On the impossibility of measuring the general relativistic part of the terrestrial acceleration of gravity with superconducting gravimeters

TL;DR

This paper explores the feasibility of detecting relativistic effects on Earth's gravity using superconducting gravimeters, concluding that current uncertainties and measurement limitations prevent successful detection.

Contribution

It provides a preliminary analysis showing the current technological and geophysical challenges in measuring relativistic gravity components on Earth.

Findings

Relativistic effects are too small compared to uncertainties in Earth's parameters.

Current superconducting gravimeters can only perform relative measurements, not absolute.

Systematic errors exceed the relativistic signals by 1-2 orders of magnitude.

Abstract

In this paper we very preliminarily investigate the possibility of measuring the post-Newtonian general relativistic gravitoelectric and gravitomagnetic components of the acceleration of gravity on the Earth, in continuous regime, with two absolute measurements at the equator and the south pole with superconducting gravimeters. The magnitudes of such relativistic effects are 10^-10 m s^-2 and 10^-11 m s^-2, respectively. Unfortunately, the present-day uncertainties in the Earth's geodetic parameters which enter the classical Newtonian terms induce systematic errors 1-2 orders of magnitude larger than the relativistic ones. Moreover, a \sim 1 ngal sensitivity can be reached by the currently available superconducting gravimeters, but only for relative measurements.