Measuring the relativistic perigee advance with Satellite Laser Ranging

One of the most famous classical tests of General Relativity is the gravitoelectric secular advance of the pericenter of a test body in the gravitational field of a central mass. In this paper we explore the possibility of performing a measurement of the gravitoelectric pericenter advance in the gravitational field of the Earth by analyzing the laser-ranged data to some existing, or proposed, laser-ranged geodetic satellites. At the present level of knowledge of various error sources, the relative precision obtainable with the data from LAGEOS and LAGEOS II, suitably combined, is of the order of $10^{\rm -3}$. Nevertheless, these accuracies could sensibly be improved in the near future when the new data on the terrestrial gravitational field from the CHAMP and GRACE missions will be available. The use of the perigee of LARES (LAser RElativity Satellite), in the context of a suitable combination of orbital residuals including also LAGEOS II, should further raise the precision of the measurement. As a secondary outcome of the proposed experiment, with the so obtained value of \ppn and with \et=4\beta-\gamma-3 from Lunar Laser Ranging it could be possible to obtain an estimate of the PPN parameters $\gamma$ and $\beta$ at the $10^{-2}-10^{-3}$ level.Comment: LaTex2e, 14 pages, no figures, 2 tables. To appear in Classical and Quantum Gravit

Fracture behaviour of alloys for a new laser ranged satellite

A new laser-ranged satellite called LARES 2 (Laser Relativity Satellite 2) has been recently designed for accurate tests of Einsten's theory of General Relativity and space geodesy. Some high density alloys (8.6-9.3 g/dm3) have been studied and characterised for producing the LARES 2 passive satellite. The considered materials were Copper and Nickel based alloys that have been produced and characterised. Aim of this work was to analyse their fracture behaviour that is a requirement for materials to be used for space applications. Fracture tests have been carried out on several specimens and fracture surfaces have been analysed

On a new observable for measuring the Lense-Thirring effect with Satellite Laser Ranging

In this paper we present a rather extensive error budget for the difference of the perigees of a pair of supplementary SLR satellites aimed to the detection of the Lense-Thirring effect.Comment: LaTex2e, 14 pages, 1 table, no figures. Some changes and additions to the abstract, Introduction and Conclusions. References updated, typos corrected. Equation corrected. To appear in General Relativity and Gravitatio

Mathematical prediction of the time evolution of the COVID-19 pandemic in Italy by a Gauss error function and Monte Carlo simulations

none2noIn this paper are presented mathematical predictions on the evolution in time of the number of positive cases in Italy of the COVID-19 pandemic based on official data and on the use of a function of the type of a Gauss error function, with four parameters, as a cumulative distribution function. We have analyzed the available data for China and Italy. The evolution in time of the number of cumulative diagnosed positive cases of COVID-19 in China very well approximates a distribution of the type of the error function, that is, the integral of a normal, Gaussian distribution. We have then used such a function to study the potential evolution in time of the number of positive cases in Italy by performing a number of fits of the official data so far available. We then found a statistical prediction for the day in which the peak of the number of daily positive cases in Italy occurs, corresponding to the flex of the fit, that is, to the change in sign of its second derivative (i.e., the change from acceleration to deceleration), as well as of the day in which a substantial attenuation of such number of daily cases is reached. We have also analyzed the predictions of the cumulative number of fatalities in both China and Italy, obtaining consistent results. We have then performed 150 Monte Carlo simulations to have a more robust prediction of the day of the above-mentioned peak and of the day of the substantial decrease in the number of daily positive cases and fatalities. Although official data have been used, those predictions are obtained with a heuristic approach since they are based on a statistical approach and do not take into account either a number of relevant issues (such as number of daily nasopharyngeal swabs, medical, social distancing, virological and epidemiological) or models of contamination diffusion.openCiufolini I.; Paolozzi A.Ciufolini, I.; Paolozzi, A

Geodesic motion in General Relativity: LARES in Earth's gravity

According to General Relativity, as distinct from Newtonian gravity, motion under gravity is treated by a theory that deals, initially, only with test particles. At the same time, satellite measurements deal with extended bodies. We discuss the correspondence between geodesic motion in General Relativity and the motion of an extended body by means of the Ehlers-Geroch theorem, and in the context of the recently launched LAser RElativity Satellite (LARES). Being possibly the highest mean density orbiting body in the Solar system, this satellite provides the best realization of a test particle ever reached experimentally and provides a unique possibility for testing the predictions of General Relativity.Comment: 4 pages, 1 imag

How to reach a few percent level in determining the Lense-Thirring effect?

