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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.

We present a new experiment called SaToR-G (Satellites Tests of Relativistic Gravity) which mainly concerns on verifying the gravitational interaction beyond the predictions of General Relativity, looking for possible effects connected with new physics, and foreseen by different alternative theories of gravitation. SaToR-G exploits the improvement of the dynamical model of the two LAGEOS and of LARES satellites performed within the previous research program called LAser RAnged Satellites Experiment (LARASE: 2013-2019) and funded by the Italian INFN (Istituto Nazionale di Fisica Nucleare). Within LARASE we achieved a new measurement of the Lense-Thirring precession with an accuracy better than 2%. To reach the objectives foreseen by SaToR-G, we need to provide a precise orbit determination of a set of laser-ranged satellites, such as the two LAGEOS, LARES, and the forthcoming LARES-2, whose launch is expected before the end of this year. The state-of-the-art regarding the modelling improvements currently reached with LARASE will be presented together with the main objectives of SaToR-G in the fields of relativistic measurements and space geodesy.

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 Laser Ranged Satellites Experiment (LARASE) aims to test the gravitational interaction in the weak-field and slow-motion limit and compare, consequently, the predictions of Einstein's theory of general relativity (GR) with those of other alternative theories of gravitation. In particular, a goal of LARASE is to improve the modelling of the non-gravitational perturbations (NGP) on the LAGEOS, LAGEOS II and LARES satellites in such a way to further improve their precise orbit determination in order to better extract, from their orbital residuals, the expected tiny relativistic effects. Indeed, the motion of these passive laser-ranged satellites along nearly geodesics of spacetime may be a posteriori reconstructed through a careful modelling of the main NGP that act on their surface and, in more general terms, of their overall dynamical models. We will focus upon two recent LARASE results: the development of a new model for the spin evolution of the satellites and of one to account for the very subtle effects on their orbits that are produced by the thermal thrust perturbations. Concerning the gravitational perturbations due to the deviation of the Earth's mass distribution from that of a perfect sphere, we will discuss our improvements in the modelling of the Earth's even zonal harmonics coefficients based on GRACE data, specifically in their time-dependency. Finally, we will show our new results for a refined measurement of the Lense-Thirring precession on the combined orbits of the LAGEOS, LAGEOS II and LARES satellites. This relativistic precession arises from the gravitomagnetic field of the Earth produced by its angular momentum. Gravitomagnetism describes, in Einstein's GR, the curvature of spacetime produced by mass-currents, with important consequences in the astrophysics of high-energy phenomena as well as possible cosmological consequences related to Mach's Principle.

Gravitomagnetism represents one of the most peculiar predictions of Einstein's geometrodynamics and describes the spacetime curvature effects due to mass-currents. Following Einstein, gravitomagnetism is responsible of the so-called dragging of the local inertial frames, whose axes are defined by the orientation of gyroscopes with respect to the distant stars. The orbital plane of an Earth-orbiting satellite is a sort of enormous gyroscope once removed all classical perturbations that arise from the main gravitational and non-gravitational perturbations. We present a new measurement of the dragging effect on the combined orbits of the two LAGEOS satellites with that of LARES, which results in both a precise and accurate measurement of the Earth's gravitomagnetic field, towards an assessment of about a 1% of the main systematic sources of error. This result was achieved by the LARASE experiment under the astroparticle physics experiments of the National Scientific Committee 2 of the INFN.

