Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect

TL;DR

This paper evaluates whether non-gravitational perturbations hinder the detection of the Earth's gravitomagnetic clock effect using laser-ranged satellites, concluding that with proper satellite design, the effect remains measurable despite systematic errors.

Contribution

It provides an assessment of non-gravitational perturbations' impact on measuring the gravitomagnetic clock effect with laser-ranged satellites, highlighting the dominant uncertainty from Earth's GM.

Findings

Non-gravitational perturbations can be controlled within required measurement constraints.

Dense satellites with small area-to-mass ratios improve measurement accuracy.

Uncertainty in Earth's GM significantly affects azimuthal position accuracy.

Abstract

The general relativistic gravitomagnetic clock effect consists in the fact that two massive test bodies orbiting a central spinning mass in its equatorial plane along two identical circular trajectories, but in opposite directions, take different times in describing a full revolution with respect to an asymptotically inertial observer. In the field of the Earth such time shift amounts to 10^{-7} s. Detecting it by means of a space based mission with artificial satellites is a very demanding task because there are severe constraints on the precision with which the radial and azimuthal positions of a satellite must be known: delta r= 10^{-2} cm and delta phi= 10^{-2} milliarcseconds per revolution. In this paper we assess if the systematic errors induced by various non-gravitational perturbations allow to meet such stringent requirements. A couple of identical, passive laser-ranged satellites of LAGEOS type with their spins aligned with the Earth's one is considered. It turns out that all the non vanishing non-gravitational perturbations induce systematic errors in r and phi within the required constraints for a reasonable assumption of the mismodeling in some satellite's and Earth's parameters and/or by using dense satellites with small area-to-mass ratio. However, the error in the Earth's GM is by far the largest source of uncertainty in the azimuthal location which is affected at a level of 1.2 milliarcseconds per revolution.