Measuring the difference in gravitational potentials of ground points using the duplex satellite method

The issue of measuring the difference in gravitational potentials and the corresponding difference in orthometric heights based on two spatially separated highly stable ground-based hydrogen quantum clocks is investigated. The relevance of the presented study and its practical significance are determined, in particular, by the prospects for measuring the difference in orthometric heights using the duplex method of comparing the time scales of remote consumers via a geostationary communications satellite. The problem of determining the difference in gravitational potentials and the corresponding difference in orthometric heights between points on the Earth's surface is considered. A solution is proposed for measuring the difference in orthometric heights using the duplex method of comparing time scales of remote consumers via a geostationary communications satellite. A scheme of an original experiment is described for measuring the difference in gravitational potentials and the corresponding difference in orthometric heights based on two spatially separated highly stable ground-based hydrogen quantum clocks. In accordance with the proposed scheme, for the first time in the Russian Federation, the difference in gravitational potentials and orthometric heights of ground points located at a distance of 825 m from each other was measured based on the duplex satellite method and transportable quantum hydrogen clocks. The domestic geostationary satellite Express-80 was used in the geostationary repeater satellite; duplex communication was established using stationary and relocatable sets of duplex equipment. With a relative instability of quantum clocks of 10–15 and a difference in orthometric heights of about 21 m, the measurement error was 2.8 m. The results obtained are relevant for geodetic gravimetry when solving problems of constructing a unified altitude base using highly stable quantum frequency standards.

1. Fateev V. F. Relativistic metrology of near-Earth space-time. FSUE VNIIFTRI, Mendeleevo (2017). (In Russ.)

2. Fateev V. F., Rybakov E.A., Smirnov F.R. et al. Quantum levels and the quantum footstock network. Theory, experiments, modeling. FSUE VNIIFTRI, Mendeleevo (2024). (In Russ.)

3. Fateev V. F., Rybakov E. A., Smirnov F. R. A method of relativistic synchronization of moving atomic clocks and experimental verification thereof. Technical Physics Letters, 43(5), 456–459, (2017). https://doi.org/10.1134/S1063785017050182

4. Fateev V. F., Rybakov E. A. Experimental verification of the quantum level on a mobile quantum clock. Doklady Physics, 66(1), 17–19, (2021). https://doi.org/10.1134/S1028335820110038

5. Fateev V. F., Ignatenko I. Ju. On the possibility of measuring the parameters of the earth’s gravitational field using quantum-optical systems. Almanac of Modern Metrology, (1(29)), 106–114. (2022). (In Russ.) https://elibrary.ru/mfekvm

6. Naumov A. V. Method of two-way transmission time and frequency signals via geostationary satellites (TWSTFT). Almanac of Modern Metrology, (8), 162–197 (2016). (In Russ.) https://elibrary.ru/xrzlsf

7. Kanushin V. F., Karpik A. P., Goldobin D. N., Ganagina I. G.,. Gienko E. G., Kosarev N. S. The definition of gravity potential and heights differences in geodesy by gravimetric and satellite measurements. Vestnik SSUGT, (3(31)), 53–69 (2015). (In Russ.) https://elibrary.ru/vnvvgh

8. Mazurova E. M., Petrov A. N. Quantum footstocks and the Sagnac effect. Abstracts of the X All-Russian Conference with International Participation “Fundamental and Applied Coordinate-Temporal and Navigation Support” (KVNO-2023), St. Petersburg, Russia, April 17–21, 2023, pp. 121–122. Institute of Applied Astronomy RAS, St. Petersburg (2023).

9. Mazurova E. M., Petrov A. N., The Sagnac effect in optic fiber link synchronization of high-precision frequency standards. Geodesy and cartography, 83(12), 12–21 (2022). (In Russ.). https://doi.org/10.22389/0016-7126-2022-990-12-12-21

10. Gienko E. G., Kopeikin S. M., Kanushin V. F. et al. Determination of altitude differences by gravitational frequency shift of a mobile standard. Proc. of the VIII International Symposium “Metrology of time and space”, St. Petersburg, Russia, September 14–16, 2016, pp. 164–168. FSUE VNIIFTRI, Mendeleevo (2016).

11. Cheng P., Shen W., Sun X., Cai C., Wu K., Shen Z. Measuri ng height difference using two-way satellite time and frequency transfer. Remote Sensing, 14(3), 451 (2022). https://doi.org/10.3390/rs14030451

12. Fateev V. F., Smirnov F. R., Karaush A. A. An experiment to improve the accuracy of a quantum level using hydrogen quantum clock with GLONASS/GPS phase measurements. Technical Physics, 68(8), 1098–1103 (2023). https://doi.org/10.61011/TP.2023.08.57271.32-23

13. Noretz I. B., Karaush A. A., Kupalov D. S., Smirnov Yu. F., Donchenko S. I., Denisenko O. V., Slusarev S. N., Fedotov V. N., Khromov M. N. GET 1-2022 State primary standard for time and frequency units and the national time scale: contribution to the Coordinated Universal Time. Measurement Techniques, 66(10), 729–735 (2024). https://doi.org/10.1007/s11018-024-02286-1

14. Fateev V. F., Smirnov F. R., Karaush A. A. Method for relative syntonization of quantum clocks: experimental studies. Measurement Techniques, 66(4), 265–272 (2023). https://doi.org/10.1007/s11018-023-02220-x