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The semi-empirical atmospheric density models widely used by the space community were mainly developed taking into account satellite drag measurements and other observations, either in situ and ground based, acquired at relatively low altitudes, mostly below 500-600 km, and in general below 1000 km. The launch of the Italian geodetic satellite LARES, in 2012, at the altitude of about 1450 km and with an inclination of 70 degrees, offered however the rare possibility of probing the atmosphere at such height. This spherical satellite, fully covered with corner-cube laser retro-reflectors, has the highest area-to-mass ratio of any artificial object launched so far, being therefore not well suited for detecting small non-gravitational forces, like atmospheric drag. However, the very high accuracy of its orbit determinations, made possible by the laser tracking technique, more than compensated its unfavorable area-to-mass ratio, and the signature of atmospheric drag was extremely evident in the measured semi-major axis decay. Such decay, observed since 2012, was therefore used to infer the neutral atmosphere drag at the height of LARES during a 7-year span of solar cycle 24, covering the solar maximum, the declining phase and the beginning of the minimum. These measurements were compared with the predictions of six semi-empirical density models (JR-71, MSIS-86, MSISE-90, NRLMSISE-00, GOST-2004, and JB2008), employed well outside of their typical application ranges. In general, their predictions resulted quite satisfactory, with uncertainties not so far from those already known at lower altitudes. This study was also supplemented by the simultaneous analysis of another spherical geodetic satellite, the Japanese Ajisai, just 50 km higher, but with an area-to-mass ratio nearly 20 times greater than that of LARES and a smaller inclination of 50 degrees. An attempt was also made to estimate the physical drag coefficients of both satellites, in order to derive the mean density biases of the models. None of them could be considered unconditionally the best, the specific outcome depending on solar activity and on the regions of the atmosphere crossed by the satellites. Moreover, during solar maximum conditions, an additional density bias, probably linked to the different high latitudes overflown by the satellites, was detected.

This presentation outlines the final results of the LARASE experiment and the on-going activities of the SaToR-G experiment.

This presentation outlines the role played by CNR-ISTI in the LARASE and SaToR-G experiments, in particular regarding the modeling of atmospheric drag.

Introduction to the LARASE and SaToR-G experiments and review of the LARASE results.

The acceleration due to the direct solar radiation pressure on LARES (LAser RElativity Satellite) represents the larger non-gravitational acceleration that acts on its orbit (about 1.2x10^-9 m/s^2). It is a factor of 3 smaller than that on LAGEOS satellites (LAser GEOdynamic Satellite) thanks to its smaller area-to-mass (A/M) ratio. However, despite the smaller A/M the acceleration due to the neutral atmosphere is a factor of 50 larger than that on the two LAGEOS satellites. This aspect radically changes the perspective with which the effects of the neutral drag should be considered for LARES, compared to what was done in the past for the LAGEOS satellites. Of course, this arises because of the much lower height of LARES (about 1450 km) with respect to that of the two LAGEOS satellites (about 5900 km), with several important consequences. Indeed, in previous work (2016EGUGA..1814231P) we have been able to show that decay of the semi-major axis of LARES orbit (close to 1 m/yr over the analyzed timespan) was almost all explainable in term of the drag effects due to the neutral atmosphere. Conversely, for the two LAGEOS, the role of the neutral drag was a minority in explaining the observed decay (about 10%), resulting largely exceeded by thermal drag effects and charged particles effects. However, in the previous work, we also showed that after modelling the neutral atmosphere a residual along-track acceleration was still there, a factor of 70 smaller than that estimated to account for the effect of the neutral drag (about -1.4x10-^11 m/s^2) and that this was the evidence that other (possible) unmodeled non-gravitational perturbations were at work on LARES orbit. Recently, we extended this study to all orbital elements of LARES, and we considered also a larger timespan that covers almost all the time elapsed since the launch of this passive laser-ranged satellite. Our study is based on a careful analysis of the orbit of LARES with two different software, GEODYN II and SATRAP. The comparison between the residuals of the orbital elements of LARES obtained with GEODYN, with the effects on the same elements due to the neutral drag, that we derived by a parallel analysis with SATRAP, clearly show other underlying effects, possibly to be explainable by thermal drag like effects. This work is part of those of the LAser RAnged Satellites Experiment (LARASE). The main goal of LARASE is to improve the modelling of both the gravitational and non-gravitational perturbations on the LAGEOS, LAGEOS II and LARES satellites in such a way to further improve their precise orbit determination to better determine tiny relativistic effects in the weak-field and slow-motion limit of Einstein's theory of general relativity.

