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The pericenter shift of a binary system represents a suitable observable to test for possible deviations from the Newtonian inverse-square law in favor of new weak interactions between macroscopic objects. We analyzed 13 years of tracking data of the LAGEOS satellites with GEODYN II software but with no models for general relativity. From the fit of LAGEOS II pericenter residuals we have been able to obtain a 99.8% agreement with the predictions of Einstein's theory. This result may be considered as a 99.8% measurement in the field of the Earth of the combination of the γ and β parameters of general relativity, and it may be used to constrain possible deviations from the inverse-square law in favor of new weak interactions parametrized by a Yukawa-like potential with strength α and range λ. We obtained |α| 1 · 10 −11 , a huge improvement at a range of about 1 Earth radius.PACS numbers: 04.80. Cc, 91.10.Sp, 95.10.Eg, 95.40.+s Tests for Newtonian gravity and for a possible violation of the weak equivalence principle are strongly related and represent a powerful approach in order to validate Einstein's theory of general relativity (GR) with respect to alternative theories of gravity and to tune, from the experimental point of view, gravity itself into the realm of quantum physics. Moreover, new long range interactions (NLRIs) may be thought of as the residual of a cosmological primordial scalar field related with the inflationary stage (dilaton scenario) [1]. Twenty-four years ago, the possibility of a fifth force of nature prompted new experimental investigation of possible deviations from the gravitational inverse-square law [2]. In fact, the deviations from the usual 1/r law for the gravitational potential would lead to new weak interactions between macroscopic objects.Interestingly, these supplementary interactions may be either consistent with Einstein's equivalence principle or not. In this second case, nonmetric phenomena will be produced with tiny, but significant, consequences in the gravitational experiments [3]. The feature of such interactions, which are predicted by several theories, is to produce deviations for separations of masses ranging through several orders of magnitude, starting from the submillimeter level up to the astronomical scale. Among the various techniques useful for the search of this additional physics to the various scales, the accurate measurement of the pericenter shift of binary systems may be used to test for a NLRI with a characteristic range comparable with the system semimajor axis [4].These very weak NLRI are usually described by means of a Yukawa-like potential with strength α and range λ and transmitted by a field of very small mass µ = /λc. If G ∞ represents the gravitational constant, M ⊕ and m s the mass of the primary body and of the satellite, r their separation, c the speed of light and the reduced Planck constant, we can write:where the strength α depends both on the mass-energy content of the sources and on their coupling strengths, K ⊕ and K s , respectively.In...

In this work, the Laser Ranged Satellites Experiment (LARASE) is presented. This is a research program that aims to perform new refined tests and measurements of gravitation in the field of the Earth in the weak field and slow motion (WFSM) limit of general relativity (GR). For this objective we use the free available data relative to geodetic passive satellite lasers tracked from a network of ground stations by means of the satellite laser ranging (SLR) technique. After a brief introduction to GR and its WFSM limit, which aims to contextualize the physical background of the tests and measurements that LARASE will carry out, we focus on the current limits of validation of GR and on current constraints on the alternative theories of gravity that have been obtained with the precise SLR measurements of the two LAGEOS satellites performed so far. Afterward, we present the scientific goals of LARASE in terms of upcoming measurements and tests of relativistic physics. Finally, we introduce our activities and we give a number of new results regarding the improvements to the modelling of both gravitational and non-gravitational perturbations to the orbit of the satellites. These activities are a needed prerequisite to improve the forthcoming new measurements of gravitation. An innovation with respect to the past is the specialization of the models to the LARES satellite, especially for what concerns the modelling of its spin evolution, the neutral drag perturbation and the impact of Earth's solid tides on the satellite orbit.

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