A possible new method for improving the accuracy in the Lense–Thirring effect measurement

In this paper we try to suggest a possible novel method to determine some selected even zonal harmonics Jl of the Earth’s geopotential. Time series some years long of suitably linearly combined residuals of some Keplerian orbital elements of certain existing geodetic SLR satellites would be examined and corrections ∆Jl for the even zonals which we are interested in would be obtained. A CHAMP/GRACE-only background reference model should be used for the part of the geopotential which we are not interested in. The retrieved values for the even zonal harmonics of interest would be, by construction, independent of each other and of any post-Newtonian features. The so obtained mini-model could, subsequently, be used in order to enhance the accuracy and the reliability of some tests of post-Newtonian gravity, with particular emphasis to the measurement of the Lense-Thirring effect by means of LAGEOS and LAGEOS II. Reasonable evaluations of the accuracy which could be obtained for this relativistic test are given.