This work deals with the structure of the lunar Weak Stability Boundaries (WSB) in the framework of the restricted three and four body problem. Geometry and properties of the escape trajectories have been studied by changing the spacecraft orbital parameters around the Moon. Results obtained using the algorithm definition of the WSB have been compared with an analytical approximation based on the value of the Jacobi constant. Planar and three-dimensional cases have been studied in both three and four body models and the effects on the WSB structure, due to the presence of the gravitational force of the Sun and the Moon orbital eccentricity, have been investigated. The study of the dynamical evolution of the spacecraft after lunar capture allowed us to find regions of the WSB corresponding to stable and safe orbits, that is orbits that will not impact onto lunar surface after capture. By using a bicircular four body model, then, it has been possible to study low-energy transfer trajectories and results are given in terms of eccentricity, pericenter altitude and inclination of the capture orbit. Equatorial and polar capture orbits have been compared and differences in terms of energy between these two kinds of orbits are shown. Finally, the knowledge of the WSB geometry permitted us to modify the design of the low-energy capture trajectories in order to reach stable capture, which allows orbit circularization using low-thrust propulsion systems.

The aim of this paper is to quantify the performance of a flat solar sail to perform a double angular momentum reversal manoeuver and produce a new class of two-dimensional non-Keplerian orbits. The problem is addressed in an optimal formulation and using a parametric approach. Two main difficulties must be properly taken into account. On one side the sail must perform a rapid reorientation maneuver when it approaches the Sun. It is shown by simulation that this assumption is reasonable. In second place the corresponding trajectories require high performance solar sails, that is, sails with a characteristic acceleration greater than 3 mm/s 2 . Such a value, although well beyond the currently available sail performance, is comparable (or even lower) to that required by the original H-reversal maneuvers.

To cite this version:DanieleAbstract This work proposes a Lunar Global Positioning System (LGPS) and a Lunar Global Communication System (LGCS) using two constellations of satellites on Lissajous trajectories around the collinear L 1 and L 2 libration points in the Earth-Moon system. This solution is compared against a Walker constellation around the Moon similar to the one used for the Global Positioning System (GPS) on the Earth to evaluate the main differences between the two cases and the advantages of adopting the Lissajous constellations. The problem is first studied using the Circular Restricted Three Body Problem to find out its main features. The study is then repeated with higher fidelity using a four-body model and higher-order reference trajectories to simulate the Earth-Moon-spacecraft dynamics more accurately. The LGPS performance is evaluated for both on-ground and in-flight users, and a visibility study for the LGCS is used to check that communication between opposite sides of the Moon is possible. The total V required for the transfer trajectories from the Earth to the constellations and the trajectory control is calculated. Finally, the estimated propellant consumption and the total number of satellites for the Walker constellation and the Lissajous constellations is used as a performance index to compare the two proposed solutions.

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