Skip to main content
SpringerLink
Log in

The unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations

  • Article
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

From Kaula’s Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel’s general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J 2 and J 22 of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Garfinkel B. Formal solution in the problem of small divisors. Astron J, 1966, 71: 657–669

    Article  ADS  MathSciNet  Google Scholar 

  2. Jupp A H. A solution of the ideal resonance problem for the case of libration. Astron J, 1969, 74: 35–43

    Article  ADS  Google Scholar 

  3. Garfinkel B. Global solution of the ideal resonance problem. Celest Mech, 1973, 8: 207–212

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. Henrard J, Wauthier P. A geometric approach to the ideal resonance problem. Celest Mech, 1988, 44: 227–238

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Erdi B, Kovacs J. A fourth-order solution of the ideal resonace problem. Celest Mech Dyn Astron, 1993, 56: 221–230

    Article  ADS  MATH  Google Scholar 

  6. Ferraz-Mello S. Ideal resonance problem: the post-post-pendulum approximation. Celest Mech Dyn Astron, 2002, 83: 275–289

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. Garfinkel B. A theory of libration. Celest Mech, 1976, 13: 229–246

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Liu L, Innanen K A, Zhang S P. Studies on orbital resonance. I. Astron J, 1985, 90: 877–886

    Article  ADS  Google Scholar 

  9. Liu L, Innanen K A. Studies on orbital resonance. II. Astron J, 1985, 90: 887–891

    Article  ADS  Google Scholar 

  10. Liu L. Orbital resonance. Progr Astron, 1986, 4: 43–52

    Google Scholar 

  11. Liu L, Liao X H, Zhao C Y. The orbital resonances on the motions of artificial satellites. Progr Astron, 1991, 9: 298–308

    ADS  Google Scholar 

  12. Zhao C Y, Liu L. Some discussions about the ideal resonance. Acta Astron Sin, 1991, 32: 268–276

    ADS  Google Scholar 

  13. Lima Jr P H C L. Sistemas ressonantes a altas excentricidades no movimento de satélites artificiais. Tese de Doutorado, Instituto tecnológico de aeronáutica, São José dos Campos, São Paulo, 1998

    Google Scholar 

  14. Formiga J K S. Estudo de ressonâncias no movimento orbital de satélites artificiais. Faculdade de Engenharia do Campus de Guaratinguetá, Universidade Estadual Paulista, Guaratinguetá, São Paulo, 2005

    Google Scholar 

  15. Formiga J K S, Vilhena de Moraes R. Dynamical systems: an integrable kernel for resonance effects. J Comput Interdisc Sci, 2009, 1: 89–94

    Google Scholar 

  16. Sampaio J C, Vilhena de Moraes R, Fernandes S S. Artifical satellites dynamics: resonance effects. Proceedings of the 22nd International Symposium on Space Flight Dynamics, São José dos Campos, Brazil, 2011

    Google Scholar 

  17. Formiga J K S, Vilhena de Moraes R. 15:1 resonance effects on the orbital motion of artificial satellites. J Aerosp Technol Manag, 2011, 3: 251–258

    Article  Google Scholar 

  18. Kaula W M. Theory of Satellite Geodesy: Application of Satellites to Geodesy. London: Blaisdell Publishing Company, 1966

    Google Scholar 

  19. Yi Z H. An Introduction to Celestial Mechanics (in Chinese). Beijing: Science Press, 1978

    Google Scholar 

  20. Mei F X, Liu R, Luo Y. Advanced Analytical Mechanics (in Chinese). Beijing: Beijing Institute of Technology Press, 1991

    Google Scholar 

  21. Liu L. Celestial Mechanics Method (in Chinese). Nanjing: Nanjing University Press, 1998

    Google Scholar 

  22. Tapley B D, Watkins M M, Ries J C, et al. The joint gravity model 3. J Geophys Res, 1996, 101, 28029–28049

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, 210008, China

    MingJiang Zhang, ChangYin Zhao, YongQing Xiong, RongYu Sun & TingLei Zhu

  2. Key Laboratory of Space Object and Debris Observation, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, 210008, China

    MingJiang Zhang, ChangYin Zhao, YongQing Xiong, RongYu Sun & TingLei Zhu

  3. University of Chinese Academy of Sciences, Beijing, 100049, China

    MingJiang Zhang, RongYu Sun & TingLei Zhu

Authors
  1. MingJiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ChangYin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. YongQing Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. RongYu Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. TingLei Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ChangYin Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, M., Zhao, C., Xiong, Y. et al. The unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations. Sci. China Phys. Mech. Astron. 56, 840–847 (2013). https://doi.org/10.1007/s11433-013-5022-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-013-5022-8

Keywords

Search

Navigation