On a recent preliminary study for the measurement of the Lense-Thirring effect with the Galileo satellites

Abstract

It has been recently proposed to combine the node drifts of the future constellation of 27 Galileo spacecraft together with those of the existing LAGEOS-type satellites to improve the accuracy of the past and ongoing tests of the Lense-Thirring (LT) effect by removing the bias of a larger number of even zonal harmonics $J_{\ell}$ than either done or planned so far. Actually, it seems a difficult goal to be realistically achieved for a number of reasons. First, the LT range signature of a Galileo-type satellite is as little as $0.5$ mm over 3-days arcs, corresponding to a node rate of just $\dotΩ_{\rm LT}=2$ milliarcseconds per year (mas yr$^{-1}$). Some tesseral and sectorial ocean tides such as $K_1,K_2$ induce long-period harmonic node perturbations with frequencies which are integer multiples of the extremely slow Galileo's node rate $\dotΩ$ completing a full cycle in about 40 yr. Thus, over time spans $T$ of some years they would act as superimposed semi-secular aliasing trends. Since the coefficients of the $J_{\ell}$-free multisatellite linear combinations are determined only by the semimajor axis $a$, the eccentricity $e$ and the inclination $I$, which are nominally equal for all the Galileo satellites, it is not possible to include all of them. Even by using only one Galileo spacecraft together with the LAGEOS family would be unfeasible because the resulting Galileo coefficient would be $\gtrsim 1$, thus enhancing the aliasing impact of the uncancelled non-conservative and tidal perturbations.