First results in testing gravity theories with SatoR-G

The main goal of the SaToR-G (Satellite Test of Relativistic Gravity) experiment is to test and verify gravity beyond the predictions of General Relativity (GR) by focusing on possible effects connected with "new physics" and foreseen by different alternative theories of gravitation. These theories may be both metric and non-metric in their consequences. This objective can be achieved by means of a Precise Orbit Determination of the two LAGEOS and LARES satellites based on an improved dynamical model of their orbits. This implies to consider these passive geodetic satellites as "quasi-ideal" proof masses and measuring the deviation of their trajectory from the pure geodesic motion predicted by GR. A very interesting aspect is represented by the possible existence of a new long-range interaction. This kind of effect in gravitation has some importance since it cannot be interpreted within the standard Parametrized Post-Newtonian formalism currently used in the weak-field and slow-motion limit of GR. Indeed, deviations of the gravitational potential from the Newtonian law would lead to new weak interactions between macroscopic objects that are predicted by several theories of gravity. For these theories, a Yukawa-like parameterization seems general at the lowest order of the interaction and in the non-relativistic limit, independently of the nature of the new field that contributes to mediate the gravitational interaction, that is, of a possible scalar, vector or tensor field. We first introduce the constraint on a Yukawa-like long-range force obtained in the case of LAGEOS II from a precise and accurate analysis of the long-term behavior of its orbit. We then show the possible constraints to alternative theories of gravitation that can be further deduced from this result.