Relativistic effects to the onboard BeiDou satellite clocks

The relationship between the proper time of a satellite clock and the geocentric coordinate time (TCG) is discussed in the framework of general relativity. The influences of Earth's shape and the tidal potentials of the Sun and Moon are analyzed for onboard satellite clocks in different orbits. The results show that the influence of the shape of the Earth on Middle Earth Orbit (MEO) satellite reaches the level of 4.0 × 10−15, and it may be the direct cause of the half orbital-period variation in the clock frequency. The influences of the tidal potentials of the Sun and the Moon are relatively smaller. These influences on the frequencies of the clocks in the BeiDou MEO and GEO/IGSO (Geosynchronous Earth Orbit/Inclined Geosynchronous Satellite Orbit) satellites are 5.9 × 10−16 and 1.2 × 10−15, respectively, and appear to be half-day periodic variations. Therefore, these effects need to be considered in the precise assessment and application of BeiDou satellite clocks.