- PII
- S3034645225060073-1
- DOI
- 10.7868/S3034645225060073
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume / Issue number 6
- Pages
- 75-104
- Abstract
- The paper presents the principles of measuring the Earth’s global gravitational field (EGF) using a spacecraft (SC) equipped with a high-precision three-axis gravity gradiometer and located in low Earth orbit. Such a spacecraft is primarily designed to measure high-frequency EGF harmonics. Gradiometer measurements are not sensitive to low-order EGF harmonics, so to reconstruct the EGF in the entire frequency range, starting from =2, high-precision measurements of the SC orbit are required, which are performed by the onboard high-precision GNSS receiver. Theoretical aspects of satellite gradiometry are considered and the problem of reconstructing the EGF harmonics is solved based on model measurements. To calculate the “measured” components of the gravitational potential tensor, the EGM2008 EGF model was used. A program for numerical integration of the spacecraft orbit was also developed based on this model, including additional forces acting on the spacecraft. A direct method is used to reconstruct the EGF: a matrix of conditional equations is compiled relative to the Stokes coefficients. Solving this system using the least squares method allows us to obtain corrections to the harmonics of the a priori (initial) EGF model, which used the EGM96 model. This way, the harmonics of the reconstructed field are formed. The quality criterion for the solution is the agreement between the difference in the amplitudes of the harmonics of the reconstructed model and the EGM2008 model. Based on the obtained model solutions, an optimal SC orbit was selected for carrying out gradiometric measurements, and estimates of the accuracy characteristics of the main key elements of the spacecraft onboard scientific instruments were obtained.
- Keywords
- градиентометр гравитационное поле Земли тензор гравитационного потенциала
- Date of publication
- 23.03.2026
- Year of publication
- 2026
- Number of purchasers
- 0
- Views
- 33
References
- 1. Беликов М.В., Тайбаторов К.А. Эффективный метод вычисления производных от гравитационного потенциала Земли для решения задач динамики ИСЗ. Институт теоретической астрономии АН СССР. Препринт №7. 1990.
- 2. Дубошин Г.Н. Небесная механика. Методы теории движения искусственных небесных тел. М.: Наука. 1983.
- 3. Жамков А.С., Аюков С.В., Филеткин А.И., Милюков В.К., Власов И.Ю., Семенцов В.Н., Гусев Н.В., Жаров В.Е. Отечественный программный комплекс обработки информации космической геодезической системы спутник-спутник // Астрономический журнал. 2024. Т. 101. № 3. С. 271–283. DOI: 10.31857/S0004629924030087
- 4. Корн Г., Корн Т. Справочник по математике для научных работников и инженеров. М.: Наука. 1977.
- 5. Милюков В.К., Филеткин А.И., Жамков А.С. Космический гравитационный градиентометр: пути повышения точности моделей гравитационного поля Земли // Журнал экспериментальной и теоретической физики. 2023. Т. 161. № 4. С. 596–609. DOI: 10.31857/S0044451022040149
- 6. Филеткин А.И., Жамков А.С., Аюков С.В., Милюков В.К. Гравитационные миссии следующего поколения: исследование возможностей мультипарных конфигураций // Астрономический журнал. 2023. Т. 100. № 11. С. 1033–1045. DOI: 10.31857/S0004629923110063
- 7. Яшкин С.Н. Спутниковая градиентометрия и системы спутник-спутник. Изд-во МИИГАиК. 2009. ISBN 978-5-91188-020-0
- 8. Baur O., Reubelt T., Weigelt M., Roth M., Sneeuw N. GOCE orbit analysis: Long-wavelength gravity field determination using the acceleration approach // Advances in Space Research. 2012. V. 50. № 3. P. 385–396. DOI: 10.1016/j.asr.2012.04.022
- 9. Bruinsma S.L., Marty J., Balmino G., Biancale R., Foerste C., Abrikosov O., Neumayer H., Flechtner F. A gravity field model inferred from 6 months of GOCE data using the direct numerical method (Invited) // AGU Fall Meeting Abstracts. 2010. V. 2010. P. G33B–02.
- 10. Bruinsma S.L., Förste C., Abrikosov O., Marty J.-C., Rio M.-H., Mulet S., Bonvalot S. The new ESA satellite-only gravity field model via the direct approach // Geophys. Res. Lett. 2013. V. 40. № 14. P. 3607–3612. DOI: 10.1002/grl.50716
- 11. Cesare S. Performance requirements and budgets for the gradiometric mission. GO-TN-AI-0027, Thales Alenia Space. 2008.
