Investigation of proper time and inter-satellite clock difference using general relativity theory

Precise proper time and time synchronization in the order of picoseconds are of great significance to space fundamental physics and measurement science, but unexpected satellite motion in gravitational field results in obvious proper time deviation and inter-satellite clock difference. To solve this problem, this paper proposes a method to evaluate the influence of satellite motion on the proper time, and establishes the inter-satellite clock difference model using general relativity theory. First, the satellite motion equations are derived to describe the dynamics in the vicinity of Earth. Then, by adopting the developed proper-to-coordinate time transformation, the influence of satellite motion on proper time is evaluated from the aspects of single perturbation acceleration and orbital elements. The analysis results are conducive to the orbit design of space science satellites and the adjustment of on-board clocks. Finally, the inter-satellite clock difference model using satellite states is established. Simulation studies indicate that the error of clock difference is in the order of picoseconds. The proposed model is expected to estimate the clock difference between satellites to achieve high-accurate time synchronization in free space.(c) 2022 Elsevier Masson SAS. All rights reserved.