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.
Similar content being viewed by others
References
Ballinger, G., Diacu, F.N.: Rom. Astron. J. 3, 51 (1993)
Bell, J.F., Damour, T.: Astrophys. J. 464, 857 (1996)
Bertrand, J.: C. R. Acad. Sci. 77, 849 (1873)
Blome, H.J., Chicone, C., Hehl, F.W., Mashhoon, B.: Phys. Rev. D 81, 065020 (2010)
Bogorodskij, A.F.: Universal Attraction. Naukova Dumka, Kiev (1971).
Capozziello, S., Cardone, V.F., Lambiase, G., Troisi, A.: Int. J. Mod. Phys. D 15, 69 (2006)
Devaney, R.L.: In: van Strien, S., Walters, P. (eds.) Ergodic Theory and Dynamical Systems 1, p. 211. Birkhäuser, Boston (1981)
Diacu, F.N.: In: Lacomba, E., Llibre, J. (eds.) New Trends in Hamiltonian Systems and Celestial Mechanics, p. 127. World Scientific, Singapore (1995)
Fabris, J.C., Campos, J.P.: Gen. Relativ. Gravit. 41, 93 (2009)
Hehl, F.W., Mashhoon, B.: Phys. Lett. B 673, 279 (2009)
Lu, C.: Res. Astron. Astrophys. 14, 810 (2014)
McGehee, R.: J. Differ. Equ. 14, 70 (1973)
McGehee, R.: Invent. Math. 27, 191 (1974)
Mioc, V.: Rom. Astron. J. 12, 193 (2002)
Mioc, V.: Hvar Obs. Bull. 28, 167 (2004)
Mioc, V., Blaga, P.: Rom. Astron. J. 1, 103 (1991)
Mioc, V., Stavinschi, M.: Bull. Astron. Belgr. 156, 21 (1997)
Mücket, J.P., Treder, H.-J.: Astron. Nachr. 298, 65 (1977)
Ragos, O., Haranas, I., Gkigkitzis, I.: Astrophys. Space Sci. 345, 67 (2013)
Ṣelaru, D., Mihai, D., Mioc, V.: Bull. Astron. Belgr. 156, 27 (1997)
Shapiro, I.L., Sola, J., Stefanic, H.: J. Cosmol. Astropart. Phys. 1, 12 (2005)
Soleng, H.H.: Gen. Relativ. Gravit. 27, 367 (1995)
Tohline, J.E.: In: Athanassoula, E. (ed.) IAU Symposium, 100, Internal Kinematics and Dynamics of Galaxies, p. 205 (1983)
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
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
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
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-020-03906-2