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The Earth gravitomagnetic field measurement with LAGEOS satellites: impact of the time–depend part of Earth’s gravity field in the Lense–Thirring effect Error Budget

In the weak field and slow motion limit of Einstein’s general relativity (GR), mass-currents are responsible for gravitomagnetic effects similar to the magnetic effects produced by electric currents: as the Lorentz force acts on a moving-charged particle in the presence of an external magnetic field, in GR the orbit (geodesic) of a point-mass around a primary body is dragged by the gravitomagnetic field produced by the body’s rotation, i.e., by its angular momentum. As a consequence, the axes of a freely–falling frame are rotationally dragged by the angular momentum of the primary body. In 1918, Lense and Thirring computed the additional relativistic gravitomagnetic precession of the orbital plane (which can be considered as a gyroscope) of a satellite orbiting a primary. This relativistic effect is therefore known as Lense–Thirring effect. The Lense–Thirring effect is responsible of a secular shift of the satellite ascending node longitude and argument of perigee. The effect is very small, less than 2 m/yr on the node of the two LAGEOS satellites, the best tracked Earth’s satellites through the Satellite Laser Ranging (SLR) technique. The SLR technique allow the determination of the position of both LAGEOS satellites with precision of a few mm in their normal points, and a root–mean–square of their range residuals of about 2–3 cm over 15 days arcs. Therefore, from the analysis of LAGEOS satellites orbit it is possible to measure the secular precession predicted by GR. We review the error budget of the last measurement of the Lense–Thirring effect (about 5% of the GR prediction) performed by Ciufolini and Pavlis (Nature 431, 2004) with their 11 years analysis of the orbits of the two LAGEOS satellites. In this measurement, the EIGEN-GRACE02S gravity field model from the GRACE mission was used in order to model Earth’s shape and mass distribution. We highlight the role of the major gravitational and non-gravitational perturbations and the impact of their systematic effects in the measurement of the relativistic precession. In particular, we explain (from the physical point of view) the 1% result for the error due to the even zonal harmonics secular variations given by Ciufolini and Pavlis with their analysis of the satellites nodes precession. Finally, we emphasize the difficulties in improving significantly the present measure of the Lense–Thirring effect with the two LAGEOS satellites only.

LAGEOS satellites pericenter: a tool to constrain a Yukawa interaction in Earth’s field

The deviations from the usual 1/r law for the gravitational potential, as in the hypothesis of a fifth–force of nature, would lead to new weak interactions between macroscopic objects. Very significantly, these supplementary interactions may be either consistent with Einstein Equivalence Principle (EEP) or not. The characteristic of such very weak interactions, which are predicted by several theories, is to produce deviations for masses separations ranging through several orders of magnitude, starting from the sub–millimeter level up to the astronomical scale. These interactions are usually described through a Yukawa–like potential with strength \alpha and range \lambda. Among the several techniques useful for the search of this additional physics at the various scales, the accurate measurements of the pericenter shift of a binary system may be used to test for a New–Long–Range–Interaction (NLRI) with a characteristic range comparable with the system semimajor axis. The LAGEOS satellites, thanks to the very accurate determination of their orbit by the Satellite Laser Ranging (SLR) technique (with a precision of a few mm in the so–called normal points), could be considered the best candidates for the study of a possible NLRI with a characteristic range close to the Earth radius. We focus on the constrain we can obtain today for a possible Yukawa interaction from the accurate analysis of the argument of pericenter of the two LAGEOS satellites. We consider, in order to estimate a reliable error budget, the impact of the main systematic errors due to the gravitational and non–gravitational perturbations. In particular, with regard to the gravitational perturbations, we analysed the most recent gravity field models from CHAMP and GRACE space missions. Indeed, thanks to these dedicated missions, the systematic errors from Earth’s gravitational field uncertainties have been strongly reduced with respect to the previous multi–satellite models. Therefore, only the subtle effects of the non–gravitational perturbations will be effective in biasing the measurement of the strength \alpha of a possible Yukawa–like interaction with respect to the 10^(-11) value that can be in principle constrained with an accurate analysis of LAGEOS satellites orbit.