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arXiv · 2506.16377

Frequency Differences between Clocks on the Earth and the Moon

Mingyue Zhang·Jürgen Müller·Sergei M. Kopeikin
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Abstract

Based on general relativity, clock frequency comparisons support various geodetic applications on Earth, such as determining the gravitational potential and realizing a global height system. Future lunar clocks could extend these capabilities to the Moon, connect to terrestrial clock-comparison networks, and, in principle, serve as reference clocks. Meanwhile, especially driven by future lunar navigation plans, an independent lunar time system is becoming an urgent requirement and such a system would necessarily remain linked to terrestrial time standards. To support these future applications, we establish a comprehensive model for Earth-Moon clock frequency comparisons. This paper simulates fractional frequency differences between clocks on the Earth (E) and Moon (L) through four time transformations:proper-to-coordinate time for E-clocks and for L-clocks (both linked to the local gravity potential), the conversion between the Earth and Moon coordinate times, and the time signal propagation between E- and L-clocks. Gravity potential differences between the E- and L-clocks impact the frequency difference at the 10^-10 level. The effect of the coordinate time ratio is at 10^-11 level. Contributions from static, tidal, and non-tidal potentials, body self-rotation, and different celestial bodies are evaluated. Furthermore, we quantify the Doppler, atmospheric and Shapiro delay effects in Earth-Moon time signal propagation. For a single link, the first-order Doppler term dominates at the 10^-6 level and masks the gravity-potential and coordinate-time terms. A Doppler-cancelling multi-link strategy is needed to suppress the signal-propagation effect and extract these terms.

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Mingyue Zhang, Jürgen Müller, Sergei M. Kopeikin. 2026-06-12. Frequency Differences between Clocks on the Earth and the Moon. https://arxiv.org/abs/2506.16377

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