The LArase Satellites Spin mOdel Solutions (LASSOS): a comprehensive model for the spin evolution of the LAGEOS and LARES satellites

The two LAGEOS and LARES are laser-ranged satellites tracked with the best accuracy ever achieved. Using their range measurements many geophysical parameters were calculated and some General Relativity effects were directly observed. To obtain precise and refined measurements of the effects due to the predictions of General Relativity on the orbit of these satellites, it is mandatory to model with high precision and accuracy all other forces, reducing the free parameters introduced in the orbit determination. A main category of non-gravitational forces to be considered are those of thermal origin, whose fine modeling strongly depends on the knowledge of the evolution of the spin vector. We present a complete model, named LASSOS, to describe the evolution of the spin of the LAGEOS and LARES satellites. In particular, we solved Euler equations of motion considering not-averaged torques. This is the most general case, and the predictions of the model well fit the available observations of the satellites spin. We also present the predictions of our model in the fast-spin limit, based on the application of averaged equations. The results are in good agreement with those already published, but with our approach we have been able to highlight small errors within these previous works. LASSOS was developed within the LARASE research program. LARASE aims to improve the dynamical model of the two LAGEOS and LARES satellites to provide very precise and accurate measurements of relativistic effects on their orbit, and also to bring benefits to geophysics and space geodesy

Review and critical analysis of mass and moments of inertia of the LAGEOS and LAGEOS II satellites for the LARASE program

The two LAGEOS satellites, currently the best tracked satellites by the stations of the International Laser Ranging Service (ILRS), play a significant role in the fields of space geodesy and geophysics as well as in very precise measurements and constraints in fundamental physics. Specifically, for the measurements of tiny relativistic effects it is mandatory to build accurate models for the dynamics of the satellites, in particular concerning their spin evolution and the determination of their temperature distribution and thermal behavior under different physical conditions. Consequently, an accurate knowledge of both the external and internal structure of the laser-ranged satellites, and of their main dynamic parameters to be used within the orbit models, is of crucial importance. In this work we reconstruct information about the structure, the materials used, and the moments of inertia of the two LAGEOS satellites. The moments of inertia of LAGEOS resulted to be 11.42 ± 0.03 kg m2 for the cylindrical symmetry axis and 10.96 ± 0.03 kg m2 for the other two main axes. The analogous quantities for LAGEOS II are 11.45 ± 0.03 kg m2 and 11.00 ± 0.03 kg m2. We also built a 3D-CAD model of the satellites structure which is useful for finite element-based analysis. We tried to solve contradictions and overcome several misunderstanding present in the historical literature of the older LAGEOS, carefully reanalyzing the earlier technical papers. To test the results we obtained, we used our moments of inertia to compute the spin evolution of the two satellites obtaining a good agreement between measured and estimated values for the spin direction and the rotational period. We believe we now have accurate knowledge of the mass, moments of inertia, and composition of both LAGEOS satellites

Liquid actuated gravity experiments

We describe a new actuation technique for gravity experiments based on a liquid field mass. The Characterizing idea is to modulate the gravity force acting on a test mass by controlling the level of a liquid in a suitable container. This allows to obtain a periodical gravity force without moving parts (except the liquid level) close to the TM. We describe in detail the most relevant aspects of the liquid actuator and discuss how it can be used in gravity experiments. In particular we analyse an application to test the inverse square law in the mm to cm distance region

A quasi-complete mechanical model for a double torsion pendulum

We present a dynamical model for the double torsion pendulum nicknamed PETER, where one torsion pendulum hangs in cascade, but off-axis, from the other. The dynamics of interest in these devices lies around the torsional resonance, that is at very low frequencies (mHz). However, we find that, in order to properly describe the forced motion of the pendulums, also other modes must be considered, namely swinging and bouncing oscillations of the two suspended masses, that resonate at higher frequencies (Hz). Although the system has obviously 6+6 Degrees of Freedom, we find that 8 are sufficient for an accurate description of the observed motion. This model produces reliable estimates of the response to generic external disturbances and actuating forces or torques. In particular, we compute the effect of seismic floor motion (tilt noise) on the low frequency part of the signal spectra and show that it properly accounts for most of the measured low frequency noise.Comment: 15 pages, 6 figure

Testing gravitation with satellite laser ranging and the LARASE experiment

The International Laser Ranging Service (ILRS) provides range measurements of pas- sive satellites around the Earth through the powerful Satellite Laser Ranging (SLR) technique. These very precise measurements of the distance between an on-ground laser station and a satellite equipped with cube corner retro-reflectors (CCRs) make possible precise tests and measurements in fundamental physics and, in particular, in gravitational physics. The LAGEOS (NASA 1976) and LAGEOS II (NASA/ASI 1992) satellites are outstanding examples of very good test particles because of their very low area-to-mass ratio as well as the high quality of their tracking data and, consequently, of the precise orbit determination (POD) we can obtain after a refined modeling of their orbit. The aim of our research program LARASE (LAser RAnged Satellites Experi- ment) is to go a step further in testing gravitation in the field of Earth by means of the joint analysis of the orbits of the two LAGEOS satellites together with that of the most recently launched LARES (ASI, 2012) satellite. Therefore, our work falls in the so-called weak field and slow motion (WFSM) limit of Einstein’s general relativity (GR) where, in terms of Newtonian physics, relativistic effects appear as two new fields to be added to the classical gravitational field: the gravitoelectric and the gravitomagnetic fields. A fundamental ingredient to reach such a goal is to provide high-quality updated models for the perturbing non-gravitational perturbations (NGP) acting on the surface of these satellites. In fact, regardless of their minimization thanks to a smaller value for the area-to-mass ratio, the subtle and complex to model perturbing effects of the NGP play a crucial role in the POD of the considered satellites, especially in the case of the thermal thrust effects. A large amount of SLR data of LAGEOS and LAGEOS II has been worked out using a set of dedicated models for the satellite dynamics and the related post-fit residuals have been analyzed. A parallel work was performed with LARES, although at a preliminary stage. Our recent work on the orbit modeling and on the data analysis of the orbit of such satellites is presented and discussed

A 1% Measurement of the gravitomagnetic field of the earth with laser-tracked satellites

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 (≃7.4×10−3, at a 95% confidence level) and accuracy (≃16×10−3), 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

Testing General Relativity vs. Alternative Theories of Gravitation with the SaToR-G Experiment

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