Relativistic Effect in the Two-Way Time Comparison Between Navigation Satellites

Abstract

Influenced by the high-speed of satellites and the gravitational field of the earth, the satellite-borne clock is affected by the effect of special and general relativity. The classic Newtonian theory in the earth space only achieves time-transfer accuracy within 1 × 10^–8, which is far from matching the performance of the current satellite-borne clock and satisfying inter-satellite time comparison accuracy. This paper has studied the inter-satellite two-way time comparison under the framework of relativity, and the real data of inter-satellite links is used to analyze the relativistic effect of the Beidou-3 inter-satellite two-way time comparison. The results have demonstrated that the gravitational delay of the inter-satellite measurement signal caused by the central gravity of the earth reaches the order of sub-nanosecond, but the asymmetry of gravitational delays in the two-way time comparison is only 0.01 ps which can be ignored with the sub-nanosecond time comparison accuracy; the amplitude of the periodic relativistic effect introduced by the central gravitational field of the earth is about ±1~ ±2 ns, which must be corrected as a systematic error; the periodic relativistic effect introduced by the gravitational J₂ perturbation of the earth reaches ±0.1 ns, which needs to be compensated with the time comparison accuracy of the sub-nanosecond order. In the currently released satellite precision clock products and broadcast ephemeris, only the relativistic effect correction caused by the central gravitational field of the earth is considered. With the continuous improvement of the performance and time transfer accuracy of the spaceborne atomic clock, further consideration of the relativistic effect modification from gravitational J₂ perturbation of the earth is required.