Skip to main content
Log in

Orbits stability under the influence of Mücket-Treder potential

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The Mücket-Treder-type potential was initially introduced to explain the discrepancy between Mercury’s observed perihelion advance and the computed value based on Newton’s law, but it can also be used for many astronomical situations as, for instance, the study of the very eccentric cometary orbits in the neighborhood of the Sun. In this paper we tackle the two-body problem in the Mücket-Treder post-Newtonian field from the particular standpoint of orbits stability. Starting from the equations of motion and first integrals written in standard polar coordinates, we apply McGehee-type transformations of the second kind. Then we depict the phase-space structure considering the foliations by the energy constant and the angular momentum constant. Various stability regions are found for each case.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

Download references

Acknowledgements

This work was supported by a grant of the Ministry of National Education and Scientific Research, PNCD III Programme, project number 16PCCDI2018.

Author information

Authors and Affiliations

Authors

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Popescu, E., Pricopi, D. Orbits stability under the influence of Mücket-Treder potential. Astrophys Space Sci 365, 191 (2020). https://doi.org/10.1007/s10509-020-03906-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10509-020-03906-2

Keywords

Navigation