Royal Observatory of Belgium Gravitational balance

TL;DR

This paper presents a gravitational measurement setup using a symmetrical vertical pendulum to determine the gravitational constant G, involving precise calibration and potential for multi-pendulum systematic studies.

Contribution

Introduction of a novel symmetrical vertical pendulum system for precise gravitational constant measurement with calibration and feedback mechanisms.

Findings

Successful monitoring of gravitational torque ratios

Calibration method using a known mass displacement

Potential for multi-pendulum systematic effect analysis

Abstract

An astatized symmetrical vertical pendulum is monitoring torque {\Gamma}(M) resulting of gravitational attractions exerted by two external masses M moving up down. Local gravity field g produce the main pendulum restoring torque combined with a very weak variable torque {\Gamma}(c) induced by rotation of watch needles fixed to the pendulum. Transfer of fundamental units to calibrate the {\Gamma}(c) torques is obtained by a reference torque {\Gamma}({\mu}) resulting of precise displacements of a well known mass {\mu}. We permanently monitored ratio between the gravitational effect {\Gamma}(M) and calibrated {\Gamma}(c) to determine G. Position of the pendulum is measured with a capacitive bridge. Bias voltages sent to two electrodes set-up at the bottom of the pendulum allows to feedback pendulum with a controlled electrostatic torque. We discuss potential interest of our prototype to design a multi pendulum system to check systematic effects for different geometries and various kinds of materials.