The impact of the orbital decay of the LAGEOS satellites on the frame-dragging tests

TL;DR

The paper investigates how the orbital decay of LAGEOS satellites affects the precision of frame-dragging tests, highlighting the need for improved measurements and data analysis methods to mitigate systematic biases in relativistic experiments.

Contribution

It identifies the impact of satellite orbital decay on Lense-Thirring effect measurements and emphasizes the necessity of refining measurement accuracy and data processing to reduce systematic errors.

Findings

Current measurement errors in orbital decay are comparable to the relativistic signal.

Systematic bias increases linearly with the analysis time span.

Significant improvements in decay measurement accuracy are required for precise relativistic tests.

Abstract

The laser-tracked geodetic satellites LAGEOS, LAGEOS II and LARES are currently employed, among other things, to measure the general relativistic Lense-Thirring effect in the gravitomagnetic field of the spinning Earth with the hope of providing a more accurate test of such a prediction of the Einstein's theory of gravitation than the existing ones. The secular decay $\dot a$ of the semimajor axes $a$ of such spacecrafts, recently measured in an independent way to a $\sigma_{\dot a}\approx 0.1-0.01$ m yr$^{-1}$ accuracy level, may indirectly impact the proposed relativistic experiment through its connection with the classical orbital precessions induced by the Earth's oblateness $J_2$. \textcolor{black}{Indeed,} the systematic bias due to the current measurement errors $\sigma_{\dot a}$ is of the same order of magnitude of, or even larger than, the expected relativistic signal itself; moreover, it grows linearly with the time span $T$ of the analysis. \textcolor{black}{Therefore, the parameter-fitting algorithms must be properly updated in order to suitably cope with such a new source of systematic uncertainty. Otherwise,} an improvement of one-two orders of magnitude in measuring the orbital decay of the satellites of the LAGEOS family would be required to reduce this source of systematic uncertainty to a percent fraction of the Lense-Thirring signature.