The equations of motion of an Earth satellite are usually written for its center of mass (COM), as the point ideally in free fall in the external gravitational field. However, the range measurements performed by the on-ground laser-ranging stations refer to a different point, close to the satellite surface and depending on the laser-system detector. Consequently, it is necessary to refer this "reflecting-point" to the COM by means of the so-called range-correction. In this regard, a key point is represented by the knowledge of the orientation of the satellite with respect to the inertial space. A refined knowledge for the spin evolution is also important for the improvements that can be achieved in modeling tiny non-gravitational perturbations: as for thermal thrust perturbations and a possible asymmetric reflectivity of the hemispheres of LAGEOS satellites. The better the models for the orbit perturbations, the better the precise orbit determination and, consequently, the better will be the measurements of the geophysical parameters of interest. Indeed, improved models for the perturbations together with an improved knowledge of the COM of geodetic satellites are very important issues for a refined definition of the International Terrestrial Reference Frame and for the measurements of the geocenter variations. Finally, the knowledge of the spin vector represents a key factor for time transfer experiments and for general relativity measurements with passive satellites. We present the spin model LASSOS (LArase Satellites Spin mOdel Solutions) that we have developed to understand the rotational dynamics of the two LAGEOS satellites and of the LARES one. This model is general, not restricted to the fast rotation regime, as in the case of previous models, and it is based on the solution of the full set of Euler equations. The results related to the main thermal thrust perturbations will also be presented.

The laser-ranged satellite LARES is expected to provide new refined measurements of relativistic physics, as well as significant contributions to space geodesy and geophysics. The very low area-to-mass ratio of this passive and dense satellite was chosen to reduce as much as possible the disturbing effects of non-gravitational perturbations. However, because of its height, about 1450 km compared with about 5800-5900 km for the two LAGEOS satellites, LARES is exposed to a much stronger drag due to neutral atmosphere. From a precise orbit determination, analyzing the laser ranging normal points of LARES over a time span of about 3.7 years with the GEODYN II (NASA/GSFC) code, it was found an average semi-major axis decay rate of -0.999 m per year, corresponding to a non-conservative net force acting nearly opposite to the velocity vector of the satellite and with a mean along-track acceleration of -1.444 x 10-11 m/s^2. By means of a modified version of the SATRAP (ISTI/CNR) code, the neutral drag perturbation acting on LARES was evaluated over the same time span, taking into account the real evolution of solar and geomagnetic activities, with five thermospheric density models (JR-71, MSIS-86, MSISE-90, NRLMSISE-00 and GOST-2004). All of them were able to model most of the observed semi-major axis decay, with differences among the average drag coefficients smaller than 10%. Moreover, when the same models (JR-71 and MSIS-86) were used within GEODYN in a least-squares fit of the tracking data, the differences between the average drag coefficients estimated with SATRAP and GEODYN were of the order of 1% or less. Adding to this a further independent check carried out analyzing the orbital decay of a passive spherical satellite (Ajisai) just 40 km higher than LARES, it was then concluded that some of the currently best models developed for neutral atmosphere, within their uncertainties and range of applicability, were able to account for most (about 98.6%) of the observed semi-major axis decay of LARES. Finally, after modeling the neutral atmosphere drag in GEODYN, a residual semi-major axis decay, corresponding to an average along-track acceleration of about -2 x 10-13 m/s^2 (i.e. approximately 1/72 of neutral drag), was detected as well. It was 50%, or less, of that previously reported and is probably linked to thermal thrust effects, but further and more detailed investigations, including the detection of the signature of the periodic terms, will be needed in order to characterize such smaller non-gravitational perturbations.

