Some comments on a recent paper on the impact of the secular variations of the even zonal harmonics on the Lense-Thirring tests with the LAGEOS satellites

In this paper we critically discuss the recent paper gr-qc/0412001 by Ciufolini about the impact of the secular variations J̇l of the even zonal harmonic coefficients of the Newtonian multipolar expansion of the terrestrial gravitational field on the performed tests aimed at the detection of the post-Newtonian gravitomagnetic Lense-Thirring effect in the gravitational field of the Earth with the LAGEOS satellites. While the post-Newtonian Lense-Thirring and the Newtonian precessions due to Jl are linear features, the effect of J̇l is quadratic. It turns out that the slope of the Lense-Thirring linear trend has been measured by using an effective J̇4 which is strongly correlated with the Lense-Thirring effect itself. Moreover, the time series of the combined residuals of the nodes of LAGEOS and LAGEOS II used in the analysis has been fitted also with a parabolic signal. This may cause biasing effects in the genuine linear signal of interest.