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

In this paper, we provide a detailed description of our recent analysis and determination of the frame-dragging effect obtained using the nodes of the satellites LAGEOS and LAGEOS 2, in reply to the paper "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. IorioComment: Added: the precise references to the the ArXiv papers of L. Iorio: gr-qc/0411024 v9 19 Apr 2005 and gr-qc/0411084 v5 19 Apr 2005, explicitly containing his proposal to use the mean anomal

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

Measuring the Lense-Thirring precession using a second Lageos satellite

A complete numerical simulation and error analysis was performed for the proposed experiment with the objective of establishing an accurate assessment of the feasibility and the potential accuracy of the measurement of the Lense-Thirring precession. Consideration was given to identifying the error sources which limit the accuracy of the experiment and proposing procedures for eliminating or reducing the effect of these errors. Analytic investigations were conducted to study the effects of major error sources with the objective of providing error bounds on the experiment. The analysis of realistic simulated data is used to demonstrate that satellite laser ranging of two Lageos satellites, orbiting with supplemental inclinations, collected for a period of 3 years or more, can be used to verify the Lense-Thirring precession. A comprehensive covariance analysis for the solution was also developed

Is it possible to test directly General Relativity in the gravitational field of the Moon?

In this paper the possibility of measuring some general relativistic effects in the gravitational field of the Moon via selenodetic missions, with particular emphasis to the future Japanese SELENE mission, is investigated. For a typical selenodetic orbital configuration the post-Newtonian Lense-Thirring gravitomagnetic and the Einstein's gravitoelectric effects on the satellites orbits are calculated and compared to the present-day orbit accuracy of lunar missions. It turns out that for SELENE's Main Orbiter, at present, the gravitoelectric periselenium shift, which is the largest general relativistic effect, is 1 or 2 orders of magnitude smaller than the experimental sensitivity. The systematic error induced by the mismodelled classical periselenium precession due to the first even zonal harmonic J2 of the Moon's non-spherical gravitational potential is 3 orders of magnitude larger than the general relativistic gravitoelectric precession. The estimates of this work could be used for future lunar missions having as their goals relativistic measurements as well.Comment: Latex2e, 7 pages, no figures, ets2000.cls and art12.sty used. Major rewriting in introduction. References adde

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

The impact of the new Earth gravity model EIGEN-CG03C on the measurement of the Lense-Thirring effect with some existing Earth satellites

The impact of the latest combined CHAMP/GRACE/terrestrial measurements Earth gravity model EIGEN-CG03C on the measurement of the Lense-Thirring effect with some linear combinations of the nodes of some of the existing Earth's artificial satellites is presented. The 1-sigma upper bound of the systematic error in the node-node LAGEOS-LAGEOS II combination is 3.9% (4% with EIGEN-GRACE02S, \sim 6% with EIGEN-CG01C and \sim 9% with GGM02S), while it is 1$% for the node-only LAGEOS-LAGEOS II-Ajisai-Jason-1 combination (2% with EIGEN-GRACE02S, 1.6% with EIGEN-CG01C and 2.7% with GGM02S).Comment: LaTex2e, 7 pages, 16 references, 1 table. It is an update of the impact of the even zonal harmonics of the geopotential on the Lense-Thirring effect with the EIGEN-GGM03C Earth gravity model publicly released on May 11 2005. Typos corrected. Reference added. To appear in General Relativity and Gravitation, March 200

The impact of the new CHAMP and GRACE Earth gravity models on the measurement of the general relativistic Lense--Thirring effect with the LAGEOS and LAGEOS II satellites

Among the effects predicted by the General Theory of Relativity for the orbital motion of a test particle, the post-Newtonian gravitomagnetic Lense-Thirring effect is very interesting and, up to now, there is not yet an undisputable experimental direct test of it. To date, the data analysis of the orbits of the existing geodetic LAGEOS and LAGEOS II satellites has yielded a test of the Lense-Thirring effect with a claimed accuracy of 20%-30%. According to some scientists such estimates could be optimistic. Here we wish to discuss the improvements obtainable in this measurement, in terms of reliability of the evaluation of the systematic error and reduction of its magnitude, due to the new CHAMP and GRACE Earth gravity models.Comment: LaTex2e, 6 pages, no figures, no tables. Paper presented at 2nd CHAMP science meeting, Potsdam, 1-4 September 200

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