The LARASE spin model of the two LAGEOS satellites and of LARES

Satellite Laser Ranging (SLR) represents a very important technique of the observational space geodesy. In fact, Lunar Laser Ranging, Very Long Baseline Interferometry, Global Navigation Satellite Systems, Doppler Orbitography and Radiopositioning Integrated by Satellite, together with SLR constitute the Global Geodetic Observing System (GGOS). In the context of the GGOS activities, improvements in technology and in modeling will produce advances in geodesy and geophysics as well as in General Relativity (GR) measurements. Therefore, these important research fields are not independent, but tightly related each other. The LARASE (LAser RAnged Satellites Experiment) research program has its main objectives in tests and measurements of Einstein's theory of GR via a Precise Orbit Determination (POD) from a set of geodetic satellites. In order to reach such goals by means of very precise measurements of a number of relativistic parameters (and, at the same time, to provide a robust and unassailable error budget of the main systematic effects), we are also reviewing previous models and we are developing new models of the main perturbations (both gravitational and non-gravitational) that act on the orbits of the two LAGEOS satellites and on that of LARES. Within this paper we focus on modeling the spin vector of these satellites. The spin knowledge, both in orientation and rate, is of fundamental importance in order to correctly model the thermal effects acting on the surface of these satellites. These are very important non-gravitational perturbations (NGP) that produce long-term effects on the orbit of the cited satellites, especially for the two LAGEOS, and improvements in their modeling will be very useful both in the field of GR measurements and in those of space geodesy and geophysical applications as said above. Indeed, the current RMS of the range residuals of the LAGEOS satellites, obtained by the Analysis Centers of the International Laser Ranging Service, is at the level of a few cm since 1992, down to a cm or less during last years. However, because of the incompleteness of the dynamical models of the orbit of the satellites, empirical accelerations have been strongly used to reach such results. In this context, a step forward in the models developed for the NGP will be very useful to avoid the need of empirical accelerations and it also represents an essential prerequisite to reach a sub-mm precision in the RMS of the SLR range residuals and the corresponding benefits in geophysics and geodesy, as for stations coordinates knowledge, Earth's geocenter and reference frame realization. The paper will focus upon the improvements we obtained with respect on previous models of the spin of the two LAGEOS satellites based on averaged equations for the external torques in the rapid-spin approximation, as well as in a new general model that we developed and based on the resolution of the full set of Euler equations.