The recent discoveries of natural resources on (and beneath) lunar surface has rekindled the interest about the Moon by institutional and private investors. The exploitation of these resources is representing a boost in commercial opportunities and an enabler for more distant ventures like journey to Mars. In order to support the incoming mission on our natural satellite, a continuous and reliable lunar positioning and timing system is considered an essential infrastructure to be deployed. Among the different solutions enabling the provision of a Navigation service, a GNSS-like solution can be considered also for the Lunar Mission. GNSS System relies on constellation of satellites broadcasting navigation signals to the users. Constellation design must consider some specific factors with the aim of optimizing navigation performance such as availability, number of satellites simultaneously in view of the users, achievable PDOP (Position Dilution of Precision), station keeping costs, etc. Different types of constellations can be considered: Walker, Elliptical Lunar Frozen Orbits (ELFO), Halo, hybrid constellations, etc. This work focuses on the Halo orbits with the aim of defining an optimal Halo constellation suitable for supporting and delivering a navigation service on the Moon. In the Earth-Moon binary system, simplifying the gravitational model in a Circular Restricted Three-Body Problem (CRTBP), there are some points on the orbital plane of the Moon (libration points or Lagrange points) where a third body (much less massive) could maintain a stable position w.r.t. Earth and Moon. It is possible to design some unique orbits near these points, among which Lissajous and Halo for L1 and L2, taking benefits from some space missions' heritage. Halo orbits in proximity of Earth-Moon L1 and L2 exploit the position of two collinear libration points, which maintain a direct line of sight with both sides of the Moon over time, significantly reducing the probability of solar eclipses caused by the Earth or by the Moon. The greater distances from the surface w.r.t. lunar orbits lead to larger areas covered by one satellite deployed in a Halo orbit, while the existence of Northern and Southern families gives the possibility to cover both polar and equatorial regions. In order to perform the analysis, a single shooting and a multiple shooting differential correctors have been implemented to determine CRTBP solutions of interest and to convert them in trajectories in the ephemeris model. The scope of this article is to show the performance of a GNSS-like constellation deployed in Halo orbits around Earth-Moon L1 and L2 collinear libration points. Different phases have been considered, from a minimum number of satellites able to provide a local PNT service on the South Pole, defined as Initial Operational Capability (IOC), to a final, extended constellation able to cover the whole lunar surface, defined as Final Operational Capability (FOC). The main key drivers for Halo constellation design have been the PNT service availability over the Lunar South Pole (for the IOC Phase) and over the full moon surface (for the FOC Phase) and the related accuracy performance associated with the constellation geometry properties (in terms of PDOP). The PNT service availability has been considered as the percentage of time for which at least four satellites are in view with a minimum elevation angle of 5 degrees across the entire region of interest. A dedicated tool has been developed in MATLAB in order to perform the orbit definition (single shooting algorithm), propagation (multiple shooting algorithm) and control strategy. The paper will show the used methodology and the main results of this analysis.
