On testing frame-dragging with LAGEOS and a recently announced geodetic satellite

Recently, Ciufolini and coworkers announced the forthcoming launch of a new cannonball geodetic satellite in 2019. It should be injected in an essentially circular path with the same semimajor axis $a$ of LAGEOS, in orbit since 1976, and an inclination $I$ of its orbital plane supplementary with respect to that of its existing cousin. According to their proponents, the sum of the satellites' precessions of the longitudes of the ascending nodes $\Omega$ should allow one to test the general relativistic Lense-Thirring effect to a $\simeq 0.2\%$ accuracy level, with a contribution of the mismodeling in the even zonal harmonics $J_\ell,~\ell=2,4,6,\ldots$ of the geopotential to the total error budget as little as $0.1\%$. Actually, such an ambitious goal seems to be hardly attainable because of the direct and indirect impact of, at least, the first even zonal $J_2$. On the one hand, the lingering scatter of the estimated values of such a key geophysical parameter from different recent GRACE/GOCE-based global gravity field solutions is representative of an uncertainty which may directly impact the summed Lense-Thirring node precessions at a $\simeq 70-80\%$ in the worst scenarios, and to a $\simeq 3-10\%$ level in other, more favorable cases. On the other hand, the phenomenologically measured secular decay $\dot a$ of the semimajor axis of LAGEOS (and, presumably, of the other satellite as well), currently known at a $\sigma_{\dot a}\simeq 0.03~\textrm{m~yr}^{-1}$ level after more than 30 yr, will couple with the sum of the $J_2$-induced node precessions yielding an overall bias as large as $\simeq 20-40\%$ after $5-10$ yr. A further systematic error of the order of $\simeq 2-14\%$ may arise from an analogous interplay of the secular decay of the inclination $\dot I$ with the oblateness-driven node precessions.