In this paper we discuss and compare a node-only LAGEOS-LAGEOS II combination and a node-only LAGEOS-LAGEOS II-Ajisai-Jason1 combination for the determination of the Lense-Thirring effect. The new combined EIGEN-CG01C Earth gravity model has been adopted. The second combination cancels the first three even zonal harmonics along with their secular variations but introduces the non-gravitational perturbations of Jason1. The first combination is less sensitive to the non-conservative forces but is sensitive to the secular variations of the uncancelled even zonal harmonics of low degree J4 and J6 whose impact grows linearly in time.Comment: Latex2e, 22 pag. 1 table, 2 figures, 45 references. Changes in the Abstract, Introduction and Conclusions. Discussion on the non-gravitational perturbations on Ajisai and on the impact of the secular rates of the even zonal harmonics added. EIGEN-CG01C CHAMP+GRACE+terrestrial gravimetry/altimetry Earth gravity model used. Reference adde

Global aspects of gravitomagnetism

We consider global properties of gravitomagnetism by investigating the gravitomagnetic field of a rotating cosmic string. We show that although the gravitomagnetic field produced by such a configuration of matter vanishes locally, it can be detected globally. In this context we discuss the gravitational analogue of the Aharonov-Bohm effect.Comment: 10 pages - Typeset using REVTE

On the Earth's tidal perturbations for the LARES satellite

Frame dragging, one of the outstanding phenomena predicted by General Relativity, is efficiently studied by means of the laser-ranged satellites LARES, LAGEOS and LAGEOS 2. The accurate analysis of the orbital perturbations of Earth's solid and ocean tides has been relevant for increasing the accuracy in the test of frame-dragging using these three satellites. The Earth's tidal perturbations acting on the LARES satellite are obtained for the 110 significant modes of corresponding Doodson number and are exhibited to enable the comparison to those of the LAGEOS and LAGEOS-2 satellites. For LARES we represent 29 perturbation modes for l=2,3,4 for ocean tides.Comment: 14 pages, 9 figures, to appear in Eur Phys J Plus (subm. Sept 20, 2017

LARES/WEBER-SAT and the equivalence principle

It has often been claimed that the proposed Earth artificial satellite LARES/WEBER-SAT-whose primary goal is, in fact, the measurement of the general relativistic Lense-Thirring effect at a some percent level-would allow to greatly improve, among (many) other things, the present-day (10^-13) level of accuracy in testing the equivalence principle as well. Recent claims point towards even two orders of magnitude better, i.e. 10^-15. In this note we show that such a goal is, in fact, unattainable by many orders of magnitude being, instead, the achievable level of the order of 10^-9.Comment: LaTex, 4 pages, no figures, no tables, 26 references. Proofs corrections included. To appear in EPL (Europhysics Letters

Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense-Thirring test

We deal with the test of the general relativistic gravitomagnetic Lense-Thirring effect currently ongoing in the Earth's gravitational field with the combined nodes \Omega of the laser-ranged geodetic satellites LAGEOS and LAGEOS II. One of the most important source of systematic uncertainty on the orbits of the LAGEOS satellites, with respect to the Lense-Thirring signature, is the bias due to the even zonal harmonic coefficients J_L of the multipolar expansion of the Earth's geopotential which account for the departures from sphericity of the terrestrial gravitational potential induced by the centrifugal effects of its diurnal rotation. The issue addressed here is: are the so far published evaluations of such a systematic error reliable and realistic? The answer is negative. Indeed, if the difference \Delta J_L among the even zonals estimated in different global solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, ITG-Grace02, ITG-Grace03s, JEM01-RL03B, EGM2008, AIUB-GRACE01S) is assumed for the uncertainties \delta J_L instead of using their more or less calibrated covariance sigmas \sigma_{J_L}, it turns out that the systematic error \delta\mu in the Lense-Thirring measurement is about 3 to 4 times larger than in the evaluations so far published based on the use of the sigmas of one model at a time separately, amounting up to 37% for the pair EIGEN-GRACE02S/ITG-Grace03s. The comparison among the other recent GRACE-based models yields bias as large as about 25-30%. The major discrepancies still occur for J_4, J_6 and J_8, which are just the zonals the combined LAGEOS/LAGOES II nodes are most sensitive to.Comment: LaTex, 12 pages, 12 tables, no figures, 64 references. To appear in Central European Journal of Physics (CEJP