RadioAstron: relativistic frequency change and time-scale shift

The plans to launch the RadioAstron space system in the near future and the realization the planned record resolution of 1 microarcsecond will require the precise determination of the satellite orbit. Suitable models for the satellite motion must be provided, including taking into account relativistic effects. We have obtained equations making it possible to construct time scales on board the satellite and at the observation point with accuracy up to 1 ps, as well as relativistic relations for measuring the distance to the satellite using one-way and two-way techniques and the Doppler effect, with a relative uncertainty of 10−15, necessary for achieving the precision required for the RadioAstron mission.