The J2 relativistic periodic component of GNSS satellite clocks

The frequency of space atomic clocks on board the satellites of global navigation satellite systems, as observed from the ground, shows different types of periodic variations, among which the J2 relativistic component due to the Earth oblateness. This component is often so small to be masked by the clock noise, but nonetheless it affects the stability of the clock’s frequency. Here, after reviewing the theory of the J2 relativistic effect, we carefully analyze GPS clocks’ data looking for the J2 periodic component. Moreover, we study its effect on the clock’s Allan deviation, showing how it deforms the shape of the bump visible at an averaging time of about one half of the satellites’ orbital period, due to periodic frequency variations of other origin.