DOI: 
10.22389/0016-7126-2024-1012-10-2-11
1 Mazurova E.M.
2 Petrov A.N.
Year: 
№: 
1012
Pages: 
2-11

Roskadastr, PLC

1, 
2, 
Abstract:
Accurate laser location of artificial Earth satellites (AES) makes it possible to obtain valuable information on the dynamic parameters of the Earth, its gravitational fields, and to clarify the global coordinates of the system. The effect of laser pulses deviation at the ranging AES is studied. The angle of deviation is formed between directions of emitted and returned signals at the point of the laser station’s location. The main contribution into the value of the angle is conditioned by relativity theory effects connected with non-inertiality of the station frame on the rotating Earth surface. In this article, the value of the deviation angle is calculated considering the Earth’s gravitational field that was not considered in previous works. Exactness of necessary approximations enables modelling a motion of AES by Keplerian orbits. The gravitational field of the Earth is described by the Schwarzschild solution, in the framework of which equations for the laser pulse trajectories are presented. All the calculations are made in the coordinates of the proper frame of the station. The obtained variation of the main deviation angle value is less for three orders with respect to the one that can be detected by the modern devices. Therefore, we can state that it should not be taken into account. Such a conclusion is very important for developments in this field because simpler methods, including analytical ones, are permissible. The efficiency of the numerical calculations of the effect for concrete AES remains high as well
The study was carried out within the framework of the Federal project “Maintenance, development and use of the GLONASS system” of the State Program of the Russian Federation “Space activities of Russia” for 2021-2030, in EGISU No. 1210806000081-5
References: 
1.   Denisov V. I., Denisov M. M. Matematicheskoe modelirovanie uglovykh iskazhenii pri lazernoi lokatsii ISZ “Radioastron”. Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki, 2008, Vol. 48, no. 8, pp. 1500–1509.
2.   Denisov M. M. Relyativistskie popravki pri lazernoi lokatsii kosmicheskikh apparatov. Matematicheskoe modelirovanie, 2008, Vol. 20, no. 6, pp. 57–66.
3.   Landau L. D., Lifshits E. M. Teoreticheskaya fizika. Teoriya polya. – 7-e izd., ispr. Moskva: Nauka. Gl. red. fiz.-mat. lit., 1988, 512 p.
4.   Mazurova E. M., Petrov A. N., Bakharev F. S., Klypin I. A. Ob otklonenii elektromagnitnykh impul'sov vo vrashchayushcheisya sisteme otscheta Zemli. Giroskopiya i navigatsiya, 2024, Vol. 32, no. 2, pp. 151–167.
5.   Ostanina M. V., Pasisnichenko M. A., Rostovskii V. S. Matematicheskoe modelirovanie relyativistskogo effekta pri lazernoi lokatsii iskusstvennykh sputnikov Zemli. Vestnik Moskovskogo Universiteta. Ser. 3. Fizika. Astronomiya, 2013, no. 6, pp. 42–46.
6.   Ashby N. (2003) Relativity in the Global Positioning System. Living Reviews in Relativity, no. 6, pp. 1–42. URL: http://www.livingreviews.org/lrr-2003-1 (accessed: 21.09.2022).
7.   Bartels N., Allenspacher P., Hampf D., Heidenreich B., Keil D., Schafer E., Riede W. (2022) Space object identification via polarimetric satellite laser ranging. Communications Engineering, Volume 1, no. 5, DOI: 10.1038/s44172-022-00003-w.
8.   Glaser S., König R., Neumayer K. H., Balidakis K., Schuh H. (2019) Future SLR station networks in the framework of simulated multi-technique terrestrial reference frames. Journal of Geodesy, no. 93 (1), pp. 2275–2291. DOI: 10.1007/s00190-019-01256-8.
9.   Hampf D., Schafer E., Sproll F., Otsubo T., Wagner P., Riede W. (2019) Satellite laser ranging at 100 kHz pulse repetition rate. CEAS Space Journal, no. 11, pp. 363–370. DOI: 10.1007/s12567-019-00247-x.
10.   Kucharski D., Kirchner G., Otsubo T., Koidl F. (2015) A method to calculate zero-signature satellite laser ranging normal points for millimeter geodesy – a case study with Ajisai. Earth, Planets and Space, Volume 67, no. 34, DOI: 10.1186/s40623-015-0204-4.
11.   Wilkinson M., Schreiber U., Procházka I., et al. (2019) The next generation of satellite laser ranging systems. Journal of Geodesy, no. 93 (1), pp. 2227–2247. DOI: 10.1007/s00190-018-1196-1.
12.   Xue L., Li Z., Zhang L., et al. (2016) Satellite laser ranging using superconducting nanowire single-photondetectors at 1064 nm wavelength. Optics Letters, no. 41 (16), pp. 3848–3851. DOI: 10.1364/OL.41.003848.
Citation:
Mazurova E.M., 
Petrov A.N., 
(2024) Calculating deviation of laser pulses at ranging artificial Earth satellites considering its gravitational field. Geodesy and cartography = Geodezia i Kartografia, 85(10), pp. 2-11. (In Russian). DOI: 10.22389/0016-7126-2024-1012-10-2-11
Publication History
Received: 20.09.2024
Accepted: 30.10.2024
Published: 20.11.2024

Content

2024 October DOI:
10.22389/0016-7126-2024-1012-10