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One hundred years ago, a collaboration between the astronomer and mathematician Josef Lense, and the physicist Hans Thirring, opened the experimental verification to one new, and very important, prediction of Einstein’s novel theory of General Relativity: Gravitomagnetism. The problem was posed by Thirring in terms of the integration of the equations of motion of a test body into the field of a rotating mass by means of the perturbation theory, a branch of mathematical physics in which Lense was very expert. Their results were applied to the orbit of the planets and of their moons. Lense and Thirring pointed out that, in 1918, the new effects of Einstein’s theory were too small to be measured accurately within the solar system [1]. Today, 100-yr after the original papers of Lense and Thirring, despite the improvements in the knowledge of the ephemerides of the orbits of planets and moons, the measurement of the Lense-Thirring effect, albeit noticeably improved, has not yet been achieved with sufficient accuracy in the solar system [2,3]. Conversely, more precise results have been obtained in the field of the Earth by means of measurements of the orbit of laser-ranged satellites [4-7]. However, for these measurements a refined and robust error budget, based on a reliable assessment of the systematic sources of error, it has not yet been fully achieved. In this context, we present the current results obtained by the LARASE experiment for the measurement of the Lense-Thirring precession on the combined orbits of the LAGEOS, LAGEOS II and LARES satellites. The goals of the LAser RAnged Satellites Experiment (LARASE) are to provide precise and accurate measurements of the predictions of General Relativity in its weak-field and slow-motion limit. The test particles of LARASE are the above satellites, precisely tracked by means of the powerful Satellite Laser Ranging technique [8]. A peculiarity of LARASE is to develop new models to better manage the subtle effects that arise from the complex non-gravitational perturbations. After a description of the work performed to model the spin evolution of these satellites, and of the thermal effects due to the solar radiation pressure, we focus upon a recent precise and accurate measurement of the Lense-Thirring precession with the two LAGEOS and the LARES satellites. The details of the precise orbit determination of the satellites, the role of the unmodelled periodic effects and of the systematic errors related to the deviation from the spherical symmetry of the Earth's mass distribution will be discussed. References [1] Lense, J., Thirring, H. Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys. Z., 19, 156, 1918. [2] Iorio, L., Lichtenegger, H.I.M., Ruggiero, M.L., Corda, C., Phenomenology of the Lense-Thirring effect in the Solar System. Astrophysics and Space Science, Vol. 331, 2, 351–395, 2011 [3] Iorio, L., The Solar Lense-Thirring effect: perspectives for a future measurement. WSPC proceedings 2016. The Fourteenth Marcel Grossmann Meeting, 2017. [4] Ciufolini, I., Pavlis, E.C., A confirmation of the general relativistic prediction of the Lense-Thirring effect, Nature 431, 958, 2004. [5] Lucchesi, D.M., The Lense-Thirring effect measurement and LAGEOS satellites orbit analysis with the new gravity field model from the CHAMP mission. Adv. Space Res. 39(2), 324, 2007. [6] Ciufolini, I., Paolozzi, A., Pavlis, E.C., Koenig, R., Ries, J., Gurzadyan, V., Matzner, R., Penrose, R., Sindoni, G., Paris, C., Khachatryan, H., Mirzoyan, S., A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model. Measurement of Earth's dragging of inertial frames, European Physical Journal C 76, 120, 2016. [7] Lucchesi, D.M., Magnafico, C., Peron, R., Visco, M., Anselmo, L., Pardini, C., Bassan, M., Pucacco, G., Stanga, R., The LARASE research program. State of the art on Modelling and Measurements of General Relativity effects in the field of the Earth: a preliminary measurement of the Lense-Thirring effect. In 2017 IEEE International Workshop on Metrology for AeroSpace (MetroAeroSpace), pp. 131-145, 2017. [8] Pearlman, M.R., Degnan, J.J. and Bosworth, J.M., The international laser ranging service. Adv. Space Res. 30, 135 (2002).

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In order to ensure precise as well as accurate measurements (i.e. based on a careful assessment of the systematic errors) of relativistic gravity in the field of the Earth, it is necessary to have a reliable dynamical model for the orbit determination of a satellite. This model is used to properly handle the main perturbations on the orbit of a satellite, in such a way to have the smallest differences between the predictions of the model for the satellite position in space with respect to the observations provided by the Satellite Laser Ranging (SLR) technique [1]. These differences are the residuals in the position of a satellite with respect to a network of ground stations, differences that are minimized in a least-squares fit of the orbit. The LAser RAnged Satellites Experiment (LARASE) aims to provide precise and accurate measurements of the predictions of Einstein’s theory of General Relativity (GR) in its weak-field and slow-motion (WFSM) limit [2]. The proof masses of LARASE are the LAGEOS and LARES satellites, precisely tracked by means of the powerful SLR technique. A peculiarity of LARASE is to develop new models to better handle the effects that arise from the subtle and complex non-gravitational perturbations (NGP). These NGP are responsible of long-term perturbations on the orbit that may alter the measurement of its secular precession produced by the gravitoelectric and gravitomagnetic fields of GR [3,4,5]. We focus on the activities carried out for the development of new models for the NGP and on the analysis of the main sources of systematic errors due to the deviation of the Earth's mass distribution from the spherical symmetry. Finally, we provide the result for a recent precise, and accurate, measurement of the Lense-Thirring precession on the combined orbits of LAGEOS, LAGEOS II and LARES. The goals of LARASE in term of future relativistic measurements in the WFSM limit of GR will be discussed together with the new constraints that can be achieved for the predictions of alternative theories of gravitation. References [1] Pearlman, M.R., Degnan, J.J. and Bosworth, J.M., The international laser ranging service. Adv. Space Res. 30, 135 (2002). [2] Lucchesi, D., Anselmo, L., Bassan, M., Pardini, C., Peron, R., Pucacco, G., Visco, M., Testing the gravitational interaction in the field of the Earth via satellite laser ranging and the Laser Ranged Satellites Experiment (LARASE), Class. Quantum Grav. 32, 155012, 2015. [3] Einstein, A., Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik, 354, 769–822, 1916. [4] de Sitter, W. On Einstein’s theory of gravitation and its astronomical consequences. Second paper. Mon. Not. R. Astron. Soc., 77, 155–184, 1916. [5] Lense, J., Thirring, H. Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys. Z., 19, 156, 1918.

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