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The effect of the relativistic transformation law of angles on laser ranging of satellites moving in circular orbits equipped with a single retroreflector

  • Physics of Earth, Atmosphere, and Hydrosphere
  • Published:
Moscow University Physics Bulletin Aims and scope

Abstract

It is shown that due to the relativistic transformation law of angles, a laser pulse reflected from a moving retroreflector propagates not strictly back, but at a small angle to the direction of the laser station. For this reason, the ray located on the periphery of a pulse reaches the receiving telescope of the laser station instead of the central ray of a pulse. As a result, the flux of electromagnetic energy received by the laser station is certainly less than the flux of energy in the vicinity of the central ray. The energy flux attenuation coefficient is assessed on the basis of numerical analysis. It is shown that if the receiving telescope is separated from the laser station in order to be mobile and is moving along the Earth’s surface so that the center of each spot formed by a pulse of the reflected light hits the telescope, then the electromagnetic energy flux during laser probing of the satellite will be higher by more than 100 times in comparison with the energy flux received by the stationary telescope of the laser station. From our study it follows that the maximum speed of motion of the centers of spots on the Earth’s surface does not exceed 8 km/h.

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References

  1. V. V. Batygin and I. N. Toptygin, Problem Book in Electrodynamics (Nauka, Moscow, 1970).

    Google Scholar 

  2. N. Ashby and B. Bertotti, Phys. Rev. 34, 2246 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  3. M. M. Denisov, Elektromagn. Volny Elektron. Sist. 15, 33 (2010).

    MathSciNet  Google Scholar 

  4. Yu. L. Kokurin, Quantum Electron. 33, 45 (2003).

    Article  ADS  Google Scholar 

  5. J. Degnan, presented at ILRS Technical Laser Workshop “Satellite, Lunar and Planetary Laser Ranging: Characterizing the Space Segment,” Frascatti, 2012.

    Google Scholar 

  6. V. I. Denisov, B. N. Shvilkin, V. A. Sokolov, and M. I. Vasili’ev, Phys. Rev. D 94, 045021 (2016).

    Article  ADS  Google Scholar 

  7. A. Einstein, Collected Works (Moscow, 1965), Vol. 1.

    Google Scholar 

  8. L. D. Landau and E. M. Lifshitz, Hydrodynamics (Nauka, Moscow, 1988).

    Google Scholar 

  9. V. A. Fock, Theory of Space, Time, and Gravity (Gos. Izd. Fiz.-Mat. Lit., Moscow, 1961).

    Google Scholar 

  10. L. E. El’sgol’ts, Differential Equations and Variational Calculus (Nauka, Moscow, 1965).

    Google Scholar 

  11. V. I. Denisov, V. A. Sokolov, and M. I. Vasiliev, Phys. Rev. D 90, 02301 (2014).

    Article  Google Scholar 

  12. V. I. Denisov, I. P. Denisova, and S. I. Svertilov, Theor. Math. Phys. 135, 720 (2003).

    Article  Google Scholar 

  13. M. M. Denisov, Astron. Rep. 51, 512 (2007).

    Article  ADS  Google Scholar 

  14. M. M. Denisov, N. V. Kravtsov, and I. V. Krivchenkov, JETP Lett. 85, 412 (2007).

    ADS  Google Scholar 

  15. M. M. Denisov and A. A. Zubrilo, Moscow Univ. Phys. Bull. 64, 569 (2009). doi 10.3103/S0027134909060022

    Article  ADS  Google Scholar 

  16. V. I. Denisov and M. M. Denisov, Comput. Math. Math. Phys. 48, 1418 (2008).

    Article  MathSciNet  Google Scholar 

  17. M. V. Ostanina, M. A. Pasisnichenko, and V. S. Rostovskii, Moscow Univ. Phys. Bull. 68, 478 (2013). doi 10.3103/S0027134913060106

    Article  ADS  Google Scholar 

  18. V. L. Denisov and S. I. Svertilov, Phys. Rev. D 71, 063002 (2005).

    Article  ADS  Google Scholar 

  19. G. N. Duboshin, Celestial Mechanics (Moscow, 1968).

    MATH  Google Scholar 

  20. M. M. Denisov, Meas. Tech. 52, 1167 (2009).

    Article  Google Scholar 

  21. http://www.npk-spp.ru.

  22. http://ilrs.gsfc.nasa.gov.

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Authors and Affiliations

  1. Department of Atmospheric Physics, Faculty of Physics, Moscow State University, Moscow, 119991, Russia

    I. V. Mazaeva

  2. Department of Applied Mathematics, Information Technology, and Electrical Engineering, National Research University Moscow Aviation Institute, Moscow, 125993, Russia

    M. A. Pasisnichenko

Authors
  1. I. V. Mazaeva
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  2. M. A. Pasisnichenko
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Corresponding author

Correspondence to I. V. Mazaeva.

Additional information

Original Russian Text © I.V. Mazaeva, M.A. Pasisnichenko, 2017, published in Vestnik Moskovskogo Universiteta, Seriya 3: Fizika, Astronomiya, 2017, No. 4, pp. 60–67.

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Mazaeva, I.V., Pasisnichenko, M.A. The effect of the relativistic transformation law of angles on laser ranging of satellites moving in circular orbits equipped with a single retroreflector. Moscow Univ. Phys. 72, 402–409 (2017). https://doi.org/10.3103/S0027134917040087

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  • DOI: https://doi.org/10.3103/S0027134917040087

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