THE IMPACT OF THE EVEN ZONAL HARMONICS SECULAR VARIATIONS ON THE LENSE–THIRRING EFFECT MEASUREMENT WITH THE TWO LAGEOS SATELLITES
Authors: LUCCHESI DAVID M. 
Published: February 2006

This work has been motivated by the criticisms raised on the error budget contribution — on a recently performed measurement of the Lense–Thirring effect — from the uncertainties of the secular variations of the Earth's even zonal harmonics. The relativistic secular precession has been observed from the analysis of 11 years of LAGEOS and LAGEOS II laser ranging data. In the analysis, the recent EIGEN–GRACE02S gravity field model (derived from GRACE data only) was used during the orbit determination process using the NASA Goddard software package GEODYN II. In particular, the measurement has been derived combining the nodes only of the two LAGEOS satellites in order to cancel the larger error source, due to the uncertainty of the first even zonal harmonic, and solved for the Lense–Thirring effect predicted by Einstein's general relativity. The authors of the relativistic measurement claimed an error of about 1% of the relativistic effect as due to the temporal variation of the even zonal harmonics. The main criticism is that on a much larger error estimate, about 11% of the relativistic effect on the analyzed time span of the two LAGEOS satellites orbital data should be considered. Moreover, the authors of the relativistic measurement emphasized that whatever the value they chose for the secular variations, in particular of the effective value for [Formula: see text], they always obtained the same discrepancy of about 1% between the observed and predicted effect, without however providing a detailed explanation. In the present work we address all the cited aspects. In particular, we explain the physical reason for the results obtained by the authors of the relativistic measurement in all their simulations. As we will see, two additional errors (linear in time) must be considered in the satellites orbit analysis if we want to correctly explain the experimental results. The first is a time-dependent error related with the mismodeling of the secular variations of the even zonal harmonics. The inclusion of this error in the error analysis explains why the same discrepancy between the observed and predicted effect has been always obtained independently of the assumed value for [Formula: see text], i.e. for the errors in the time variations of the even zonal harmonics. The second is a time-independent error related to the non-coincidence between the reference epoch of the gravity field, i.e. the middle epoch of the time span during which the gravity field has been determined by the GRACE mission, and the reference epoch fixed in the orbit analysis program. The inclusion of this error in the error analysis explains the 1% value for the discrepancy between the prediction and the observations. In order to validate our results we fitted for an effective [Formula: see text] from the combined nodes of the LAGEOS satellites with the EIGEN2S gravity field model obtained from the CHAMP mission. From our fit, we consistently confirmed our previous statements. In particular, we prove a very interesting and new approach in order to compute the effective values of the time variations of the even zonal harmonics from the estimate of the time-independent error previously cited.