Results of the substantiation of a numerical-analytical method for determining secular frequencies in the process of revealing secular resonances in the dynamics of circumplanetary objects are presented. The presented method combines two approaches: the traditional analytical approach and the numerical one. Each of the approaches has its own special features. The analytical approach is not suitable for large eccentricities, since it uses formulas obtained for small eccentricities, and the formulas that implement the numerical approach have irremovable singularities for small eccentricities and orbital inclinations. Since a special feature of the influence of secular resonances is the increase in the eccentricities from zero values to values close to unity, combining these two approaches makes it possible to obtain reliable results. This is confirmed by examples of investigation of the influence of secular resonances on the dynamics of circumlunar objects.
Similar content being viewed by others
References
S. Breiter, Celest. Mech. Dyn. Astr., 80, 1–20 (2001).
S. Breiter, Celest. Mech. Dyn. Astr., 81, 81–91 (2001).
A. J. Rosengren et al., MNRAS, 449, No. 4, 3522–3526 (2015).
J. Daquin et al., Celest Mech. Dyn. Astr., Published online 02 January 2016 .
A. Rossi, Celest. Mech. Dyn. Astr., 100, 267–286 (2008).
T. V. Bordovitsyna and I. V. Tomilova, Russ. Phys. J., 59, No. 3, 365–373 (2016).
A. G. Aleksandrova, T. V. Bordovitsyna, N. A. Popandopulo, and I. V.Tomilova, Russ. Phys. J., 63, No. 1, 64–70 (2020).
G. N. Duboshin, Reference Guide on Celestial Mechanics and Astrodynamics [in Russian], Nauka, Moscow (1976).
N. A. Popandopulo, A. G. Aleksandrova, I. V. Tomilova, et al., Sol. Syst. Res., 56, No. 4, 252–270 (2022).
G. E. Cook, Geophys. J., 6, No. 3, 271–291 (1962).
C. Murray and S. Dermott, Solar System Dynamics [Russian translation], Fizmatlit, Moscow (2010).
A. Morbidelly, Modern Celestial Mechanics. Aspects of Solar System Dynamics [Russian translation], Publishing House of the Institute of Computer Science, Moscow; Izhevsk (2014).
E. P. Aksenov, Theory of Motion of Artificial Earth’s Satellites [in Russian], Nauka, Moscow (1977).
E. I. Timashkova and K. V. Kholshevnikov, Uchenye Zapiski Leningr. Gosud. Univ., No. 373, 141–156 (1974).
Folkner W. M., Park R. S.//Planetary ephemeris DE438 for Juno, Tech. Rep. IOM392R-18-004. – Pasadena, CA: Jet Propulsion Laboratory, 2018.
A. G. Aleksandrova, E. V. Blinkova, T. V. Bordovitsyna, et al., Sol. Syst. Res., 55, No. 3, 266–281 (2021).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 47–52, June, 2022.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Popandopulo, N.A., Aleksandrova, A.G. & Bordovitsyna, T.V. To the Substantiation of a Numerical-Analytical Method for Revealing Secular Resonances. Russ Phys J 65, 959–965 (2022). https://doi.org/10.1007/s11182-022-02719-w
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-022-02719-w