Some considerations on the present-day results for the detection of frame-dragging after the final outcome of GP-B

The cancellation of the first even zonal harmonic coefficient J₂ from the linear combination f^(2L) of the nodes Ω of LAGEOS and LAGEOS II used in the latest tests of the Lense-Thirring effect cannot be perfect, contrary to what assumed so far. It is so also because of the uncertainties in the spatial orientation of the terrestrial spin axis {\hat{k}} . As a consequence of above, the coefficient c₁ entering f^(2L), which is not a solve-for parameter being, instead, theoretically computed from the analytical expressions of the classical node precessions \dot{Ω}_{J_2} due to J₂, is, on average, uncertain at a 10^-8 level over multi-decadal time spans ΔT comparable to those used in the data analyses performed so far. A further sime20% systematic uncertainty, thus, occurs. The shift Δρ_LT due to the gravitomagnetic frame-dragging on the station-spacecraft range ρ is numerically computed over ΔT=15 d and ΔT=1 y. The need to look at such a directly observable quantity is highlighted, along with some critical remarks concerning the methodology used so far to measure the Lense-Thirring effect with the LAGEOS satellites. Suggestions for a different, more trustable and reliable approach are offered.