Applied General Theory of Relativity: Physical Principles of the Global Positioning System (GPS)
Bogdan G. Dimitrov (Institute of Nuclear Research and Nuclear Energetics (INRNE))
Abstract: (The talk will be given in Russian with English slides)
Прикладная Общая Теория Относительности: физические принципы Глобальной Системы Позиционирования (GPS)
Zoom link: us04web.zoom.us/j/2084211239?pwd=bzZoZFF0RFl6TzBBZ2hHa3pZS0prQT09
A general knowledge about the fundamental physical principles of the Global Positioning System (GPS) will be presented. One of these principles is related to the fundamental fact (the Michelson-Morley experiment) about the independence of the velocity of light from the velocity of the source of light and the non-existence of “ether”, which was the starting point for the creation of the Special Theory of Relativity by Albert Einstein. Particular attention will be paid to some (elementary) model examples, resulting in important relations, concerning the frequency change of the signal between the stations on the Earth’s surface and the rotating satellites around the Earth. This frequency change depends on the rotation of the Earth, as well as on the variation of the gravitational potential. The amazing relation of these dependencies to the approach of Special Theory of Relativity will be demonstrated, also the further extension of the approach in the framework of the General Theory of Relativity, which is being applied in the theory of the Global Positioning System since 2003. The Geocentric Relativistic Reference System will be briefly reviewed, also the determination of the atomic clock times with respect to an attached to the Earth rotating coordinate system, which is important for taking into account the General Relativity Theory effects during the satellite motion in the near-Earth space. REFERENCES 1. Neil Ashby, Relativistic effects in the Global Positioning System, in Gravitation and Relativity at the Turn of the Millenium, Proceedings of the 15th International Conference on General Relativity and Gravitation, edited by N.Dadhich and J. Narlikar (International University Centre for Astronomy and Astrophysics, 1998).
2. N. Ashby, Relativity in the Global Positioning System, Living Reviews in Relativity 6, 1-42 (2003), link.springer.com/content/pdf/10.12942%2Flrr-2003-1.pdf.
3. N. Ashby, and R. A. Nelson, in Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis, Proceedings of the IAU Symposium 261 2009, edited by S. A. Klioner, P. K. Seidelmann, and M. H.Soffel (Cambridge University Press, Cambridge, 2010).
4. J. - F. Pascual Sanchez, Introducing Relativity in Global Navigation Satellite System, Ann. Phys. (Leipzig) 16, 258-273 (2007).
5. Michael H. Soffel, and Wen-Biao Han, Applied General Relativity. Theory and Applications in Astronomy, Celestial Mechanics and Metrology, Springer Nature, Switzerland AG 2019.
6. Michael H. Soffel, and R. Langhans, Space-Time Reference Systems (Springer-Verlag, Berlin Heidelberg, 2013 ).
7. Sergei M. Kopeikin, Michael Efroimsky, and George Kaplan, Relativistic Celestial Mechanics of the Solar System (Wiley-VCH, New York, 2011).
8. L. Duchayne, Transfert de temps de haute performance: le Lien Micro-Onde de la mission ACES. Physique mathematique [math-ph]. PhD Thesis, Observatoire de Paris, 2008. Francais, HAL Id: tel-00349882, tel.archives-ouvertes.fr/tel-00349882/document.
9. M. Gulklett, Relativistic effects in GPS and LEO, October 8 2003, PhD Thesis, University of Copenhagen, Denmark, Department of Geophysics, The Niels Bohr Institute for Physics, Astronomy and Geophysics, available at www.yumpu.com/en/document/view/4706552/relativistic-e_ects-in-gps-and-leo-niels-bohr-institutet.
10. B. Hofmann-Wellenhof, and H. Moritz, Physical Geodesy (Springer-Verlag, Wien-New York, 2005).
11. Slava G. Turyshev, Viktor T. Toth, and Mikhail V. Sazhin, General relativistic observables of the GRAIL mission, Phys. Rev. D87, 024020 (2013), arXiv:1212.0232v4 [gr-qc].
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14. R. A. Nelson, Relativistic time transfer in the vicinity of the Earth and in the Solar system, Metrologia 48, S171 (2011).
15. Bogdan G. Dimitrov, the (third) extended version of arXiv:1712.01101 [gr-qc] (contains a lot of references).
16. Bogdan G. Dimitrov, New Mathematical Models of GPS Intersatellite Communications in the Gravitational Field of the Near-Earth Space, AIP Confer. Proc. 2075, 040007 (2019); doi.org/10.1063/1.5091167.
Будут представлены некоторые основные сведения о фундаментальных физических принципах, на которых основано функционирование Глобальной Системы Позиционирования (GPS). Один из этих принципов имеет связь с фундаментальным фактом о независимости скорости света от скорости источника (эксперимент Майкельсона-Морли) и несуществования т.н. «эфира», которой являлся отправной точкой для построении Специальной Теории Относительности (СТО) Альбертом Эйнштейном. Особое внимание будет уделено некоторыми (элементарными) модельными примерами, на основе которых выводятся важные зависимости о частотном изменении сигнала, посылаемым станциями на Земле к спутникам (и обратно). Эта частота зависит от угловой скорости вращения Земли, а также от изменения гравитационного потенциала. Будет продемонстрировано удивительное согласование этих зависимостей с подходами Специальной Теории Относительности, а также дальнейшее расширение подхода в рамках Общей Теории Относительности (ОТО), которая применяется в теории GPS после 2003-го года. Коротко будет рассмотрена Геоцентрическая Релятивистская Система Отсчета и определение времени атомных часов относительно вращающейся вместе со Землей координатной системой. Время, которое указывают эти часы, существенно для исследования эффектов ОТО при движении спутников в пространстве вокруг Земли.
Russianmachine learningmathematical softwaresymbolic computationmathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemscomputational physicsdata analysis, statistics and probability
Audience: researchers in the topic
Mathematical models and integration methods
| Organizers: | Oleg Kaptsov, Sergey P. Tsarev*, Yury Shan'ko* |
| *contact for this listing |