LAGEOS II pericenter general relativistic precession (1993–2005): Error budget and constraints in gravitational physics

Abstract

The aim of this paper is to extend, clarify, and deepen the results of our previous work [D. M. Lucchesi and R. Peron, Phys. Rev. Lett. 105, 231103 (2010)], related to the precise measurement of LAGEOS (LAser GEOdynamics Satellite) II pericenter shift. A 13-year time span of LAGEOS satellites' laser tracking data has been considered, obtaining a very precise orbit and correspondingly residuals time series from which to extract the relevant signals. A thorough description is provided of the data analysis strategy and the dynamical models employed, along with a detailed discussion of the known sources of error in the experiment, both statistical and systematic. From this analysis, a confirmation of the predictions of Einstein's general relativity, as well as strong bounds on alternative theories of gravitation, clearly emerge. In particular, taking conservatively into account the stricter error bound due to systematic effects, general relativity has been confirmed in the Earth's field at the 98% level (meaning the measurement of a suitable combination of $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ PPN parameters in weak-field conditions). This bound has been used to constrain possible deviations from the inverse-square law parameterized by a Yukawa-like new long range interaction with strength $|\ensuremath{\alpha}|\ensuremath{\lesssim}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ at a characteristic range $\ensuremath{\lambda}\ensuremath{\simeq}1$ Earth radius, a possible nonsymmetric gravitation theory with the interaction parameter ${\mathcal{C}}_{\ensuremath{\bigoplus}\text{LAGEOS II}}{\ensuremath{\lesssim}\text{(9 \ifmmode\times\else\texttimes\fi{} 10}}^{\ensuremath{-}2}\text{ }\text{ }\mathrm{km}{)}^{4}$, and a possible spacetime torsion with a characteristic parameter combination $|2{t}_{2}+{t}_{3}|\ensuremath{\lesssim}7\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}2}$. Conversely, if we consider the results obtained from our best fit of the LAGEOS II orbit, the constraints in fundamental physics improve by at least 2 orders of magnitude.