Will the recently approved LARES mission be able to measure the Lense-Thirring effect at 1%?

After the approval by the Italian Space Agency of the LARES satellite, which should be launched at the end of 2009 with a VEGA rocket and whose claimed goal is a about 1% measurement of the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of the spinning Earth, it is of the utmost importance to reliably assess the total realistic accuracy that can be reached by such a mission. The observable is a linear combination of the nodes of the existing LAGEOS and LAGEOS II satellites and of LARES able to cancel out the impact of the first two even zonal harmonic coefficients of the multipolar expansion of the classical part of the terrestrial gravitational potential representing a major source of systematic error. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be placed at an altitude of 1450 km. Thus, it will be sensitive to much more even zonals than LAGEOS and LAGEOS II. Their corrupting impact \delta\mu has been evaluated by using the standard Kaula's approach up to degree L=70 along with the sigmas of the covariance matrices of eight different global gravity solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, JEM01-RL03B, ITG-Grace02s, ITG-Grace03, EGM2008) obtained by five institutions (GFZ, CSR, JPL, IGG, NGA) with different techniques from long data sets of the dedicated GRACE mission. It turns out \delta\mu about 100-1000% of the Lense-Thirring effect. An improvement of 2-3 orders of magnitude in the determination of the high degree even zonals would be required to constrain the bias to about 1-10%.Comment: Latex, 15 pages, 1 table, no figures. Final version matching the published one in General Relativity and Gravitation (GRG

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

Phenomenology of the Lense-Thirring effect in the Solar System

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in Astrophysics and Space Science (ApSS). Some uncited references in the text now correctly quoted. One reference added. A footnote adde

An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging

We deal with the attempts to measure the Lense-Thirring effect with the Satellite Laser Ranging (SLR) technique applied to the existing LAGEOS and LAGEOS II terrestrial satellites and to the recently approved LARES spacecraft.The first issue addressed here is: are the so far published evaluations of the systematic uncertainty induced by the bad knowledge of the even zonal harmonic coefficients J_L of the multipolar expansion of the Earth's geopotential reliable and realistic? Our answer is negative. Indeed, if the differences Delta J_L among the even zonals estimated in different Earth's gravity field global solutions from the dedicated GRACE mission are assumed for the uncertainties delta J_L instead of using their covariance sigmas sigma_JL, it turns out that the systematic uncertainty \delta\mu in the Lense-Thirring test with the nodes Omega of LAGEOS and LAGEOS II may be up to 3 to 4 times larger than in the evaluations so far published ($5-10$) based on the use of the sigmas of one model at a time separately. The second issue consists of the possibility of using a different approach in extracting the relativistic signature of interest from the LAGEOS-type data. The third issue is the possibility of reaching a realistic total accuracy of 1% with LAGEOS, LAGEOS II and LARES, which should be launched in November 2009 with a VEGA rocket. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be likely placed at an altitude of 1450 km. Thus, it will be sensitive to much more even zonals than LAGEOS and LAGEOS II. Their corrupting impact has been evaluated with the standard Kaula's approach up to degree L=60 by using Delta J_L and sigma_JL; it turns out that it may be as large as some tens percent.Comment: LaTex, 19 pages, 1 figure, 12 tables. Invited and refereed contribution to The ISSI Workshop, 6-10 October 2008, on The Nature of Gravity Confronting Theory and Experiment in Space To appear in Space Science Review

Study of the reducibility of copper in CuO-ZnO catalysts by temperature-programmed reduction

Temperature-programmed reduction (TPR) has been used in this work to study the reduction of copper in CuO-ZnO catalysts with different Cu/Zn atomic ratios using H-2 as reducing agent. In all catalysts, CuO was completely reduced to metal. The influence exerted by ZnO on the reduction of copper was evaluated for a wide range of composition and a scale of reducibility was established. ZnO affects the hydrogen reduction of copper, CuO-ZnO samples showing a different behaviour with respect to the pure copper oxide. The reduction is always promoted and, in particular, catalysts with lower copper loading (Cu:Zn < 30:70 as atomic ratio) showed the highest reactivity and are characterised by the presence of two reducible copper species. Results of a kinetic analysis based on the TPR profiles confirmed the role played by ZnO as promoter of the copper oxide reduction. The effect of the preparation method on the catalyst reducibility was also verified and discussed in a specific case, H-2-CO2-H-2 redox cycles were carried out on some representative samples which, after the first reduction in H-2, were reoxidised with CO2 and then reduced again by H-2. These experiments revealed that a small percent of metal copper formed in the CuO-ZnO catalysts is oxidised by CO2 regardless of the catalyst composition, whereas metal copper formed by reduction of pure CuO is not reoxidised at a detectable level. Furthermore, it was evidenced that the small fraction of copper reoxidised by CO2 was extremely reactive, being reduced at temperatures much lower than those found for the reduction of the as-prepared catalysts, Both the TPR investigation and the H-2-CO2-H-2 redox cycles clearly assessed the presence of a synergistic effect arising by the contact of CuO with the ZnO particles

A STUDY OF ANOMALOUS TEMPERATURE-PROGRAMMED REDUCTION PROFILES OF CU2O, CUO, AND CUO-ZNO CATALYSTS

A temperature-programmed reduction (TPR) study of CuO, Cu2O, and Cuo-ZnO catalysts, in the atomic range Cu:Zn = 92:8 to 67:33, is reported. In order to promote a correct experimental approach, much attention has been devoted to the choice of the experimental operating variables. Direct evidence is presented that the reduction profiles of the investigated specimens are markedly affected by artefacts when TPR measurements are carried out under conditions of an inadequate combination of initial amount of reducible species, total flow rate, initial hydrogen concentration, and heating rate. It is shown that under correct experimental conditions the reduction profile of each sample is characterized by a single and quite sharp reduction peak. In contrast to this, a dramatic change of shape occurs when an improper combination of the experimental operating variables is imposed: for both CuO and Cu2O an apparent double peak appears, whereas for the CuO-ZnO catalysts the reduction profiles are transformed into broad bands. In all cases, the reliability of the TPR results is completely lost. To explain the complex origin of these artefacts, it is suggested that both a special dynamic situation and activated H-2 adsorption-desorption phenomena coinciding with the chemical reduction are responsible for the observed perturbations. A simple kinetic analysis has been developed which enables a qualitative reproduction of the disturbed reduction profiles to be made. (C) 1994 Academic Press, Inc

Cell for the in situ study of heterogeneous catalysts by transmission and fluorescence XAS spectroscopy

A simple cell, assembled with commercial parts, suitable for in situ X-ray-absorption spectroscopy measurements of heterogeneous catalysts, has been designed. The cell, light and easy to handle, allows thermal treatments of the sample under investigation up to 823 K in a reducing or oxidizing atmosphere and measurements at both high and liquid-nitrogen temperature. The cell was tested by studying the decomposition, in an oxygen flow, of ammonium metatungstate to WO3. Extended X-ray absorption fine-structure measurements of the ammonium metatungstate before and after a thermal treatment at 773 K are reported