Perturbations of the local gravity field due to mass distribution on precise measuring instruments: a numerical method applied to a cold atom gravimeter

TL;DR

This paper introduces a FEM-based numerical method to calculate gravitational perturbations caused by mass distributions, applied specifically to assess the self-gravity bias in a high-precision cold atom gravimeter aiming for 10^-9 accuracy.

Contribution

The paper develops a versatile FEM simulation approach for gravitational field perturbations, specifically applied to quantify self-gravity effects in a cold atom gravimeter.

Findings

Self-gravity bias is approximately 1.3 x 10^-9 of Earth's gravity.

The numerical method accurately estimates gravitational perturbations for complex geometries.

Perturbative calculations provide a reliable bias correction for high-precision measurements.

Abstract

We present a numerical method, based on a FEM simulation, for the determination of the gravitational field generated by massive objects, whatever geometry and space mass density they have. The method was applied for the determination of the self gravity effect of an absolute cold atom gravimeter which aims at a relative uncertainty of 10-9. The deduced bias, calculated with a perturbative treatment, is finally presented. The perturbation reaches (1.3 \pm 0.1) \times 10-9 of the Earth's gravitational field.