Relativity in Low Earth Orbit Satellites

Sammanfattning

Satellite clocks are affected by two sources of time dilation: one from the difference in gravitational potential and one from high velocities. Unless compensated for, these effects can cause large errors in positioning, navigation and timing systems. Corrections for this have been developed for global navigation satellite systems (GNSS) which involve adjusting the clock frequency and adding an eccentricity correction. In this thesis, the corresponding effects in low Earth orbit (LEO) are investigated. This is done by simulating the trajectories of LEO satellites and integrating the metric along these trajectories to compute the proper time of the clocks. This analysis shows that satellite clocks at 480 km altitude may lag behind terrestrial time by more than 20 microseconds after 24 hours. After applying the corrections developed for GNSS, with parameters for LEO, the remaining error can be close to 100 nanoseconds. As the corresponding value for GNSS is less than a few nanoseconds, this confirms that LEO satellites require either more frequent synchronizations or other corrections altogether to stay within the clock accuracy of GNSS.