Gravitational forces between weights in Force Standard Machines – Simplified analytical and numerical approaches

Abstract

The gravitational field at the installation site of deadweight force standard machines has been investigated at PTB in the past. For this purpose, the local gravitational acceleration was measured prior to and after the installation of the machines. The effect of the masses of the machine frame and the load masses was simulated for the 200 kN force standard machine (FSM). In this paper, an attempt is made to calculate the gravitational forces between the weights of PTB’s 2 MN force standard machine using simplified analytical and numerical approaches and models. The aim in doing so is to determine the order of magnitude of these forces and to compare them with the force variations that arise due to tidal changes of the local gravitational acceleration.