The Galileo for Science (G4S_2.0) project: Precise Orbit Determination for fundamental physics experiments with the Galileo satellites DORESA and MILENA.

G4S_2.0 is a new project funded by the Italian Space Agency which aims to perform measurements in the field of Fundamental Physics with the two satellites DORESA (E18) and MILENA (E14) of the Galileo-FOC constellation. These satellites, as the others of the constellation, have onboard accurate atomic clocks, but are characterized by an orbit with high eccentricity. After a general introduction to the main objectives of the G4S_2.0 project, the preliminary activities developed at IAPS-INAF in Rome regarding the Precise Orbit Determination (POD) of the satellites will be presented. The PODs will be performed with two different codes, GEODYN II (NASA/GSFC) and BERNESE (AIUB), with the main aim of performing measurements of the relativistic precession of the orbits and a new accurate measurement of the gravitational redshift. In particular, an accurate measurement of the overall precession of the pericenter of the orbit allows to verify the validity of the inverse square law of the distance for the gravitational interaction on a characteristic scale of about $14000 {km}$.