear view of deep space. A small-sat could be left at the Lagrangian point as a piggyback of a larger primary spacecraft and then can perform the evasion maneuver that will be investigated in this thesis. This thesis aims to describe the numerical and physical aspects of the optimization of the Escape maneuver from the Sun-Earth collinear Lagrangian point L2. The method utilized for the optimization process is an indirect method, based on the Optimal Control Theory, that aims to the maximization of the payload fraction through the minimization of the propellant consumption. At the beginning, an overview of past and future missions from L2 will be carried out. Secondly, a brief outline of orbital mechanics and space propulsion will be given, in order to furnish all the information necessary for a full understanding of the problem. Thirdly, the general characteristics of indirect methods of space trajectory optimization are described, with a focus on the Optimal Control Theory (OCT). Then, the model adopted will be introduced, with the presentation of the main perturbations present and the specification of the boundary conditions of the problem considered. In the end, the results are reported.