Frequency Differences between Clocks on the Earth and the Moon

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.