During the last two decades significant improvements in the knowledge of the Earth's internal structure and of its time-dependent gravitational field have been reached thanks to dedicated space missions, such as CHAMP (Challenging Minisatellite Payload) and, especially, GRACE (Gravity Recovery and Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Explorer). In particular, the twin satellites of GRACE - with their inter-satellite Ka-band tracking plus their precise orbit determination (POD) via GPS and accelerometer measurements - and the gradiometric measurements of GOCE together with its GPS POD and accelerometer measurements have provided new insights not only in the physics of the solid Earth, but also in the movements of ice and water and, consequently, in oceanography and sea-level changes and, finally, gave fundamental contributions in climate research studies, geophysics and space geodesy. The great success of these missions in improving the knowledge of both the low- and medium-high degree and order of the Earth's gravitational field expansion in spherical harmonics clearly shows that the gravity variations can be very well determined and monitored from space. Therefore, the consequences of all these improvements are of fundamental importance in several fields of science and for civil applications. Among the scientific applications, a very good knowledge of the Earth's gravitational field and of its time-dependency is very important to provide refined measurements of the gravitational interaction in its weak-field and slow-motion (WFSM) limit. This will help significantly to better test the predictions of Einstein's theory of general relativity (GR) and those of other theories of gravitation in this limit. Indeed, thanks to the cited improvements in the knowledge of the Earth's gravitational field, in addition to take into account the main even zonal harmonics of low degree (also considering their time evolution) - i.e. those that are responsible for a secular precession in the right ascension of the ascending node and on the argument of pericenter of an Earth-orbiting satellite - the time dependency of other harmonics (also of higher degrees) has to be considered in order to reach a 99% (or better) accuracy for some of these fundamental physics measurements. In this talk, the results of the Laser Ranged Satellites Experiment (LARASE) will be shown regarding the modelling of the Earth's gravitational field for GR measurements in the WFSM limit of the theory. In this context, a 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 POD to better extract, from their orbital residuals analyses, the expected tiny relativistic effects. On the basis of this modelling of the Earth's gravitational field, we will show our new results for a refined measurement of the Lense-Thirring precession on the combined orbits of the two LAGEOS satellites with that of LARES.

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 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.

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.

LARASE (LAser RAnged Satellites Experiment) aims to provide refined measurements of Einstein's theory of General Relativity by means of the very precise measurements of the Satellite Laser Ranging technique. In this regard, a big effort of LARASE is devoted to improve the dynamical model of the two LAGEOS satellites and of the new satellite LARES. The target is to obtain a more precise and accurate determination of their orbit. Indeed, the systematic error sources due to both the gravitational and non-gravitational perturbations may corrupt the relativistic measurements. At the same time, it is indisputable that a more accurate and precise orbit determination (POD) of the satellites, based on a more reliable dynamical model, represents a fundamental precondition to eventually reach a sub-mm precision in the SLR range residuals and, consequently, to gather benefits in the fields of space geodesy and of geophysics. The results obtained over the last year will be presented in terms of the improvements achieved in the dynamical model, in the satellites POD and, finally, in the measurement of the relativistic Lense-Thirring precession of their orbit.

The key role that laser-ranged satellites -- such as the two LAGEOS (LAser GEOdynamic Satellite) -- have had in the field of space geodesy, with a paramount of significant applications and results in geophysics, as well in the measurements of tiny relativistic effects in the weak-field and slow-motion (WFSM) limit of Einstein's theory of general relativity (GR), is well known. In this regard, these achievements have been gathered thanks to two very important ingredients: i) the quality of the tracking observations of the orbit of the satellites, guaranteed by the powerful Satellite Laser Ranging (SLR) technique, and ii) the quality of their overall dynamical model implemented in a software code. Moreover, today, GR has to be considered a fundamental pillar of space geodesy and of geophysics in general: the use of atomic clocks on-board a navigation satellite or on-ground, are just two important examples, among many. Indeed, terms like "relativistic metrology", "relativistic geodesy" and "relativistic celestial mechanics" are very frequent in the literature, in fact they are pertinent and represent bridges among fields wrongly considereted separated in the past. The SLR technique is one of the techniques that constitute the Global Geodetic Observing System (GGOS). In the near future it is expected, within the GGOS activities, an improvement of one order of magnitude in global accuracies in the observational as well as the theoretical components of space geodesy. This implies improvements in measuring accuracies, in reference frames realization, in modelling, in the stations network geometry and, consequently, into the accuracies involved in fundamental physics measurements using space geodesy techniques. However, in order to reach these ambitious objectives with a fruitful contribution from the existing satellites, as the two LAGEOS and the more recently launched LARES, several improvements are necessary in their precise orbit determination (POD). For instance, under this point of view, an hot topic is constituted by the knowledge of the so-called center-of-mass correction for these satellites, that directly impact the range determination of the satellites, i.e. the precision of their normal points, and correlates with the so-called range bias of the Earth-bound tracking stations. One more very important aspect that deeply affects the POD of the satellites is represented by a reliable modelling of the subtle thermal effects produced by the visible solar radiation and the infrared radiation emitted by the Earth's surface. These are the Sun Yarkovsky-Schach effect and the Earth-Yarkovsky effect. Their complexity arise from two main aspects: i) the knowledge of the temperature distribution on the satellite surface, and ii) the knowledge of the satellite attitude, i.e of its spin vector evolution. In this talk, the main activities of the LAser Ranged Satellites Experiment (LARASE) will be described. The LARASE research program is funded by the Italian National Institute for Nuclear Physics (INFN) and it is a collaboration between different institutions. The main goal of LARASE is to provide accurate measurements for the gravitational interaction in the WFSM limit of GR by means of the very precise laser tracking of geodetic satellites orbiting around the Earth. In particular, LARASE aims to improve the dynamical model of the current best laser-ranged satellites in order to perform a refined POD of their orbit. This represents a first step towards new refined tests and measurements of GR in the field of the Earth and of a most profitable use of the orbit analysis of the considered satellites for space geodesy and geophysics. The current results of LARASE in terms of development of new models for the non-gravitational perturbations acting on the two LAGEOS and LARES satellites, their POD and new measurements of relativistic effects on their orbit will be shown together with an accurate evaluation of the error budget due to the main systematic sources of error.

