A relativistic time-delay model at the micrometer level for satellite laser ranging

Present accuracy of satellite laser ranging is at the millimeter level. The current time-delay equation of satellite laser ranging given by International Earth Rotation and Reference Systems Service is in agreement with this accuracy. Prospectively, the accuracy of satellite laser ranging will be improved to sub-millimeter in the future (Pearlman et al. 2007). In this paper, for theoretical interest and applications in future satellite-laser-ranging data processing, we develop a relativistic time-delay model for satellite laser ranging by the time-transfer-function method, and investigate all possible relativistic effects on the light propagation between a station and a satellite. The accuracy of our model arrives at the micrometer ( ${\sim}0.01~\mbox{ps}$ ) level. For achieving such accuracy, only the quadrupole moment of the Earth needs to be taken into account compared with the existing model. This micrometer-level model should be useful in tests of the gravitation theory, high accuracy orbital determination of satellites and geodesy in the future.