2021
Contribution to conference
Restricted

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.

**See at: **
CNR ExploRA | www.cospar2020.org

2021
Contribution to conference
Restricted

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.

**See at: **
CNR ExploRA | www.cospar2020.org

2021
Contribution to conference
Restricted

Thermal thrust forces act on the surface of a satellite as a result of a non-uniform distribution of temperature across its surface. A new thermal model for the two LAGEOS satellites will be described with the goal of providing the thermal thrust accelerations acting on their surfaces. The thermal inertia of the satellite components together with the eclipses participate in the production of these perturbations. The main effects are due to the thermal inertia of the Corner Cube Retroreflectors (CCRs) of the satellite, being the direct solar visible radiation modulated by the eclipses and the Earth's infrared radiation the main sources. In addition to these sources, the solar radiation reflected by the complex Earth-atmosphere system, i.e. the Earth's albedo, is also responsible for a non-uniform heating of the surface of the satellite. Contrary to the models previously developed in the literature for the LAGEOS satellites, our new model, that we called LATOS (LArase Thermal mOdel Solutions), is not based on averaged equations. The attitude of the satellite plays an important role in this kind of analysis; we modelled it by means of the LASSOS (LArase Satellites Spin mOdel Solutions) model. This model for the spin was developed within the LARASE (LAser RAnged Satellites Experiment) research program. In our analysis, the CERES (Clouds and the Earth's Radiant Energy System) data have been used to account for the effects of the terrestrial albedo. The results for the thermal thrust accelerations acting on the two LAGEOS satellites will be presented together with their effects on their orbital elements. These effects will be then compared with the orbital residuals of the satellites in the same elements obtained by an independent Precise Orbit Determination (POD). The consequent improvements in the POD through the inclusion of the thermal thrust accelerations in the dynamic model, in such a way to replace the empirical accelerations, will be of fundamental importance for the geophysical products that are determined by analysing the orbits of the two LAGEOS satellites. At the same time, the fundamental physics measurements that are obtained with these satellites can benefit from a more precise determination of their orbit.

**See at: **
CNR ExploRA | www.cospar2020.org

2021
Conference article
Open Access

A new experiment in the field of gravitation, SaToR-G, is presented. The experiment aims to compare the predictions of different theories of gravitation in the limit of weak-field and slow-motion. The ultimate goal of the experiment is to look for possible "new physics" beyond the current standard model of gravitation based on the predictions of General Relativity. A key role in the above perspective is the theoretical and experimental framework within which to confine our work. To this end, we will try to exploit as much as possible the framework suggested by Dicke over fifty years ago.

**See at: **
ISTI Repository | CNR ExploRA | sciforum.net

2021
Journal article
Open Access

During Solar Cycle 24, the passive spherical satellites LARES and Ajisai, placed in nearly circular orbits with mean geodetic altitudes between 1450 and 1500 km, were used as powerful tools to probe the neutral atmosphere density and the performances of six thermospheric models in orbital regimes for which the role of dominant atomic species is contended by hydrogen and helium, and accurate satellite measurements are scarce. The starting point of the analysis was the accurate determination of the secular semi-major axis decay rate and the corresponding neutral drag acceleration in a satellite centered orbital system. Then, for each satellite, thermospheric model and solar activity level, the drag coefficients capable of reproducing the orbital decay observed were found. These coefficients were finally compared with the physical drag coefficients computed for both satellites in order to assess the biases affecting the thermospheric density models. None of them could be considered unconditionally the best; the specific outcome depending on solar activity and the regions of the atmosphere crossed by the satellites. During solar maximum conditions, an additional density bias linked to the satellite orbit inclination was detected.

**See at: **
ISTI Repository | CNR ExploRA | www.jstage.jst.go.jp | TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES

2021
Journal article
Open Access

A new satellite-based experiment in the field of gravitation, SaToR-G, is presented. It aims to compare the predictions of different theories of gravitation in the limit of weak-field and slow-motion. The ultimate goal of SaToR-G is searching for possible "new physics" beyond General Relativity, which represent the state-of-the-art of our current knowledge of gravitational physics. A key role in the above perspective is the theoretical and experimental framework that confines our work. To this end, we will exploit as much as possible the classical framework suggested by R.H. Dicke over fifty years ago.

**See at: **
ISTI Repository | CNR ExploRA | www.mdpi.com

2020
Journal article
Open Access

A new measurement of the gravitomagnetic field of the Earth is presented. The measurement has been obtained through the careful evaluation of the Lense-Thirring (LT) precession on the combined orbits of three passive geodetic satellites, LAGEOS, LAGEOS II, and LARES, tracked by the Satellite Laser Ranging (SLR) technique. This general relativity precession, also known as frame-dragging, is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein's theory of gravitation. The measurement stands out, compared to previous measurements in the same context, for its precision (similar or equal to 7.4x10-3, at a 95% confidence level) and accuracy (similar or equal to 16x10-3), i.e., for a reliable and robust evaluation of the systematic sources of error due to both gravitational and non-gravitational perturbations. To achieve this measurement, we have largely exploited the results of the GRACE (Gravity Recovery And Climate Experiment) mission in order to significantly improve the description of the Earth's gravitational field, also modeling its dependence on time. In this way, we strongly reduced the systematic errors due to the uncertainty in the knowledge of the Earth even zonal harmonics and, at the same time, avoided a possible bias of the final result and, consequently, of the precision of the measurement, linked to a non-reliable handling of the unmodeled and mismodeled periodic effects.

