Relativistic tidal effects on clock-comparison experiments

TL;DR

This paper develops a relativistic framework to analyze tidal effects on clock frequency shifts, linking ground-based and space-based experiments, and proposes methods to mitigate tidal influences for high-precision timekeeping.

Contribution

It introduces a relativistic formulation for tidal effects on clock comparisons, connecting tidal responses with gravity tides, and develops a perturbed Kepler orbit method for more accurate relativistic effect calculations.

Findings

Relativistic tidal effects can be modeled using Love numbers.

A method to eliminate tidal influences using gravity tide data is proposed.

Simulations show tidal effects impact clock frequency shifts in ground and space experiments.

Abstract

We consider the relativistic tidal effects on frequency shift of clock-comparison experiments. The relativistic formulation for frequency shift and time transfer is derived in the gravitational field of a tidal, axisymmetric, and rotating Earth. With the help of Love numbers describing the tidal response of solid Earth, we formulize the mathematical connection between tidal effects from the ground-based clock-comparison experiments and the local gravity tides from the gravimeters, which in turn provides us an approach to eliminate tidal influences on clock comparison with the local gravity tides data. Moreover, we develop a method of the perturbed Kepler orbit to determine relativistic effects of clock comparison for space missions, which allows more precise calculations comparing to the conventional method of unperturbed Kepler orbit. With this perturbed method, it can give the perturbation of relativistic effects due to the orbital changes under the influences of tidal forces, Earth's oblateness etc. In addition, as the applications of our results, we simulate tidal effects in frequency shift for the clock comparison on the ground and also give some estimates for TianQin mission and GPS.