基于广义相对论的轨道摄动卫星皮秒计时与时间比对研究

Time comparison in picoseconds has been proposed for various space-based scientific missions, such as atomic clock ensemble in space, measurement of fine-structure constants, gravitational redshift measurement, deep space exploration, and large-scale quantum communication. It is necessary to establish more accurate coordinate-timing and time-comparison models of satellites based on general relativity. In this study, we developed an orbit dynamics model of satellites based on the metric tensor. Considering the effect of orbit perturbations, we developed coordinate-timing and time-caparison models with higher accuracy. The developed time-caparison model provides theoretical support for picosecond time comparison among satellites with longer time. Further, we simulated geostationary satellites, and the results indicate that the effect of the general relativity term on the satellite velocity is in the order of μm/s. The effect of the general relativity term on the satellite position increases with time, reaching 3.46 mm (11.53 ps) at 10000 s. The coordinate-timing and time-comparison errors resulting from the orbit perturbations reach 15.36 and 56.69 ps, respectively, at 10000 s. The simulation results of general orbits show that the coordinate-timing and time-comparison errors are lower at higher orbits in the vicinity of Earth.