The Lense–Thirring effect measurement and LAGEOS satellites orbit analysis with the new gravity field model from the CHAMP mission

Abstract

The Lense–Thirring effect – one of the main predictions of Einstein’s theory of gravitation in the limit of weak field and slow motion – represents a tiny relativistic precession of the orbital plane of a satellite produced by the angular momentum of the primary. In the present work, we estimated an updated error budget for the Lense–Thirring effect measurement through the accurate analysis of the orbit of the passive laser-ranged LAGEOS satellites. This error budget has been estimated over a 9 years time span. The error estimate has been performed on a nodes-only combination of the satellites orbital residuals. The advantage is the smaller impact of the non-gravitational perturbations with respect to a combination involving also LAGEOS II argument of perigee. The recent gravity model EIGEN-2 for the Earth’s gravity field has been considered. Indeed, with the nodes-only combination the error budget from the non-gravitational perturbation is about a few parts of % of the relativistic effect (48.1 mas/yr), while the error from the full covariance matrix of the EIGEN-2 solution is about 17.8%. Therefore, taking into consideration these two sources of error, we obtained an error budget less than 18% for the Lense–Thirring effect measurement (computed in a root–sum–square fashion). The contribution from other gravitational error sources has been considered, as solid and oceans tides, odd zonal harmonics, and secular variations in the even zonal harmonics. All these perturbations are responsible, with the exception of the secular variations in the even zonal harmonics, of systematic effects smaller than those estimated for the non-gravitational perturbations. The open problems related with a full calibration of the errors from the new gravity field models are outlined.