Numerical analysis of the new type retroreflector application effectiveness while laser ranging of a spacecraft

Mathematica modeling, numerical technique and program complexes


Anzheurov A. S.1*, Denisova I. P.1*, Kostikov Y. A.1*, Pasisnichenko M. A.2

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Company "SIBINTEK", 1, Zagorodnoe shosse, page 1, Moscow, 117152, Russia



When laser ranging of a spacecraft the light impulse reflected from retroreflector , forms spot on the Earth surface, which center is usually located at a significant distance (from hundreds to thousands meters) from the station’s receiving telescope, due to the velocity aberration effect. Thus, the receiving telescope appears to be at periphery of the spot.

Due to the fact, that the electromagnetic radiation energy flow in the pulse decreases as distancing from the pulse axis to its periphery, only a small portion of the light energy hits the receiving telescope. Often, this portion is not enough to register the moment of the reflected impulse arrival at the laser station. To eliminate this shortcoming the Research and production Corporation “Systems of precision instrument making” suggested the retroreflector of a new type, in which maximum of intensity of the reflected impulse’ direction diagram was shifted from optical axis to periphery by coating the retroreflector edges with various coatings, so that the spot changed into a luminous ring. It allowed shifting the intensity maximum to about 1.2 arcseconds from the reflector optical axis with angular width at the level of half-power of about one arcsecond.

Mathematical modeling and numerical analysis of a new type retroreflector implementation effectiveness for laser ranging of high-orbit and low-orbit spacecraft were performed in this work. The conducted study revealed that ensuring the most favorable conditions for low-orbit spacecraft ranging (the orbit height of 300−550 km) in retroreflctor of a new type requires shifting of annular directional diagram maximum of the reflected impulse relative to the central beam not by 1.2 arc-seconds, but several times more, i. e. approximately by 9.7 arc-seconds. High-orbit spacecraft (orbit height of 6000−34000 km) for the same purpose must be equipped with retroreflectors of a new type, in which the maximum of the directional diagram of the reflected impulse is shifted relative to the Central beam by about five arc-seconds.

This means that at the stage of designing of each spacecraft the unique retroreflector of a new type should be developed and manufactured maximally effective for operation at the projected orbit.


retroreflector, low-orbit spacecraft, high-orbit spacecraft, laser ranging, high intensity


  1. Manuel Salvoldi, Daniel Choukroun. Intersatellite Laser Ranging and Attitude Robust Measurement Planning, AIAA Guidance, Navigation, and Control Conference, San Diego, California, USA, 2016, available at:

  2. Filippo Ales, Peter F. Gath, Ulrich Johann, and Claus Braxmaier. Modeling and Simulation of a Laser Ranging Interferometer Acquisition and Guidance Algorithm, Journal of Spacecraft and Rockets, January 2014, vol. 51, no. 1 pp. 226 – 238, available at:

  3. Paul W. Schumacher, G. Charmaine Gilbreath, Mark A. Davis, and Edward D. Lydick. Precision of Satellite Laser Ranging Calibration of the Naval Space Surveillance System, Journal of Guidance, Control, and Dynamics, September 2001, vol. 24, no. 5. pp. 925 – 932, available at:

  4. Dustin R. Buccino, Jill A. Seubert, Sami W. Asmar, and Ryan S. Park. Optical Ranging Measurement with a Lunar Orbiter: Limitations and Potential, Journal of Spacecraft and Rockets, May 2016, vol. 53, no. 3, pp. 457 – 463, available at:

  5. Michael E. Hough. Precise Orbit Determination Using Satellite Radar Ranging, Journal of Guidance, Control, and Dynamics, July 2012, vol. 35, no. 4, pp. 1048 – 1058, available at:

  6. Brumberg V.A. Relyativistskaya nebesnaya mekhanika (Relativistic celestial mechanics), Moscow, Nauka, 1972, 382 p.

  7. Ostanina M.V., Pasisnichenko M.A., Rostovskii V.S. Vestnik Moskovskogo universiteta. Fizika. Astronomiya, 2013, no. 6, pp. 42 – 46.

  8. Denisov M.M., Denisova I.P., Pasisnichenko M.A. Elektromagnitnye volny i elektronnye sistemy, 2016, vol. 21, no. 4, pp. 3 – 10.

  9. Degnan John. Presentation and Paper from ILRS Technical Laser Workshop, Satellite, Lunar and Planetary Laser Ranging: Characterizing the Space Segment. INFN-LNF. Frascatti, Italy, November 05–09, 2012.

  10. Murashkin V.V., Sadovnikov M.A., Sokolov A.L., Shargorodskii V.D. Elektromagnitnye volny i elektronnye sistemy, 2011, vol. 16, no. 3, pp. 47 – 50.

  11. Samarskii A.A. Vvedenie v chislennye metody (Introduction to numerical methods), Moscow, Nauka, 1997, 239 p.

  12. Samarskii A.A. Chislennye metody i vychislitel’nyi eksperiment (Numerical methods and computer experiment), Moscow, Nauka, 1998, 518 p.

  13. Duboshin G.N. Nebesnaya mekhanika (Celestial mechanics), Moscow, Nauka, 1968, 799 p.

  14. Shatina A.V., Sherstnyov E.V. Satellite motion in the gravitational field f a viscoelastic planet with a core, Cosmic Research, 2015, vol. 53, no. 2, pp. 163 – 170.

  15. Denisov M.M. Elektromagnitnye volny i elektronnye sistemy, 2010, vol. 15, no. 4, pp. 33 – 38.

  16. Semenov V.F., Sizentsev G.A., Sotnikov B.I., Sytin O.G. Izvestiya RAN. Energetika, 2006, no. 1, pp. 21 – 30.

  17. Starovoitov E.I. Trudy MAI, 2017, no. 94, available at:

  18. Denisov M.M., Denisova I.P. Trudy MAI, 2016, no. 85, available at:

  19. Denisov V.I., Denisov M.M. Mathematical Modeling of Angular Distortions in Laser Ranging of the RadioAstron Satellite, Computational Mathematics and Mathematical Physics, 2008, vol. 48, issue 8, pp. 1418 – 1427.

  20. Enshtein A. Sobranie nauchnykh trudov (A collection of scientific papers), Moscow, Nauka, 1965, vol. 2. 878 p.

  21. Landau L.D., Lifshits E.M. Teoriya polya (Field theory), Moscow, Nauka, 1988, 512 p.

  22. Ashby N., Bertotti B. Relativistic effects in local inertial frames, Physical Review, 1986, vol. 34, no. 8, pp. 2246 – 2258.

Download — informational site MAI

Copyright © 2000-2021 by MAI