The LARASE Spin Model of the two LAGEOS and LARES satellites.

The orbital decay of the semi-major axis of LARES and the LARASE contribution to SLR measurements for applications in the fields of space geodesy and geophysics.

The LARASE (LAser RAnged Satellites Experiment) research program has its main objectives in tests and measurements of general relativity (GR) via a precise orbit determination (POD) of 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, with the objective to provide a robust and unassailable error budget of the main systematic effects), beside reviewing previous models we are also developing new models for the main perturbations that act on the orbits of the two LAGEOS satellites and on that of the new LARES satellite. In this talk we focus on the modeling of the spin vector of these satellites. Indeed, the spin knowledge, both in orientation and rate, is of fundamental importance in order to correctly model the thermal effects on the surface of these satellites, as in the case of the solar Yarkovsky-Schach effect and of the Earth's Thermal drag (also known as Earth-Yarkovsky effect or Rubincam effect). These are very important non-gravitational perturbations (NGP) that produce long-term effects on the orbit of the cited satellites. Therefore, the improvement of the accuracy of the models developed to handle these NGP represents a very significant result. Such improvements, with the possibility of a more reliable POD for the satellites, will be very useful in the field of GR measurements with laser-ranged satellites, as well as in the field of space geodesy and, in general, in those of geophysics.

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.

The new laser-ranged satellite LARES (LAser RElativity Satellite) is expected to provide new refined measurements of relativistic physics as well as significant contributions to space geodesy and geophysics. The very low area-to-mass ratio of this passive and dense satellite was chosen to reduce as much as possible the disturbing effects due to the non-gravitational perturbations in order to compensate for its much lower altitude with respect to the two older LAGEOS (LAser GEOdynamic Satellite) satellites, currently the best tracked satellites of the International Laser Ranging Service network. Indeed, because of its height, about 1450 km with respect to the 5900 km of the two LAGEOS, LARES is subject to a much stronger perturbation provoked by the neutral drag than that on the two LAGEOS. From a Precise Orbit Determination (POD) of LARES over a time span of about 3.7 years we have been able to measure an orbital decay in the residuals of its semi-major axis of about 1 m/yr, that corresponds to a transversal mean acceleration of about -1.457 x 10-11 m/s^2. This POD has been obtained analyzing LARES normal points with the GEODYN II (NASA/GSFC) software. Neither the neutral drag nor the thermal effects have been included in the dynamical models of GEODYN II. By means of a modified version of the SATellite Reentry Analysis Program (SATRAP) of ISTI/CNR, the neutral drag perturbation has been computed over the same time span accounting for the measured decay and considering the real evolution of the solar and geomagnetic activities for several atmospheric models. In particular, assuming as reference for the unmodeled transversal acceleration due to the neutral atmosphere the above value, the drag coefficient estimated by SATRAP is comparable to the average value estimated by GEODYN II in a least square fit of the tracking data. This means that the current best models developed for the atmosphere behavior are able to account for the observed decay, within their errors and range of applicability. A further analysis is needed in order to extract from the observed decay a possible smaller contribution related with other unmodeled effects, as the thermal ones, acting on the satellite. In this context it will be necessary to fix the contribution of the signature of the drag and of the thermal effects in the residuals of the other orbital elements of LARES. This study falls within the activities of the LARASE (LAser RAnged Satellites Experiment) research program. LARASE main goal is to provide new and refined measurements of the relativistic effects acting on the orbit of the two LAGEOS and LARES satellites. In particular, a major point of these activities is to provide a final robust and reliable error budget for the main systematic effects of gravitational and non-gravitational origin. Therefore, a special attention is devoted to the modeling of the non-gravitational perturbations acting on these passive laser-ranged satellites. Improvements in their modeling will be useful both in the field of general relativity measurements and in those of space geodesy and geophysical applications.

