Will LAGEOS and LARES 2 succeed in accurately measuring frame-dragging?

Abstract

The current LAGEOS-LARES 2 experiment aims to accurately measure the general relativistic Lense-Thirring effect in the gravitomagnetic field of the spinning Earth generated by the latter's angular momentum $\boldsymbol{J}$. The key quantity to a priori analytically assess the overall systematic uncertainty is the ratio $\mathcal{R}^{J_2}$ of the sum of the classical precessions of the satellites' nodes $\Omega$ induced by the Earth's oblateness $J_2$ to the sum of their post-Newtonian counterparts. $In$ $principle$, if the sum of the inclinations $I$ of both satellites were $exactly$ $180^\circ$, the semimajor axes $a$ and the eccentricities $e$ being $identical$, $\mathcal{R}^{J_2}$ would $exactly$ vanish. Actually, it is $not$ so by a large amount because of the departures of the $real$ satellites' orbital configurations from their $ideal$ ones. Thus, $J_2$ impacts not only directly through its own uncertainty, but also $indirectly$ through the errors in all the other physical and orbital parameters entering $\mathcal{R}^{J_2}$. The consequences of this fact are examined in greater details than done so far in the literature. The Van Patten and Everitt's proposal in 1976 of looking at the sum of the node precessions of two counter-orbiting spacecraft in (low-altitude) circular polar orbits is revamped rebranding it POLAr RElativity Satellites (POLARES). (Abridged)