Skip to main content
SpringerLink
Log in

Quasi-Keplerian motion under the generally parameterized post-Newtonian force

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

The analytical solutions for the quasi-Keplerian motion under the generally parameterized post-Newtonian force are derived in the Brumberg–Damour–Deruelle representation. The solutions are formulated in terms of the orbital energy and angular momentum. The achieved results can be applied to not only the motion of a test particle but also the relative motion of a binary system in a broad spectrum of gravitation theories.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Brumberg, V.: Relativistic celesctial mechanics. Nauka, Moscow (1972). (in Russian)

    Google Scholar 

  2. Brumberg, V.: Essential Relativistic Celesctial Mechanics. Taylor & Francis Group, Abingdon (1991)

    MATH  Google Scholar 

  3. Soffel, M.H.: Relativity in Astrometry, Celestial Mechanics and Geodesy. Springer, Berlin (1989)

    Book  Google Scholar 

  4. Klioner, S.A., Kopeikin, S.M.: Astrophys. J. 427, 951 (1994)

    Article  ADS  Google Scholar 

  5. Will, C.M.: Living Rev. Relativ. 17, 4 (2014)

    Article  ADS  Google Scholar 

  6. Soffel, M.H., Han, W.B.: Applied General Relativity: Theory and Applications in Astronomy, Celestial Mechanics and Metrology. Springer, Berlin (2019)

    Book  Google Scholar 

  7. Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972)

    Google Scholar 

  8. Damour, T., Deruelle, N.: Ann. Inst. H. Poincaré. 43, 107 (1985)

    Google Scholar 

  9. Epstein, R.: Astrophys. J. 219, 92 (1977)

    Article  ADS  Google Scholar 

  10. Haugan, M.P.: Astrophys. J. 296, 1 (1985)

    Article  ADS  Google Scholar 

  11. Soffel, M.H., Ruder, H., Schneider, M.: Celestial Mech. 40, 77 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  12. Memmesheimer, R.M., Gopakumar, A., Schäfer, G.: Phys. Rev. D 70, 104011 (2004)

    Article  ADS  Google Scholar 

  13. Königsdörffer, C., Gopakumar, A.: Phys. Rev. D 71, 024039 (2005)

    Article  ADS  Google Scholar 

  14. Tessmer, M., Hartung, J., Shäfer, G.: Class. Quantum Gravit. 27, 165005 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewer for providing useful suggestions to promote the quality of this paper.

Author information

Authors and Affiliations

  1. School of Physical Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China

    Bo Yang & Wenbin Lin

  2. School of Mathematics and Physics, University of South China, Hengyang, 421001, China

    Wenbin Lin

Authors
  1. Bo Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenbin Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wenbin Lin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11973025 and 11947404).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, B., Lin, W. Quasi-Keplerian motion under the generally parameterized post-Newtonian force. Gen Relativ Gravit 52, 49 (2020). https://doi.org/10.1007/s10714-020-02700-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-020-02700-3

Keywords

Search

Navigation