关键词: classical general relativity, post-Newtonian approximation, phase shifting interferometry

Abstract: Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE (Gravity Recovery and Climate Experiment) Follow-On-like missions and gravitational wave detectors. For such accuracy of modern space missions, a precise relativistic model of light propagation is required. With the post-Newtonian approximation, we utilize the Synge world function method to study the light propagation in the Earth's gravitational field, deriving the gravitational delays up to order $c^{-4}$. Then, we investigate the influences of gravitational delays in three inter-satellite laser ranging techniques, including one-way ranging, dual one-way ranging, and transponder-based ranging. By combining the parameters of Kepler orbit, the gravitational delays are expanded up to the order of $e^2$ ($e$ is the orbital eccentricity). Finally, considering the GRACE Follow-On-like missions, we estimate the gravitational delays to the level of picometer. The results demonstrate some high-order gravitational and coupling effects, such as $c^{-4}$-order gravitational delays and coupling of Shapiro and beat frequency, which may be non-negligible for higher precision laser ranging in the future.

Key words: classical general relativity, post-Newtonian approximation, phase shifting interferometry