Measuring the Lense-Thirring precession of the orbits of laser-ranged satellites: State of the art and perspectives from the LARASE experiment

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.