- 12. Drinkwater M.R., Floberghagen R., Haagmans R., Muzi D., Popescu A. GOCE: ESA’s first earth explorer core mission / G. Beutler, M.R. Drinkwater, R. Rummel, R. Von Steiger (eds.). Earth Gravity Field from Space — From Sensors to Earth Sciences: Proceedings of an ISSI Workshop 11–15 March 2002, Bern, Switzerland. P. 419–432. Springer Netherlands, Dordrecht. 2003. ISBN 978-94-017-1333-7. DOI: 10.1007/978-94-017-1333-7_36
- 13. Gill E.K.A., Montenbruck O. Satellite orbits: Models, methods and applications. Springer. 2013. DOI: 10.1007/978-3-642-58351-3
- 14. Heiskanen W.A., Moritz H. Physical Geodesy. Series of books in geology / W.H. Freeman (ed.). 1967. ISBN 9780608309231
- 15. Johannessen J.A., Balmino G., Le Provost C., Rummel R., Sabadini R., Sünkel H., Tscherning C.C., Visser P., Woodworth P., Hughes C., Legrand P., Sneeuw N., Perosanz F., Aguirre-Martinez M., Rebhan H., Drinkwater M. The European Gravity Field and Steady–State Ocean Circulation Explorer Satellite Mission Its Impact on Geophysics // Surveys in Geophysics. 2003. V. 24. № 4. P. 339–386. DOI: 10.1023/B:GEOP.0000004264.04667.5e
- 16. Koch K.-R., Kusche J. Regularization of geopotential determination from satellite data by variance components // Journal of Geodesy. 2002. V. 76. P. 259–268. DOI: 10.1007/s00190-002-0245-x
- 17. Lemoine F., Kenyon S.C., Factor J., Trimmer R., Pavlis N., Chinn D., Cox C., Klosko S., Luthcke S., Torrence M., Wang Y., Williamson R., Pavlis E., Rapp R., Olson T. The development of the joint NASA GSFC and the national imagery and mapping agency (NIMA) geopotential model EGM96. Technical report. NASA Goddard Space Flight Center. 1998.
- 18. Metzler B., Pail R. GOCE data processing: The spherical cap regularization approach // Stud. Geophys. Geod. 2005. V. 49. P. 441–462. DOI: 10.1007/s11200-005-0021-5
- 19. Pail R., Bruinsma S., Migliaccio F., Forste C., Goiginger H., Schuh W.-D., Höck E., Reguzzoni M., Brockmann J.M., Abrikosov O., Veicherts M., Fecher T., Mayrhofer R., Krasbutter I., Sansò F., Tscherning C.C. First GOCE gravity field models derived by three different approaches // Journal of Geodesy. 2011. V. 85. № 11. P. 819–843. DOI: 10.1007/s00190-011-0467-x
- 20. Pavlis N.K., Holmes S.A., Kenyon S.C., Factor J.K. The development and evaluation of the earth gravitational model 2008 (EGM2008) // Journal of Geophysical Research: Solid Earth. 2012. V. 117. B04406. DOI: 10.1029/2011JB008916
- 21. Petit G., Luzum B. IERS conventions (2010). IERS Technical Note № 36. January 2010.
- 22. Picone J.M., Hedin A.E., Drob D.P., Aikin A.C. NRLMSISE–00 empirical model of the atmosphere: Statistical comparisons and scientific issues // Journal of Geophysical Research (Space Physics). 2002. V. 107. № A12. P. 1468. DOI: 10.1029/2002JA009430
- 23. Rummel R., Wang Y., Stummer C. GOCE gravitational gradiometry // Journal of Geodesy. 2011. V. 85. № 11. P. 777–790. DOI: 10.1007/s00190-011-0500-0
- 24. Sünkel H. From eötvös to milligal. ESA final report. Graz, Austria. 2000. 418 p.
- 25. Tapley B.D., Bettadpur S., Watkins M., Reigber C. The gravity recovery and climate experiment: Mission overview and early results // Geophysical Research Letters. 2004. V. 31. № 9. 4 p. DOI: 10.1029/2004GL019920
- 26. Voevodin V.V., Antonov A.S., Nikitenko D.A., Shvets P.A., Sobolev S.I., Sidorov I. Yu., Stefanov K.S., Voevodin Va. V., Zhumatiy S.A. Supercomputer Lomonosov–2: Large scale, deep monitoring and fine analytics for the user community // Supercomputing Frontiers and Innovations. 2019. V. 6. № 2. P. 4–11. DOI: 10.14529/jsfi190201
- 27. Zhamkov A.S., Milyukov V.K., Ayukov S.V., Filetkin A.I., Vlasov I. Yu., Zharov V.E. Modeling the recovery of the Earth’s gravitational field from satellite measurements using parallel computations // Supercomputing Frontiers and Innovations. 2024. V. 11. № 1. P. 67–80. DOI: 10.14529/jsfi240103
- 28. Zhivomirov H. Method for colored noise generation // Romanian Journal of Acoustics and Vibration. 2018. V. 15. № 1. P. 14–19.