Passive laser-ranged satellites, launched for geodynamics and geophysics purposes, not only have contributed to significant measurements in space geodesy [1,2], but also provided an outstanding test bench to fundamental physics. Significant examples are represented by the measurement of the Lense-Thirring precession on the combined nodes of the two LAGEOS satellites [3], and by the measurement of the total relativistic precession of the argument of pericenter of LAGEOS II [4,5]. Indeed, the physical characteristics of such satellites and of their orbit, and the availability of high-quality tracking data provided by the International Laser Ranging Service (ILRS) [6], allow for precise tests of gravitational theories. The aim of LARASE (LAser RAnged Satellites Experiment) is to go a step further in the tests of the gravitational interaction in the field of Earth (i.e. in the weak-field and-slow motion (WFSM) limit of general relativity (GR)) by the joint analysis of the orbits of the two LAGEOS satellites and that of LARES [7]. To reach such a goal a key ingredient is to provide high-quality updated models for the perturbing non-gravitational forces acting on such satellites. A large amount of Satellite Laser Ranging (SLR) data of LAGEOS and LAGEOS II has been analyzed using a set of dedicated models for their dynamics, and the related post-fit residuals have been analyzed. A parallel work is ongoing for LARES that, due to its much lower altitude, is subject to larger gravitational and non-gravitational effects; the latter are in part mitigated by its much lower area-to-mass ratio. Recent work on the data analysis of the orbit of such satellites will be presented together with the development of some new refined model to account for the impact of the subtle non-gravitational perturbations.

LAser RAnged Satellites Experiment (LARASE): Investigation on the neutral atmospheric drag and drag coefficients at the LARES and AJISAI satellites altitude.

Passive laser-ranged satellites, launched for geodynamics and geophysics purposes, not only have contributed to significant measurements in space geodesy that enabled, among several aspects, a deeper knowledge of the Earth's geopotential, but they also provided an outstanding test bench to fundamental physics, as in the case of the measurement of the gravito-magnetic and gravito-electric precession that are predicted by Einstein's theory of general relativity (GR). Indeed, the physical characteristics of such satellites - such as their low area-to-mass ratio - as well as those of their orbits, and the availability of high-quality tracking data provided by the International Laser Ranging Service (ILRS), allow for precise and accurate tests of gravitational theories. The precise orbit determination (POD) represents the first issue to be fulfilled, to be followed by a solve for the unknown parameters. The POD requires two main features: i) high-quality observations and ii) high-quality dynamical models. The first point is provided by the ILRS by means of the very precise Satellite Laser Ranging (SLR) technique. With regard to the second point, a big effort has been done to develop models for the non-gravitational forces on passive satellites, with significant results in the literature in the case of the two LAGEOS satellites. The aim of LARASE (LAser RAnged Satellites Experiment) is to go a step further in the tests of the gravitational interaction in the field of Earth, i.e. in the weak-field and-slow motion limit of GR, by the joint analysis of the orbits of the two LAGEOS satellites and that of the most recent LARES satellite. One of the key ingredients to reach such a goal is to provide high-quality updated models for the perturbing non-gravitational forces acting on the surface of these satellites. Therefore, in the context of the LARASE collaboration, we started an activity dedicated to revisit, extend and improve current models for the non-gravitational perturbations in the case of LAGEOS-type satellites. We discuss the spin modelling problem and its intimate relationship with the thermal thrust forces; also the atmospheric drag impact on the orbit will be discussed, especially in the case of LARES due to its much lower altitude with respect to that of the two LAGEOS. Also the effects of the Earth's tidal perturbations will be addressed for the LARES satellite. Finally, we present our recent results on the data analysis of the orbit of the two LAGEOS satellites and on that of LARES with our results on relativistic measurements in the case of the orbit of the two LAGEOS satellites with updated constraints on non-Newtonian gravitational dynamics.