LARASE is an experiment devoted to test General Relativity in its weak-field linearized approximation using the geodetic satellites LAGEOS and LARES. One main target is the measurements of the Lense-Thirring effect with an accuracy higher than in the past. We present the LARASE activitities and a preliminary measurement of the effect.

The main goal of the LARASE (LAser RAnged Satellites Experiment) research program is to obtain refined tests of Einstein's theory of General Relativity (GR) by means of very precise measurements of the round-trip time among a number of ground stations of the International Laser Ranging Service (ILRS) network and a set of geodetic satellites. These measurements are guaranteed by means of the powerful and precise Satellite Laser Ranging (SLR) technique. In particular, a big effort of LARASE is dedicated to improve the dynamical models of the LAGEOS, LAGEOS II and LARES satellites, with the objective to reach a more precise and accurate determination of their orbit. These activities contribute to reach a final error budget that should be robust and reliable in the evaluation of the main systematic errors sources that come to play a major role in masking the relativistic precession on the orbit of these laser-ranged satellites. These error sources may be of gravitational and non-gravitational origin. It is important to stress that a more accurate and precise orbit determination, based on more reliable dynamical models, represents a fundamental prerequisite in order to reach a sub-mm precision in the root-mean-square of the SLR range residuals and, consequently, to gather benefits in the fields of geophysics and space geodesy, such as stations coordinates knowledge, Earth's geocenter determination and the realization of the Earth's reference frame. The results reached over the last year will be presented in terms of the improvements achieved in the dynamical model, in the orbit determination and, finally, in the measurement of the relativistic precessions that act on the orbit of the satellites considered.

The main goal of the LARASE (LAser RAnged Satellites Experiment) research program is to obtain refined tests of Einstein's theory of General Relativity by means of very precise laser measurements of the round-trip time from ground stations to a set of geodetic satellites. In particular, a big effort of LARASE is dedicated to improve the dynamical models of the LAGEOS, LAGEOS II and LARES satellites, with the objective to obtain a more precise and accurate determination of their orbit. These activities contribute also to reach a reliable and robust error budget for the main sources of systematic errors. The results reached over the last year will be presented in terms of the improvements achieved in the dynamical model, in the orbit determination and, finally, in the measurement of the relativistic precessions that act on the orbit of the satellites.

The importance of General Relativity (GR) for space geodesy -- and for geodesy in general -- is well known since several decades and it has been confirmed by a number of very significant results. For instance, GR plays a fundamental role for the following very notable techniques: Satellite-and-Lunar Laser Ranging (SLR/LLR), Very Long Baseline Interferometry (VLBI), Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS), and Global Navigation Satellite Systems (GNSS). Each of these techniques is intimately and closely related with both GR and geodesy, i.e. they are linked in a loop where benefits in one field provide positive improvements in the other ones. A common ingredient for a suitable and reliable use of each of these techniques is represented by the knowledge of the Earth's gravitational field, both in its static and temporal dependence. Spaceborne gravimetry, with the inclusion of accelerometers and gradiometers on board dedicated satellites, together with microwave links between satellites and GPS measurements, have allowed a huge improvement in the determination of the Earth's geopotential during the last 15 years. In the near future, further improvements are expected in this knowledge thanks to the inclusion of laser inter-satellite link and the possibility to compare frequency and atomic standards by a direct use of atomic clocks, both on the Earth's surface and in space. Such results will be also important for the possibility to further improve the GR tests and measurements in the field of the Earth with laser-ranged satellites in order to compare the predictions of Einstein's theory with those of other (proposed) relativistic theories for the interpretation of the gravitational interaction. Within the present paper we describe the state of the art of such measurements with geodetic satellites, as the two LAGEOS and LARES, and we discuss the effective impact of the systematic errors of gravitational origin on the measurement of the relativistic precessions expected on some of the orbital elements of these laser-ranged satellites.

