A critical analysis of the recent test of the Thirring-Lense effect with the LAGEOS satel- lites

We quantitatively discuss the impact of the current uncertainties in the even zonal harmonic coefficients Jl of the Newtonian part of the terrestrial gravitational potential on the measurement of the general relativistic Thirring-Lense effect using a suitable linear combination of the nodes Ω of the laser-ranged LAGEOS and LAGEOS II satellites. The 1-sigma systematic error due to the mismodelling in the Jl coefficients ranges from ∼ 4% for the EIGEN-GRACE02S gravity field model to ∼ 9% for the GGM02S gravity field model. Another important source of systematic error of gravitational origin is represented by the secular variations J̇l of the even zonal harmonics. While the relativistic and Jl signals are linear in time, the shift due to J̇l is quadratic. We quantitatively assess their impact on the measurement of the Thirring-Lense effect obtaining, on average, a 1-sigma error ∼ 13% over 11 years. This yields a 1-sigma ∼ 19% total error in the test performed by Ciufolini and Pavlis in 2004 with EIGENGRACE02S over 11 years: their 1-sigma estimate for the total error is, instead, 5%.