Lunar tidal response-induced clock frequency variations on the Moon

Abstract

As clock performance improves, the instability and uncertainty of the clock's fractional frequency shift (FFS) become comparable to the FFS caused by the lunar tidal response (LTR), so the influence of the LTR on lunar time needs to be investigated. In this paper, we used the Keplerian expansions method to study the FFS to the level of $10^{-18}$ caused by the LTR between two clocks placed in different positions on the Moon. We consider the case of the Moon orbiting in an elliptical orbit, which is closer to the actual situation compared to the case of the Moon moving in a circular orbit. An interesting phenomenon is found that the longitude difference between two clocks can cause a change in the amplitude and phase of the FFS due to the LTR, but the latitude difference only changes the amplitude of the FFS. We further estimated the clock difference between two clocks near the Moon caused by the LTR. When one clock is on the lunar surface, and the other is on the Earth's surface, the LTR will cause a clock difference of $\mu$s/day between the two clocks. These are significant for the construction of a lunar time and clock synchronization near the Moon.

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