How can one detect the rotation of the Earth "around the Moon"? Part 3. With a simple pendulum

TL;DR

This paper explores detecting Earth's rotation around the Moon by measuring tiny variations in a simple pendulum's period caused by lunar tidal forces, proposing feasible experimental approaches despite extremely small effects.

Contribution

It introduces a method to detect Earth's rotation around the Moon using precise measurements of pendulum period changes induced by lunar tidal forces.

Findings

Tidal forces cause measurable tiny changes in pendulum period.

Detection of Earth's rotation around the Moon is theoretically possible with improved accuracy.

Preliminary results suggest feasible experimental setups for future research.

Abstract

The attraction of the Moon on objects at the surface of the Earth gives rise to a so-called tidal force which is of the order of 1/10,000,000 times the gravitational force of the Earth. For instance, when the Moon is located between the Earth and the Sun (new moon) the distance from a given terrestrial location to the Moon is shorter at noon than at midnight. This reduces the gravitational acceleration and therefore increases the period of a simple pendulum by a small amount. Although the change is of the order of 100 nanoseconds it appears that it can be detected. We give some preliminary results and discuss how the accuracy can be further improved. It is hoped that the present paper will encourage new experiments in this direction.