How can one detect the rotation of the Earth "around the Moon"? Part 1: With a Foucault pendulum

TL;DR

This paper proposes using a Foucault pendulum to detect the Earth's rotation around the Earth-Moon barycenter by comparing deflections at noon and midnight, suggesting a feasible experimental approach with potential for new observations.

Contribution

It introduces a method to detect Earth's rotation around the Moon using Foucault pendulum deflections at different times of day.

Findings

Midnight deflection is about 4% larger than at noon on June 21.

Repeated measurements improve detection accuracy through averaging.

The effect is detectable with moderate-accuracy pendulums, encouraging new experiments.

Abstract

It will be shown that the rotation of the Earth in the Earth-Moon system can be detected by comparing the deflection of a Foucault pendulum at noon on the one hand and at midnight on the other hand. More precisely, on 21 June the midnight experiment would give a deflection about 4% larger than at noon. In other words, with a Foucault pendulum having an accuracy of the order of 1% one should be able to identify this effect through a single measurement. Moreover, if the experiment is repeated on N successive days, the division of the error bar by the square-root of N which comes with the averaging process will allow identification of the Moon effect even with a pendulum of poorer accuracy, say of the order of a few percent. In spite of the fact that this effect appears fairly easy to detect, it does not seem that its observation has attracted much attention so far. We hope that this paper will encourage some new observations.