Perspectives in measuring the PPN parameters beta and gamma in the Earth's gravitational fields with the CHAMP/GRACE models

The current bounds on the PPN parameters gamma and beta are of the order of 10^-4-10^-5. Various missions aimed at improving such limits by several orders of magnitude have more or less recently been proposed like LATOR, ASTROD, BepiColombo and GAIA. They involve the use of various spacecraft, to be launched along interplanetary trajectories, for measuring the effects of the solar gravity on the propagation of electromagnetic waves. In this paper we investigate what is needed to measure the combination nu=(2+2gamma-beta)/3 of the post-Newtonian gravitoelectric Einstein perigee precession of a test particle to an accuracy of about 10^-5 with a pair of drag-free spacecraft in the Earth's gravitational field. It turns out that the latest gravity models from the dedicated CHAMP and GRACE missions would allow to reduce the systematic error of gravitational origin just to this demanding level of accuracy. In regard to the non-gravitational errors, the spectral noise density of the drag-free sensors required to reach such level of accuracy would amounts to 10^-8-10^-9 cm s^-2 Hz^-1/2 over very low frequencies. Although not yet obtainable with the present technologies, such level of compensation is much less demanding than those required for, e.g., LISA. As a by-product, an independent measurement of the post-Newtonian gravitomagnetic Lense-Thirring effect with a 0.9% accuracy would be possible as well. The forthcoming Earth gravity models from CHAMP and GRACE will further reduce the systematic gravitational errors in both of such tests.Comment: LaTex2e, 14 pages, 3 tables, no figures, 75 references. To appear in Int. J. Mod. Phys.

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

On the use of Ajisai and Jason-1 satellites for tests of General Relativity

Here we analyze in detail some aspects of the proposed use of Ajisai and Jason-1, together with the LAGEOS satellites, to measure the general relativistic Lense-Thirring effect in the gravitational field of the Earth. A linear combination of the nodes of such satellites is the proposed observable. The systematic error due to the mismodelling in the uncancelled even zonal harmonics would be \sim 1% according to the latest present-day CHAMP/GRACE-based Earth gravity models. In regard to the non-gravitational perturbations especially affecting Jason-1, only relatively high-frequency harmonic perturbations should occur: neither semisecular nor secular bias of non-gravitational origin should affect the proposed combination: their maximum impact is evaluated to \sim 4% over 2 years. Our estimation of the root-sum-square total error is about 4-5% over at least 3 years of data analysis required to average out the uncancelled tidal perturbations.Comment: Latex, 24 pages, 5 tables, 1 figure. Two references added, minor modifications. To appear in New Astronom

The relativistic precession of the orbits

The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.Comment: Accepted for publication in Astrophysics & Space Scienc

An assessment of the measurement of the Lense-Thirring effect in the Earth gravity field, in reply to: ``On the measurement of the Lense-Thirring effect using the nodes of the LAGEOS satellites, in reply to ``On the reliability of the so far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites'' by L. Iorio,'' by I. Ciufolini and E. Pavlis

In this paper we reply to recent claims by Ciufolini and Pavlis about certain aspects of the measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth. I) The proposal by such authors of using the existing satellites endowed with some active mechanism of compensation of the non-gravitational perturbations as an alternative strategy to improve the currently ongoing Lense-Thirring tests is unfeasible because of the impact of the uncancelled even zonal harmonics of the geopotential and of some time-dependent tidal perturbations. II) It is shown that their criticisms about the possibility of using the existing altimeter Jason-1 and laser-ranged Ajisai satellites are groundless.III) Ciufolini and Pavlis also claimed that we would have explicitly proposed to use the mean anomaly of the LAGEOS satellites in order to improve the accuracy of the Lense-Thirrring tests. We prove that it is false. In regard to the mean anomaly of the LAGEOS satellites, Ciufolini himself did use such an orbital element in some previously published tests. About the latest test performed with the LAGEOS satellites, IV) we discuss the cross-coupling between the inclination errors and the first even zonal harmonic as another possible source of systematic error affecting it with an additional 9% bias. V) Finally, we stress the weak points of the claims about the origin of the two-nodes LAGEOS-LAGEOS II combination used in that test.Comment: LaTex2e, 22 pages, no figures, no tables. To appear in Planetary and Space Science. Reference Ries et al. 2003a added and properly cite

