On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites

In this paper, we critically discuss the so-far performed attempts aimed at the detection of the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of the Earth with the existing LAGEOS satellites. In the latest reported measurement of the gravitomagnetic shift with the nodes of the LAGEOS satellites and the second generation GRACE-only EIGEN-GRACE02S Earth gravity model over an observational time span of 11 years a 5-10% total accuracy is claimed at 1-3σ, respectively. We will show that, instead, it might be 15-45% (1-3σ) if the impact of the secular variations of the even zonal harmonics is considered. Possible strategies in order both to make more robust and reliable the tests with the node-only LAGEOS-LAGEOS II combination used and to overcome the problems affecting it with other alternative combinations are presented.