V.F. Fateev

FSUE “VNIIFTRI”, Mendeleevo, Moscow region, Russia
generalfat@mail.ru

Al’manac of Modern Metrology № 2 (34) 2023, pages 43–64

Abstract. For the first time, a ratio has been obtained that determines the current mutual relative relativistic frequency shift of the driving generators of ground and satellite quantum clocks located in an arbitrary elliptical orbit. The relativistic discrepancy of the frequency and time of ground and satellite clocks is presented in three equal forms: based on Bessel functions, based on an eccentric anomaly, and also in coordinate form. The relativistic phenomena in relation to the prospective geosynchronous GLONASS orbit are investigated, and the relativistic effects of frequency and time in relation to the regular GNSS orbits are clarified. The influence of the inhomogeneity of the Earth’s field, the influence of the fields of the Moon and the Sun, as well as the unevenness of the Earth’s rotation are estimated.

Keywords: relativistic effects, discrepancy of the onboard time scale, gravitational frequency shift, quantum clock, global navigation satellite systems.

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