State of the art of the measurement of the Lense-Thirring effect after a century from its formulation

The motion of passive laser-ranged satellites along nearly geodesics of spacetime may be a posteriori reconstructed through a careful modelling of the main non-gravitational perturbations (NGP) acting on their surface. The Laser Ranged Satellites Experiment (LARASE) [1] aims to test the predictions of Einstein's theory of general relativity (GR) in its weak-field and slow-motion limit with respect to those of alternative theories of gravitation. An effort of the LARASE activities is to strongly improve the modelling of the NGP on the two LAGEOS and LARES satellites in such a way to further improve the orbit determination of these satellites and extract from their orbital residuals the sough for relativistic effects. Among some of the recent activities of LARASE regarding the NGP, we focus upon the development of a new model for the spin evolution of the satellites [2] and that for the subtle effects on their orbit produced by the thermal thrust perturbations. Concerning the gravitational perturbations, we discuss our improvements in the knowledge of the even zonal harmonics coefficients based on a re-analysis of GRACE data. With all this information we provide our results for a new measurement of the Earth's gravitomagnetic effect based on the analysis of the Lense-Thirring precession on the combined orbits of the LAGEOS, LAGEOS II and LARES satellites. We provided a precise and accurate measurement of the Lense-Thirring precession. Gravitomagnetism plays a special role in Einstein's geometrodynamics, it describes the curvature of spacetime produced by mass-currents, with important consequences in the high-energy astrophysical aspects of the theory as well as for its possible cosmological consequences related with Mach's principle.