The influence of lunar tidal potential on clock frequencies at different positions on Earth

With the advancements in clock timing technology, increasingly smaller time differences can be distinguished. Therefore, it is critical to investigate the fractional frequency shift of clocks at different locations on Earth. In this paper, we study it systematically under the influence of a subtle lunar tidal potential based on a new method. Our calculations in the geocentric Fermi frame show that when two clocks are located at the same latitude, the longitude difference changes the fractional frequency shift between them. A similar phenomenon occurs when there is a difference in latitude between two clocks on the ground at the same longitude. Interestingly, when the Moon's longitude changes, the phase and amplitude of the lunar tidal fractional frequency shift between two clocks with the same longitude difference will change, while the change in the Moon's latitude only affects the amplitude of the fractional frequency shift of these two clocks. Our results provide useful information for the calibration and synchronization of clocks on Earth.