Prospects for Measuring the Gravitational Time Dilation Effect Using Clocks in a Distant Retrograde Lunar Orbit

The prospects for testing the Einstein Equivalence Principle by measuring the gravitational time dilation effect using clocks in a distant retrograde orbit around the Moon are investigated. To obtain estimates of the accuracy that can be achieved in such an experiment, we constructed a model that accounts for the colored nature of the clock noise, as well as a possible clock frequency bias and drift. This model is applied to the case of a lunar distant retrograde orbit (a $$2:1$$ resonance) and three types of clocks characterized by qualitatively different stability and accuracy parameters: hydrogen masers (VCH-1010 and VCH-2021), a cesium fountain clock (PHARAO), and a strontium optical clock (I-SOC). Assuming 5 years of data accumulation, the following estimates for the achievable accuracy of the experiment were obtained: 6× 10⁻⁴ for VCH-1010, 1× 10⁻⁵ for VCH-2021, 2× 10⁻⁵ for PHARAO, and 3× 10⁻⁷ for I-SOC. These estimates show that an experiment with an optical clock would significantly improve upon both the current best result ( (2-3)× 10⁻⁵ , GREAT project) and the anticipated results of experiments on the ISS and Tiangong orbital stations. A comparison of our results with previous studies that do not account for clock drift and frequency bias is provided.