Mission Applications for Continuous-Thrust Spacecraft within a Three-Body Problem

This Thesis presents a study of possible mission scenarios for spacecraft propelled by continuous-thrust propulsion systems within a gravitational model of three bodies. The first Part concerns the study of the existence, stability, and control of Artificial Equilibrium Points. A general mathematical model (referred to as Generalized Sail) for the propulsive acceleration of a spacecraft subjected to a continuous and purely radial thrust is proposed. Based on the choice of a coefficient related to the propulsion system and of a parameter (the lightness number) related to the system performance, the propulsive acceleration model encompasses the behavior of different propulsion systems, like Solar Sails, Electric Solar Wind Sails, Magnetic Sails and Electric Thrusters. The continuous propulsive acceleration provided by a Generalized Sail is used to create and maintain Artificial Equilibrium Points. The loci (curves in the space) and the stability of such Artificial Equilibrium Points are discussed both in the Circular and in the Elliptic Restricted Three-Body Problem. Even though similarities between the two problems exist in the description of the geometrical loci, some differences in the stability analysis are shown. Moreover, a Generalized Sail is required to provide a varying lightness number in the elliptical problem to maintain an Artificial Equilibrium Point. The stabilization and control of a interesting class of Artificial Equilibrium Points, the L1-type points, is also discussed to show how a simple Proportional-Derivative feedback control logic, based on the variation of the lightness number, is able to guarantee asymptotical stability. In this respect, two control techniques for Solar Sail based spacecraft are examined: Solar Balloon and Electrochromic Material Panels. A Solar Balloon can provide a passive Proportional control, however, if manufactured with the current technology, it is shown to be unable to stabilize an Artificial Equilibrium Point. Electrochromic Material Panels are, instead, used for an active control system. A suitable dimensioning of such a system provides asymptotical stability for the Artificial Equilibrium Points, when saturation effects are counteracted by means of an anti-windup compensator. In the first Part, the Artificial Equilibrium Points created by an Electric Solar Wind Sail are also investigated. In this case, the radial thrust hypothesis is left, and the Electric Solar Wind Sail is assumed to maintain a constant attitude with respect to an orbital reference frame. This increases the number of attainable Artificial Equilibrium Points, and the loci now become space regions, whose extension depends on the thrust capabilities of the spacecraft. For those points a linear stability analysis is also provided. In the second Part, new frozen orbits are sought for Solar Sail based spacecraft around an oblate planet and under the effects of the Sun’s gravitational attraction. An averaging method of the Hamiltonian that describes the spacecraft motion is used to find new families of displaced frozen orbits, varying the sail lightness number. These orbits are examined both analytically and numerically when Mercury is the reference planet.