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Revisiting the Dynamics of Two-Body Problem in the Framework of the Continued Fraction Potential

Author

Listed:
  • Sergey Ershkov

    (Department of Scientific Researches, Plekhanov Russian University of Economics, Scopus Number 60030998, 36 Stremyanny Lane, 117997 Moscow, Russia
    Sternberg Astronomical Institute, M.V. Lomonosov’s Moscow State University, 13 Universitetskij Prospect, 119992 Moscow, Russia)

  • Ghada F. Mohamdien

    (Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt)

  • M. Javed Idrisi

    (Department of Mathematics, College of Natural and Computational Science, Mizan-Tepi University, Tepi 121, Ethiopia)

  • Elbaz I. Abouelmagd

    (Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt)

Abstract

In this analytical study, a novel solving method for determining the precise coordinates of a mass point in orbit around a significantly more massive primary body, operating within the confines of the restricted two-body problem (R2BP), has been introduced. Such an approach entails the utilization of a continued fraction potential diverging from the conventional potential function used in Kepler’s formulation of the R2BP. Furthermore, a system of equations of motion has been successfully explored to identify an analytical means of representing the solution in polar coordinates. An analytical approach for obtaining the function t = t ( r ), incorporating an elliptic integral, is developed. Additionally, by establishing the inverse function r = r ( t ), further solutions can be extrapolated through quasi-periodic cycles. Consequently, the previously elusive restricted two-body problem (R2BP) with a continued fraction potential stands fully and analytically solved.

Suggested Citation

  • Sergey Ershkov & Ghada F. Mohamdien & M. Javed Idrisi & Elbaz I. Abouelmagd, 2024. "Revisiting the Dynamics of Two-Body Problem in the Framework of the Continued Fraction Potential," Mathematics, MDPI, vol. 12(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:590-:d:1340083
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    Cited by:

    1. Abouelmagd, Elbaz I. & Alshaery, A.A. & Gao, Fabao, 2024. "New dynamical system for circular satellites relative motion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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