Limitations in Testing the Lense-Thirring Effect with LAGEOS and the Newly Launched Geodetic Satellite LARES 2

The new geodetic satellite LARES 2, cousin of LAGEOS and sharing with it almost the same orbital parameters apart from the inclination, displaced by 180 deg, was launched last year. Its proponents suggest using the sum of the nodes of LAGEOS and of LARES 2 to measure the sum of the Lense-Thirring node precessions independently of the systematic bias caused by the even zonal harmonics of the geopotential, claiming a final $\simeq 0.2$ percent total accuracy. In fact, the actual orbital configurations of the two satellites do not allow one to attain the sought for mutual cancellation of their classical node precessions due to the Earth's quadrupole mass moment, as their sum is still $\simeq 5000$ times larger than the added general relativistic rates. This has important consequences. One is that the current uncertainties in the eccentricities and the inclinations of both satellites do not presently allow the stated accuracy goal to be met, needing improvements of 3-4 orders of magnitude. Furthermore, the imperfect knowledge of the Earth's angular momentum $S$ impacts the uncancelled sum of the node precessions, from 150 to 4900 percent of the relativistic signal depending on the uncertainty assumed in $S$. It is finally remarked that the real breakthrough in reliably testing the gravitomagnetic field of the Earth would consist in modeling it and simultaneously estimating one or more dedicated parameter(s) along with other ones characterising the geopotential, as is customarily performed for any other dynamical feature.