Relativistic justification of the experiment to determine the difference in gravitational potentials between ground points based on measuring the gravitational frequency shift in a duplex satellite communication channel

Vyacheslav F. Fateev

FSUE “VNIIFTRI”, Mendeleevo, Moscow region, Russia
generalfat@mail.ru, SPIN-code: 5385-8126, ORCID: 0000-0001-7902-0212

Al’manac of Modern Metrology № 4 (44) 2025, pages 129–149

The page of the article in Russian

Original article

Abstract. The possibility of determining the difference in gravitational potentials and orthometric heights of separated ground points by measuring the gravitational frequency shift in a duplex satellite radio system equipped with a relocatable highly stable hydrogen quantum clock is considered. For the first time, it has been established that the meas­ured gravitational frequency shift in a duplex satellite system has a quadruple value, the relative magnitude of which, with an altitude difference of 2000 m (Caucasus), reaches 8.7 × 10–13. This ensures high accuracy of geodetic measurements based on it. The parasitic Doppler shift caused by the residual velocity of the geostationary satellite is compensated. The calibration technical initial frequency offset of the master oscillator of the rebased clock is doubled, which places increased demands on the accuracy of its initial determina­tion and storage. The residual influence of a turbulent atmosphere limits the accuracy of measurements and requires a calibration determination before starting the experiment. The possibility of measuring the gravitational frequency shift using a pair of hydrogen quantum clocks placed in the Ostankino TV tower at a height difference of 300 m was assessed.

Keywords: gravitational potentials, orthometric heights, duplex satellite system, quan­tum clock, geostationary satellite

For citation: Fateev V.F. Relativistic justification of the experiment to determine the difference in gravitational potentials between ground points based on measuring the gravitational frequency shift in a duplex satellite communication channel. Almanac of Modern Metrology. 44 (4), 129–149 (2025).

Funding. The study was carried out with the financial support of the Russian Science Foundation within the framework of scientific project № 23-67-10007, https://rscf.ru/project/23-67-10007/.
Conflict of interests. The author declare that he has no potential conflict of interest related to the research presented in this article.

The article was submitted 27.08.2025; approved after reviewing 01.12.2025; accepted for publication 02.12.2025.

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