Skip to main content
Log in

Dynamic Structure of the GLONASS and GPS Orbital Space: Problem of Disposal of Retired Objects

  • Published:
Solar System Research Aims and scope Submit manuscript

Abstract

The paper presents the results of a study of the dynamic structure of the orbital space of the navigation systems GLONASS and GPS. It is shown that the dynamic structure of the GLONASS region is determined by the action of one stable Lidov–Kozai secular resonance. The motion of almost all the retired objects of the GLONASS system is stable throughout the 100-year study period. In the GPS region, there is an orbital resonance and a large number of secular resonances. Their combined influence leads to a rapid increase in the eccentricity of the orbits of the retired objects of the system. Features of the dynamic structure of the orbital space are used to find the graveyard (parking) orbits of the retired objects of navigation systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aleksandrova, A.G., Bordovitsyna, T.V, and Chuvashov, I.N., Numerical simulation in the problems on the near- Earth objects dynamics, Izv. Vyssh. Uchebn. Zaved., Fiz., 2017, vol. 60, no. 1, pp. 69–76.

    Google Scholar 

  • Aleksandrova, A.G., Bordovitsyna, T.V, and Tomilova, I.V., The correlation between light pressure and dynamic of near-Earth objects being at resonance orbits, Sol. Syst. Res., 2018, vol. 52, no. 5 (in press).

    Google Scholar 

  • Avdyushev, V.A., Gauss-Everhart integrator, Vychisl. Tekhnol., 2010, vol. 15, no. 4, pp. 31–47.

    MATH  Google Scholar 

  • Bordovitsyna, T.V., Aleksandrova, A.G., and Chuvashov, I.N., Complex of algorithms and software for researching chaoticity in the Earth’s artificial satellites dynamics, Izv. Vyssh. Uchebn. Zaved., Fiz., 2010, vol. 53, no. 8/2, pp. 14–21.

    Google Scholar 

  • Bordovitsyna, T.V., Tomilova, I.V., and Chuvashov, I.N., The effect of secular resonances on the long-term orbital evolution of uncontrollable objects on satellite radio navigation systems in the MEO region, Sol. Syst. Res., 2012, vol. 46, no. 5, pp. 329–340.

    Article  ADS  Google Scholar 

  • Bordovitsyna, T.V and Tomilova, I.V., Structure features of century resonances in the near-Earth space objects dynamics, Izv. Vyssh. Uchebn. Zaved., Fiz., 2016, vol. 59, no. 3, pp. 41–48.

    MATH  Google Scholar 

  • Breiter, S., Lunisolar apsidal resonances at lowsatellite orbits, Celest. Mech. Dyn. Astron., 1999, vol. 74, pp. 253–274.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Breiter, S., The prograde C7 resonance for Earth and Mars satellite orbits, Celest. Mech. Dyn. Astron., 2000, vol. 77, pp. 201–214.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Breiter, S., On the coupling of lunisolar resonances for Earth satellite orbits, Celest. Mech. Dyn. Astron., 2001a, vol. 80, pp. 1–20.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Breiter, S., Lunisolar resonances revisited, Celest. Mech. Dyn. Astron., 2001b, vol. 81, pp. 81–91.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Chao, C. and Gick, R., Long-term evolution of navigation satellite orbits, Adv. Space Res., 2004, vol. 34, pp. 1221–1226.

    Article  ADS  Google Scholar 

  • Chuvashov, I.N., Krasavin, D.S., and Bordovitsyna, T.V., Features of longitude orbital evolution of Etalon-1 and Etalon-2 satellites, Izv. Vyssh. Uchebn. Zaved., Fiz., 2017, vol. 60, no. 3, pp. 64–69.

    Google Scholar 

  • Cincotta, P.M. and Simó, C., Simple tools to study global dynamics in non-axisymmetric galactic potentials—I, Astron. Astrophys. Suppl., 2000, vol. 147, pp. 205–228.

    Article  ADS  Google Scholar 

  • Cincotta, P.M., Girdano, C.M., and Simo, C., Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits, Phys. D, 2003, vol. 182, pp. 151–178.

    Article  MathSciNet  MATH  Google Scholar 

  • Cook, G.E., Luni-Solar perturbations of the orbit of an Earth satellite, Geophys. J., 1962, vol. 6, no. 3, pp. 271–291.

    Article  ADS  MATH  Google Scholar 

  • Daquin, J., Rosengren, A.J., Alessi, E.M., Deleflie, F., Valsecchi, G.B., and Rossi, A., The dynamical structure of the MEO region: long-term stability, chaos, and transport, Celest. Mech. Dyn. Astron., 2016, vol. 124, no. 4, pp. 335–366.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kozai, Y., Secular perturbations of asteroids with high inclination and eccentricity, Astron. J., 1962, vol. 67, pp. 591–598.

    Article  ADS  MathSciNet  Google Scholar 

  • Kuznetsov, E.D., Zakharova, P.E., Glamazda, D.V., Shagabutdinov, A.I., and Kudryavtsev, S.O., Light pressure effect on the orbital evolution of objects moving in the neighborhood of loworder resonances, Sol. Syst. Res., 2012, vol. 46, no. 6, pp. 442–449.

    Article  ADS  Google Scholar 

  • Lidov, M.L., Evolution of planets’ artificial satellites caused by external body gravitation perturbation, Iskusstv. Sputniki Zemli, 1961, vol. 8, pp. 5–45.

    Google Scholar 

  • Morbidelli, A., Modern Celestial Mechanics: Dynamics in the Solar System, CRC Press, 2002.

    Google Scholar 

  • Murray, C.D. and Dermott, S.F., Solar System Dynamics, Cambridge Univ. Press, 2000.

    Book  MATH  Google Scholar 

  • Rossi, A., Resonant dynamics of medium Earth orbits: space debris, Celest. Mech. Dyn. Astron., 2008, vol. 100, pp. 267–286.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Tomilova, I.V. and Bordovitsyna, T.V, Features of structure resonance perturbations of incontrollable objects of GLONASS and GPS navigation systems. Effect on orbital evolution, Izv. Vyssh. Uchebn. Zaved., Fiz., 2017, vol. 60, no. 4, pp. 119–125.

    Google Scholar 

  • Valk, S., Delsate, N., Lemaitre, A., and Carletti, T., Global dynamics of high area-to-mass ratios GEO space debris by means of the MEGNO indicator, Adv. Space Res., 2009, vol. 43, pp. 1509–1526.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. V. Tomilova.

Additional information

Original Russian Text © I.V. Tomilova, T.V. Bordovitsyna, D.S. Krasavin, 2018, published in Astronomicheskii Vestnik, 2018, Vol. 52, No. 5, pp. 463–478.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tomilova, I.V., Bordovitsyna, T.V. & Krasavin, D.S. Dynamic Structure of the GLONASS and GPS Orbital Space: Problem of Disposal of Retired Objects. Sol Syst Res 52, 450–465 (2018). https://doi.org/10.1134/S0038094618050088

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0038094618050088

Keywords

Navigation