Passive laser-ranged satellites, launched for geodynamics and geophysics purposes, not only have contributed to significant measurements in space geodesy that enabled, among several aspects, a deeper knowledge of the Earth's geopotential (both in its static and dynamic behavior), as well as of the geocenter motion and GM value up to the denition of the terrestrial reference frame, but they also provided an outstanding test bench to fundamental physics, as in the case of the first measurement of the Lense-Thirring precession on the combined nodes of the two LAGEOS satellites, or in the case of the total relativistic precession of the argument of pericenter of LAGEOS II. Indeed, the physical characteristics of such satellites - such as their low area-to-mass ratio - as well as those of their orbits, and the availability of high-quality tracking data provided by the International Laser Ranging Service (ILRS), allow for precise tests of gravitational theories. The aim of LARASE (LAser RAnged Satellites Experiment) is to go a step further in the tests of the gravitational interaction in the field of Earth, i.e. in the weak-field and slow-motion limit of general relativity, by the joint analysis of the orbits of the two LAGEOS satellites and that of the most recent LARES satellite. One of the key ingredients to reach such a goal is to provide high-quality updated models for the perturbing non-gravitational forces acting on the surface of such satellites. A large amount of Satellite Laser Ranging (SLR) data of LAGEOS and LAGEOS II has been analyzed using a set of dedicated models for satellite dynamics, and the related post-fit residuals have been analyzed. A parallel work is on-going in the case of LARES that, due to its much lower altitude, is subject to larger gravitational and non-gravitational effects; the latter are mitigated in part by its much lower area-to-mass ratio. Recent work on the data analysis of the orbit of such satellites will be presented together with the development of some new refined models to account for the impact of the subtle and complex non-gravitational perturbations. The general relativistic effects leave peculiar imprint on the satellite orbit, namely in the secular behavior of its three Euler angles. Recent results will be provided together with updated constraints on non-Newtonian gravitational dynamics. The measurement error budget will be discussed, emphasizing the role of the modeling of gravitational and, especially, non-gravitational forces on the overall precise orbit determination quality, as well as on future new measurements and constraints of the gravitational interaction.

Laser ranging to passive (cannonball) satellites like the two LAGEOS still represents a way to extract relevant information on Earth's internal structure, its surface and the way it interacts with the surrounding medium, the atmosphere. The related precise orbit determination (POD) represents the first issue to be fulfilled, to be followed by a solve for the unknown global parameters. The POD requires two main features: i) high-quality observations and ii) high-quality dynamical models. The first item, i.e., the availability of high-quality tracking data, is provided by the International Laser Ranging Service (ILRS) by means of the very precise Satellite Laser Ranging (SLR) technique. With regard to the second point, a big effort has been done to develop models for the non-gravitational forces (i.e., non-conservative forces) on passive satellites, especially for the two LAGEOS, since early '80s, with significant results in the literature. However, some of the models built were valid only under particular approximations or simplifications, as for the spin model and the thermal thrust forces, and have not been generalized or tested under different conditions. Other aspects, such as the asymmetric reflectivity of the two LAGEOS satellites, are not fully understood. For instance, one of the main parameters that enters in these models is the spin rate of the satellite and its slowing down due to the coupling of the induced magnetic moment produced by eddy currents with the external geomagnetic field. Once the value of the spin period is close to other characteristics time scales, as the thermal inertia of the cube corner retroreflectors or the orbital period of the satellite, resonances are present and more complicated (non-averaged) equations have to be considered for a reliable model of the spin evolution. In order to account for such effects and also to extend/apply (correctly) the models to the new LARES satellite, new efforts are needed in the field of the non-gravitational forces modelling. This is also particularly important for the role played by these satellites in general relativity theory tests in the field of the Earth, wherever the tiny predictions of Einstein's geometrodynamics need a quite reliable and robust POD. The aim of LARASE (LAser RAnged Satellites Experiment) is to go a step further in the tests of the gravitational interaction in the field of the Earth and, as highlighted above, a key role to reach such a goal is played by high-quality updated models for the perturbing non-gravitational forces acting on the surface of the satellites. Therefore, in the context of the LARASE collaboration, we started an activity dedicated to revisit, extend and improve current models for the non-gravitational perturbations in the case of LAGEOS-type satellites. We discuss the spin modelling problem and its intimate relationship with the thermal thrust forces; also the atmospheric drag impact on the orbit will be discussed, especially in the case of LARES due to its much lower altitude with respect to that of the two LAGEOS. Finally, we present our recent results on the data analysis of the orbit of the two LAGEOS satellites and on that of LARES.