Effects of satellite positioning errors and Earth’s multipole moments in the detection of the gravitomagnetic field with an orbiting gravity gradiometer

The rotation of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of 10-10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-10}$$\end{document} of the Newtonian terms arising from the mass of the Earth. Detection of the gravitomagnetic field is very important, since it tests one of the most fundamental predictions of general relativity. We review the experimental scheme for detecting the gravitomagnetic effect with an orbiting gravity gradiometer in an inertial frame. Two factors which can affect the experiment, satellite positioning errors and Earth’s multipole moments, are analyzed. We derive the satellite positioning accuracy required for construction of matched templates with sufficient precision. We find that the satellite orbit must be carefully selected to avoid some dangerous altitudes at which Earth’s multipole moments can mask gravitomagnetic signals. Allowable orbit altitudes are computed. We also examine an alternative scheme, in which the gradiometer is fixed to a local inertial frame defined by gyroscopes. In this experiment, the gradient signal grows linearly with time due to the Lense–Thirring effect, and the satellite positioning errors and Earth’s multipole moments become negligible.