Recent results of the LARASE research program in terms of model improvements and relativistic measurements are presented. In particular, the results regarding the development of new models for the non-gravitational perturbations that affect the orbit of the LAGEOS and LARES satellites are described and discussed. These are subtle and complex effects that need a deep knowledge of the structure and the physical characteristics of the satellites in order to be correctly accounted for. In the field of gravitational measurements, we present a new measurement of the relativistic Lense-Thirring precession with a $0.5\%$ precision. In this measurement, together with the relativistic effect we also estimated two even zonal harmonics coefficients. The uncertainties of the even zonal harmonics of the gravitational field of the Earth have been responsible, until now, of the larger systematic uncertainty in the error budget of this kind of measurements. For this reason, the role of the errors related to the model used for the gravitational field of the Earth in these measurements is discussed. In particular, emphasis is given to GRACE temporal models, that strongly help to reduce this kind of systematic errors.

Resonant gravitational wave detectors with an observation bandwidth of tens of hertz are a reality: the antenna Explorer, operated at CERN by the ROG Collaboration, has been upgraded with a new readout. In this new configuration, it exhibits an unprecedented useful bandwidth: in over 55 Hz about its center operating frequency of 919 Hz the spectral sensitivity is better than ${10}^{-20}{\mathrm{H}\mathrm{z}}^{-1/2}$. We describe the detector and its sensitivity and discuss the foreseeable upgrades to even larger bandwidths.

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 ($\simeq 7.4\times {10}^{-3}$, at a 95% confidence level) and accuracy ($\simeq 16\times {10}^{-3}$), 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.

A torsion pendulum with 2 soft degrees of freedom (DOFs), realized by off-axis cascading two torsion fibers, has been built and operated. This instrument helps characterize the geodesic motion of a test mass for LISA Pathfinder or any other free-fall space mission, providing information on cross talk and other effects that cannot be detected when monitoring a single DOF. We show that it is possible to simultaneously measure both the residual force and the residual torque acting on a quasifree test mass. As an example of the investigations that a double pendulum allows, we report the measurement of the force-to-torque cross talk, i.e., the amount of actuation signal, produced by applying a force on the suspended test mass, that leaks into the rotational DOF, detected by measuring the corresponding (unwanted) torque.

Data obtained during five months of 2001 with the gravitational wave (GW) detectors EXPLORER and NAUTILUS, operating with a bandwidth of a few Hz at frequencies near 900 Hz, were studied in correlation with the gamma ray burst data (GRB) obtained with the BeppoSAX satellite. During this period BeppoSAX was the only GRB satellite in operation, while EXPLORER and NAUTILUS were the only GW detectors in operation. No correlation between the GW data and the GRB bursts was found. The analysis, performed over 47 GRB’s, excludes the presence of signals of amplitude $h>~6.5\times {10}^{-19},$ with 95% probability, if we allow a time delay between GW bursts and GRB within $\pm 5\mathrm{s},$ and $h>~1.2\times {10}^{-18},$ if the time delay is within $\pm 400\mathrm{s}.$ The result is also provided in the form of scaled likelihood for unbiased interpretation and easier use for further analysis.

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.