**See at: **
Universe | OA@INAF - Istituto Nazionale di Astrofisica | ISTI Repository | CNR ExploRA | Universe | Universe

2020
Contribution to conference
Open Access

Thermal thrust forces are non-conservative forces that act on the surface of a satellite as a result of temperature gradients across its surface. In the case of the older LAGEOS satellite these kinds of perturbations have been well-known since the end of 80s. The main effects are due to the thermal inertia of the corner cube retroreflectors (CCRs) of the satellites with sources the Earth's infrared radiation and the direct solar visible radiation modulated by the eclipses. However, the solar radiation reflected by the complex Earth-atmosphere system, i.e. the albedo, is also responsible for a non-uniform heating of the satellite surface. We reconsider such perturbations by means of a new thermal model for the satellites called LATOS (LArase Thermal mOdel Solutions), which is not based on averaged equations as those previously developed in the literature. Of course, in such analyses the attitude of the satellite plays an important key role; we modeled it by means of the LASSOS (LArase Satellites Spin mOdel Solutions) model for the evolution of the spin-vector that we have already developed within the LARASE (LAser RAnged Satellites Experiment) research program. We also included the contribution of the Earth's albedo in the determination of the overall distribution of temperature on the surface of the satellites, that was not considered in previous works. The CERES (Clouds and the Earth's Radiant Energy System) data have been used to account for this effect. The thermal thrust accelerations have been computed together with their effects on the orbital elements by means of the Gauss equations. These effects are compared with the orbit residuals of the satellites in the same elements, obtained by an independent Precise Orbit Determination (POD), in order to highlight the signature of the unmodeled effects. The improvement in the POD that can be achieved through a better modeling of the thermal thrust perturbations is of fundamental importance for the geophysical products that are determined by means of the analysis of the orbits of the two LAGEOS satellites. Similarly, the measurements in the field of fundamental physics that are obtained with these satellites can benefit from a more precise modeling of their orbit.

**See at: **
meetingorganizer.copernicus.org | ISTI Repository | CNR ExploRA | doi.org

2020
Contribution to conference
Open Access

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

**See at: **
agenda.infn.it | ISTI Repository | CNR ExploRA

2020
Contribution to conference
Open Access

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

**See at: **
agenda.infn.it | ISTI Repository | CNR ExploRA

2020
Contribution to conference
Open Access

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

**See at: **
agenda.infn.it | ISTI Repository | CNR ExploRA

2019
Journal article
Open Access

The paper presents the results of an ambient vibration monitoring campaign conducted on theso-called "Clock Tower" (Torre delle Ore), one of the best known and most visited monuments inthe historic centre of Lucca. The vibrations of the tower were continuously monitored fromNovember 2017 to March 2018 using high-sensitivity instrumentation. In particular, four seismicstations provided by the Istituto Nazionale di Geofisica e Vulcanologia and two three-axialaccelerometers developed by AGI S.r.l., spin-off of the National Institute for Astrophysics, wereinstalled on the tower. The measured vibration level was generally very low, since the structurelies in the middle of a limited traffic area. Nevertheless, the availability of two different types ofhighly sensitive and accurate instruments allowed the authors to follow the dynamic behaviour ofthe tower during the entire monitoring period and has moreover provided cross-validation of theresults.

**See at: **
arXiv.org e-Print Archive | International Journal of Architectural Heritage | OA@INAF - Istituto Nazionale di Astrofisica | ISTI Repository | ISTI Repository | International Journal of Architectural Heritage | doi.org | CNR ExploRA | www.tandfonline.com

2019
Conference article
Open Access

The passive spherical satellites LARES and Ajisai, placed in nearly circular orbits with mean geodetic altitudes between 1450 and 1500 km, were used, during Solar Cycle 24, as powerful tools to probe the neutral atmosphere density and the performances of six thermospheric models in orbital regimes for which the role of dominant atomic species is contended by hydrogen and helium, and accurate satellite measurements are scarce. The starting point of the analysis was the accurate determination of the secular semi-major axis decay rate, leading to the estimation of drag coefficients for each satellite, thermospheric model and solar activity condition. The associated components of the neutral drag acceleration in a satellite-centered orbital system were computed as well. Following the estimation of the physical drag coefficients for LARES and Ajisai, it was then possible 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. During solar maximum conditions, an additional density bias linked to the satellite orbit inclination was detected.

**See at: **
archive.ists.or.jp | CNR ExploRA

2019
Contribution to conference
Open Access

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.

**See at: **
ISTI Repository | agenda.infn.it | CNR ExploRA

2019
Contribution to conference
Open Access

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.

**See at: **
cddis.nasa.gov | ISTI Repository | CNR ExploRA

2019
Contribution to conference
Open Access

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.

**See at: **
ISTI Repository | CNR ExploRA | www.geophysical-research-abstracts.net

2019
Contribution to conference
Open Access

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.

**See at: **
ISTI Repository | CNR ExploRA | www.geophysical-research-abstracts.net

2019
Contribution to conference
Open Access

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.

**See at: **
ISTI Repository | CNR ExploRA

2019
Contribution to conference
Restricted

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.

**See at: **
CNR ExploRA

2018
Report
Unknown

Il documento descrive le attività conclusive del progetto TITANIO (Sensori innovativi per il monitoraggio del patrimonio architettonico), finanziato dalla Fondazione Carilucca per il biennio 2016-2018.

**See at: **
CNR ExploRA