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

TL;DR

This paper critically examines the feasibility of testing the Lense-Thirring effect using LAGEOS and a new geodetic satellite, highlighting significant challenges from Earth's gravity field uncertainties and orbital decay effects.

Contribution

It provides a detailed analysis of the potential errors and limitations in using these satellites for precise relativistic measurements, questioning the claimed accuracy of upcoming tests.

Findings

Uncertainty in Earth's gravity models can cause 70-80% error in Lense-Thirring measurements.

Orbital decay of LAGEOS introduces a 20-40% bias over 5-10 years.

Systematic errors from inclination decay can reach 2-14%.

Abstract

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.