Fundamental physics with the Galileo FOC satellites and the G4S_2.0 project

This Thesis has been developed within the Galileo for Science Project (G4S_2.0) since its beginning in 2021. The G4S_2.0 is an ongoing project developed under the auspices of the Italian Space Agency (ASI) in collaboration with the National Institute for Astrophysics (INAF) and Politecnico di Torino. The project has several goals in the field of Fundamental Physics by exploiting the Global Navigation Satellite System (GNSS) Galileo, in particular the Full Operational Capability (FOC) Constellation. The relatively high eccentricity (≃ 0.16) of the two FOC in elliptical orbits, GSAT0201 and GSAT0202, and the accuracy of their atomic clocks allow to measure the gravitational redshift and the relativistic precessions of the orbits. Furthermore, the analysis of the atomic clock data of the entire Galileo FOC constellation also allows us to probe the presence of DomainWall (DW) Dark matter in the Milky Way and to place severe constraints on their interaction with ordinary matter. This work outlines the state of the art of the G4S_2.0 activities necessary for the gravitational redshift and the relativistic precessions measurements and for Dark Matter constraints. For all these measurements, a fundamental point is to obtain a suitable satellite orbit solution by performing an accurate Precise Orbit Determination (POD) with a reliable estimate of the clock-bias of the onboard atomic clocks. This work presents the efforts to achieve this, starting with the development of a dynamical model to account for the complex effects of the non-gravitational perturbations, in particular those related to the direct solar radiation pressure, and performing dedicated PODs to test our results. Based on the PODs results, we requested a dedicated Satellite Laser Ranging campaign to the International Laser Ranging Service to improve the available number of laser observations, given their importance for some of the G4S_2.0 measurements. Regarding Dark Matter constraints, this work describes the strategy adopted to analyse the on-board atomic clock data, stressing the original statistical approach: a physical simulation pipeline is developed to simulate the interaction between a set of Galileo FOC satellites and a DW, allowing the study of the detection efficiency of the considered clock-network. Finally, we present our reflections and prospects for the future.