Towards a high-performance Foucault pendulum for the measurement of relativistic gravity

Cartmell, Matthew P. and Lockerbie, Nicholas A. and Faller, James E. (2021) Towards a high-performance Foucault pendulum for the measurement of relativistic gravity. In: NODYCON 2021 - Second International Nonlinear Dynamics Conference, 2021-02-16 - 2021-02-19.

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Abstract

The Foucault pendulum has become one of the fundamental experiments of physics since Léon Foucault's famous demonstration of a 67 metre pendulum with a 22 kg bob mass at the Panthéon in Paris in 1851. This paper attempts to show that Foucault's fundamental experiment could perhaps be developed into a highly sensitive measurement system capable of resolving the tiny precessional motions of relativistic frame-dragging. The authors have shown that their mathematical model of a Foucault pendulum performs extremely well in terms of predicting the Newtonian rotation of the Earth. The model takes account of latitude and incorporates parametric excitation of the length as a harmonic modulating motion of ≤ 0.01 of the nominal pendulum length. The main aim of the ongoing work discussed in this paper is to try to resolve the tiny motions of Lense-Thirring frame-dragging precession, for which we confirm that a first approximation prediction at a chosen terrestrial latitude can be obtained through an analogy between Maxwellian electrodynamics and gravitoelectromagnetism. A new experimental measurement will require an increase in resolution of at least 2 × 10' over that required for measuring the Newtonian rotation of the Earth.

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