The Galileo for science (G4S_2.0) project: precise orbit determination for fundamental physics and space geodesy

G4S_2.0 is a project funded by the Italian Space Agency aiming to perform a set of Fundamental Physics measurements using the two Galileo FOC satellites GSAT0201 (Doresa) and GSAT0202 (Milena). Indeed, the orbits of these satellites are characterized by a relatively high eccentricity, about 0.16, which represents a good prerequisite for a series of tests and measurements concerning the predictions of different theories of gravitation, as compared with the General Relativity (GR) ones. The main objectives include a new measurement of the gravitational redshift effect of the on-board atomic clocks --- thanks to its modulation with the orbital period due to the high eccentricity of the orbits --- and the measurement of the main precessions of relativistic origin, primarily the Schwarzschild one. To achieve these significant results, and possibly improve the current constraints of several theories of gravitation with respect to GR, it is of fundamental importance to take a step forward --- compared to the state of the art --- in the reliability of the dynamic model used for the orbits of the satellites and, as a direct consequence of this, in their precise orbit determination (POD). In this context, non-gravitational perturbations (NGPs) are the most subtle and difficult to model because of the complex shape of the Galileo satellites and their attitude law. In this regard, the main challenge is represented by a more refined and reliable model for the direct solar radiation pressure (SRP), the largest NGP on Galileo satellites, as well as on every satellite of every GNSS constellation. Our final goal is to build a finite element model (FEM) of the Galileo FOC spacecraft, as refined as possible, and apply a dedicated raytracing technique to it to compute the perturbing accelerations due to radiation pressure. In view of this, we have already developed a 3D-CAD model of the spacecraft. As an intermediate step, we have built a Box-Wing (BW) model based on the relatively poor information presently available on the geometrical and physical properties of the spacecraft. This BW model has been used to compute the perturbing accelerations due to the direct SRP and to the Earth's albedo and infrared radiation. The results obtained for the accelerations, to be included in the POD process, will be presented in various cases. Then, by computing the residuals in the orbital elements, it will be possible to verify the goodness of the POD results and observe the expected progressive improvement starting from the BW model towards the FEM one. The present analyses were made using the nominal attitude law of the Galileo FOC spacecraft; the application of this law will be discussed in the case of satellites in elliptical orbit. We finally highlight that the results of G4S_2.0 in terms of POD improvements are particularly useful for all applications of the Galileo FOC satellites in the fields of space Geodesy and Geophysics.