Does Cassini allow to measure relativistic orbital effects in the Saturnian system of satellites?

TL;DR

This paper investigates whether current Cassini data can detect relativistic orbital effects in Saturn's moons, concluding that systematic errors currently overshadow the relativistic signals for most satellites.

Contribution

It provides an analysis of the limitations of current orbit determination accuracy in detecting relativistic effects in the Saturnian system.

Findings

Relativistic effects are undetectable with current data accuracy.

Systematic errors from gravitational field modeling dominate the relativistic signals.

Proposed orbital element combinations cannot currently isolate relativistic effects.

Abstract

In this paper we address the following question: do the recent advances in the orbit determination of the major natural satellites of Saturn obtained with the analysis of the first data sets from the Cassini mission allow to detect the general relativistic gravitoelectric orbital precessions of such moons? The answer is still negative. The present-day down-track accuracy would be adequate for Mimas, Enceladus, Thetys, Dione, Rhea and Titan and inadequate for Hyperion, Iapetus and Phoebe. Instead, the size of the systematic errors induced by the mismodelling in the key parameters of the Saturnian gravitational field like the even zonal harmonics Jl are larger than the relativistic down-track shifts by about one order of magnitude, mainly for the inner satellites like Mimas, Enceladus, Thetys, Dione, Rhea, Titan and Hyperion. Iapetus and Phoebe are not sensibly affected by such kind of perturbations. Moreover, the bias due to the uncertainty in Saturn's GM is larger than the relativistic down-track effects for all such moons. Proposed linear combinations of the satellites' orbital elements would allow to cancel out the impact of the mismodelling in the low-degree even zonal harmonics and GM, but the combined down-track errors would be larger than the combined relativistic signature.