Satellite gravitational orbital perturbations and the gravitomagnetic clock effect

TL;DR

This paper assesses whether current gravitational perturbation knowledge allows detecting the gravitomagnetic clock effect via two satellites, finding that present accuracy levels are insufficient for short-arc observations.

Contribution

The study evaluates the impact of Earth's gravitational perturbations on satellite positioning accuracy for detecting the gravitomagnetic clock effect.

Findings

Radial perturbations are harmonic with periods up to tens of days.

Azimuthal perturbations include secular drifts and long-period effects.

Current knowledge of Earth's tides and geopotential is insufficient for short-arc detection.

Abstract

In order to detect the gravitomagnetic clock effect by means of two counter-orbiting satellites placed on identical equatorial and circular orbits around the Earth with radius 7000 km their radial and azimuthal positions must be known with an accuracy of delta r =10^{-1} mm and delta phi =10^{-2} mas per revolution. In this work we investigate if the radial and azimuthal perturbations induced by the dynamical and static parts of the Earth' s gravitational field meet this requirements. While the radial direction is affected only by harmonic perturbations with periods up to some tens of days, the azimuthal location is perturbed by a secular drift and very long period effects.It results that the present level of accuracy in the knowledge both of the Earth solid and ocean tides, and of the static part of the geopotential does not allow an easy detection of the gravitomagnetic clock effect, at least by using short arcs only.