Solar sailing trajectory optimization for escape maneuvers and transfers in the Sun-Earth-Moon system

Solar sailing is an emerging propulsion technology that utilizes the momentum transfer from solar photons impinging on the sail to propel spacecraft without the need for stored propellant. The aim of this thesis is to analyze the reachability of the photo-gravitational libration point L1 of the Sun-Earth-Moon system, by employing a spacecraft propelled solely by a solar sail departing from a Low Earth Orbit (LEO). To do so, the overall mission is split into two phases: an Escape phase from the Earth-Moon system, and a transfer phase from the Earth-Moon system to L1. In the first part of the mission analysis, the present work answers the following question: What is the minimum altitude from which it is possible to escape from Earth? This problem is addressed by considering the effects of atmospheric drag and a near-optimal controller. Results are provided in terms of time of flight and minimum departure altitude for multiple values of sail’s mass-to-area ratio and departure time. In the second part of the mission analysis, the goal is to find the optimal transfer trajectory towards the desired point, in terms of time of flight and the required ΔV for nullifying the spacecraft momentum. The thesis opens with a comprehensive description of the dynamic models governing the motion of a satellite endowed with a solar sail, as well as the perturbative accelerations taken into account. Firstly, in order to consider the combined attraction of Sun, Earth and Moon, the BiCircular Restricted 4 Body Problem (BCR4BP) is described. It constitutes a simplified version of the more general 4 body problem and it is based on the assumption that the Earth and Moon move in a circular motion around their mutual barycenter B1, and that the Sun and B1 rotate around the barycenter of the entire system, B2, on another coplanar circular path. Subsequently, the solar radiation pressure model is detailed, exploring two different mathematical representations of the solar sail's thrust: the simpler perfectly reflecting sail, and a more accurate optical model, where the optical properties of existing sails are taken into account. In order to complete the modeling of the operating environment, routines were also implemented to calculate the air density at the current altitude for aerodynamic drag evaluation, the perturbations caused by Earth’s oblateness, and the effects of eclipses. After outlining the external factors that influence the satellites' motion, two different control laws are derived, one for the escape from the Earth-Moon system, and one for the transfer to L1. For the first part of the mission, an energy-gain control law is derived for both models of solar sail thrust, considering the combined effect of the solar radiation pressure and the atmospheric drag. The results are summarised in the form of colourmaps relating the sail’s mass-to-area ratio and the departure time to the minimum height at which that specific sail is able to overcome the disturbances, and the time of flight required for the maneuver. As regards the transfer to L1, in this case the ideal trajectory is investigated via optimal control theory, by solving the Euler-Lagrange equation for the considered dynamic system.