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 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.

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.

LARASE aims to perform reliable measurements of the gravitational interaction in the weak-field and slow-motion limit of General Relativity (GR) by means of the laser tracking of the two LAGEOS and LARES satellites. These satellites are orbiting the Earth at a rather high altitude and their trajectory is known with an accuracy of a few cm level. By a least-squares fit of the ranging data it is possible to extract the GR effects on the orbital elements, namely in the Euler angles that define the orientation in space of the orbit, and by means of suitable combinations of such observables it is therefore possible to obtain the measurements of the GR precessions that arise from the Earth's gravitoelectric and gravitomagnetic fields, as well as from the de Sitter effect. These measurements represent the first step to obtain constraints of selected post-Newtonian parameter values in the field of the Earth, as well as to check the predictions of GR with respect to those of other theories for the gravitational interaction. In order to obtain these precise measurements of relativistic effects it is of primary importance to provide a reliable error budget based on an accurate evaluation of the main systematic error sources due to gravitational and nongravitational perturbations. In this talk the various ongoing LARASE activities will be presented and discussed, along with the current results regarding satellites dynamics modeling improvements, precise orbit determination and preliminary measurements of relativistic effects, with the perspectives for the final goals of this research program.

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.

Precise Orbit Determination of the two LAGEOS and LARES satellites and the LARASE activities.

The LAser RAnged Satellites Experiment (LARASE) research program aims to provide an original contribution in testing and verifying Einstein's theory of General Relativity (GR) in its Weak-Field and Slow-Motion (WFSM) limit by means of the powerful Satellite Laser Ranging (SLR) technique. Therefore, in this perspective, a Precise Orbit Determination (POD) of a dedicated set of passive laser-ranged satellites is required. In particular, the joint analysis of the orbit of the two LAGEOS (LAser GEOdynamic Satellite) satellites with that of the more recently launched LARES (LAser RElativity Satellite) satellite will be exploited in order to obtain precise measurements of the gravitational interaction in the field of the Earth. A major point to be reached within the activities of LARASE is to provide the relativistic measurements with an error budget of the various systematic effects (both gravitational and non-gravitational) that be robust and reliable. This requires a careful analysis of the various disturbing effects on the orbit of the considered satellites, especially for the new LARES. This activity has been planned both for the gravitational and the non-gravitational perturbations (NGP).Therefore, we started to re-visit, update and improve previous dynamical models, especially for the NGP, and we also developed new models in such a way to improve the current dynamical models used in space geodesy to account for the main perturbations acting on the orbit of LAGEOS and LARES. We focused especially on the spin dynamics, the drag effects (especially for LARES, because of its much lower height with respect to the two LAGEOS) and, at a preliminary level, the thermal ones that, as it is well known from the literature, are very important for the LAGEOS satellites. These studies are of fundamental importance not only for the objective of a reliable error budget, but also in order to improve the POD. In this context, because of the importance of the LAGEOS satellites in the fields of space geodesy and geophysics (and the foreseeable importance of LARES in the near future) we expect that all the geodetic products within those provided the International Laser Ranging Service (ILRS) will benefit of such improvements in order to contribute to the goal of a sub-mm precision in the RMS of the SLR residuals with respect to the current cm precision. In this paper we are going to focus upon the POD results we obtained for the considered satellites within the LARASE activities. The analysis strategy and models setup will be discussed, along with the POD quality in terms of fit statistics and residuals. The current level of accuracy will be briefly assessed, along with current work for its improvement. The use of empirical accelerations will be described, as well as their removal (or minor role) in the case of the implementation in the POD software of new improved dynamical models.