The impact of the new Earth gravity models on the measurement of the Lense–Thirring effect

In this paper we use, in a very preliminary way, the recently released EIGEN2 Earth gravity model, which is based on six months of data of CHAMP only, in order to reassess the systematic error due to the mismodelling in the even zonal harmonics of geopotential which represents one of the major sources of systematic errors in the LAGEOS–LAGEOS II Lense–Thirring experiment involving the nodes of both the LAGEOS satellites and the perigee of LAGEOS II. Concerning the EIGEN2 solution, it should be pointed out that the calibration of its errors, especially at degrees lower than l = 15 to which the orbits of the LAGEOS satellites are particularly sensitive, must still be extensively and exhaustively checked. It must be recalled that the perigee of LAGEOS II is particularly sensitive to a whole host of insidious nongravitational orbital perturbations. This fact makes very difficult to assess reliably and trustworthily the overall error budget of the currently performed LAGEOS– LAGEOS II Lense–Thirring experiment. If the correlations among the various even zonal coefficients of the geopotential are accounted for up to degree l = 70 the gravitational error in the combination of the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II changes from 13%, obtained with the EGM96 model, to 7%. If correlations are neglected, it changes from 45%, with EGM96, to 9%. These results should be further improved by the forthcoming more robust solutions for Earth gravity models from both CHAMP and, especially, GRACE. For example, they could allow to use a suitable combination of the nodes of LAGEOS and LAGEOS II only which is particularly insensitive to the non–gravitational perturbations because it does not involve the perigee of LAGEOS II. In order to get a preliminary quantitative estimate, the results of EIGEN2 have been used. The gravitational error, which, for the nodes–only observable, would represent by far the most important source of systematic error, amounts to 17.8% with the inclusion of the correlations and 22% neglecting them. However, it must clearly be pointed out that the results presented here should be viewed as a place–holder for upcoming Lense–Thirring tests using future GRACE models if they finally will confirm the great expectations currently existing about them.