How can one detect the rotation of the Earth "around the Moon"? Part 1:   With a Foucault pendulum
  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. 
Bertrand M. Roehner
physics.class-ph