Nordic Walking promoted weight loss in overweight and obese people: A systematic review for future exercise prescription

The aim of this systematic review was to analyze the effect of Nordic Walking (NW) on anthropometric parameters, body composition, cardiovascular parameters, aerobic capacity, blood sample, and glucose tolerance in overweight and obese subjects. The main keywords "Nordic Walking" or "Pole Walking", associated with either "obese", "obesity", "overweight", or "weight loss" were used on the online database MEDLINE, PubMed, SPORTDiscus and Scopus. Additionally, references of the studies included were screened to identify eligible articles. Applying the inclusion and exclusion criteria, ten manuscripts were considered as eligible for this review. The results of the studies were categorized in several domains with regard to "anthropometric parameters and body composition", "cardiovascular parameters and aerobic capacity", and "blood sample and glucose tolerance". The results showed positive effects on the anthropometric parameters, body composition, cardiovascular parameters, blood sample, and glucose tolerance. The greatest improvements were observed in supervised and high weekly frequency of NW interventions. NW could be considered as an effective modality through which to involve the obese in physical activity. For weight loss, NW should be prescribed 4-5 times per week, at least 60 min per session, preferably combined with diet control

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

First preliminary tests of the general relativistic gravitomagnetic field of the Sun and new constraints on a Yukawa-like fifth force from planetary data

The general relativistic Lense-Thirring precessions of the perihelia of the inner planets of the Solar System are about 10^-3 arcseconds per century. Recent improvements in planetary orbit determination may yield the first observational evidence of such a tiny effect. Indeed, corrections to the known perihelion rates of -0.0036 +/- 0.0050, -0.0002 +/- 0.0004 and 0.0001 +/- 0.0005 arcseconds per century were recently estimated by E.V. Pitjeva for Mercury, the Earth and Mars, respectively, on the basis of the EPM2004 ephemerides and a set of more than 317,000 observations of various kinds. The predicted relativistic Lense-Thirring precessions for these planets are -0.0020, -0.0001 and -3 10^-5 arcseconds per century, respectively and are compatible with the determined perihelia corrections. The relativistic predictions fit better than the zero-effect hypothesis, especially if a suitable linear combination of the perihelia of Mercury and the Earth, which a priori cancels out any possible bias due to the solar quadrupole mass moment, is considered. However, the experimental errors are still large. Also the latest data for Mercury processed independently by Fienga et al. with the INPOP ephemerides yield preliminary insights about the existence of the solar Lense-Thirring effect. The data from the forthcoming planetary mission BepiColombo will improve our knowledge of the orbital motion of this planet and, consequently, the precision of the measurement of the Lense-Thirring effect. As a by-product of the present analysis, it is also possible to constrain the strength of a Yukawa-like fifth force to a 10^-12-10^-13 level at scales of about one Astronomical Unit (10^11 m).Comment: LaTex, 22 pages, 1 figure, 5 tables, 62 references. To appear in Planetary and Space Scienc

Reliability of an isometric and isokinetic strength testing protocol of the knee and ankle in young adults

Background: Isokinetic dynamometers are becoming very common in assessing muscle strength and pathology, both in research and clinical practice, but for most of those devices reliability studies are still needed to support their extended use. The aim of this study is to assess the test-retest reliability also in health adults. Methods: Thirty adults (13 male and 17 females; mean age 25.4 ± 2.7 years) were recruited among University students. They participated to two testing sessions (7 day apart) in which they performed isokinetic and isometric strength assessment of the knee and ankle flexion and extension. Results: All variable showed an Intra-class correlation coefficient higher than 0.7 (isometric knee extension 0.96; isokinetic knee extension 0.96; isokinetic knee flexion 0.97; isometric ankle right flexion pl and flexion do 0.75-0.96; isometric ankle left flexion pl and flexion do 0.78-0.97; isokinetic ankle right flexion pl and flexion do 0.88-0.73; isokinetic ankle right flexion pl and flexion do 0.88-0.85) and paired-sample t-test showed no significant difference. Moreover, most of the recorded values were included within the upper and lower limits of agreement. Conclusion: Multi-joint evaluation system is a reliable device to assess knee and ankle isokinetic and isometric strength among healthy adults

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