Frequency Differences between Clocks on the Earth and the Moon

Abstract: Based on general relativity, clock comparisons enable the determination of the gravity potential relative to a stable reference. Lunar surface clocks, owing to the Moon's low-noise conditions, high orbital stability, and broad Earth visibility, are promising reference clocks for global-scale comparisons between terrestrial clocks. Meanwhile, the need for an independent lunar time system-driven by future lunar navigation-requires maintaining links to terrestrial standards. This Letter simulates fractional frequency differences between Earth (E) and Moon (L) clocks by modeling three key time transformations: proper-to-coordinate time for E-clocks and for L-clocks (both linked to the local gravity potential), and the coordinate time relation between Earth and Moon. Signal propagation effects are not addressed. Gravity potential differences impact observations at the 10^-10 level, and the coordinate time ratio at 10^-11. Contributions from static, tidal, and non-tidal potentials, body self-rotation, and different celestial bodies are evaluated.