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Finite-Sized Orbiter’s Motion around the Natural Moons of Planets with Slow-Variable Eccentricity of Their Orbit in ER3BP

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  • Sergey Ershkov

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

  • Dmytro Leshchenko

    (Department of Theoretical Mechanics, Odessa State Academy of Civil Engineering and Architecture, 65029 Odessa, Ukraine)

  • E. Yu. Prosviryakov

    (Sector of Nonlinear Vortex Hydrodynamics, Institute of Engineering Science of Ural Branch of the Russian Academy of Sciences, 34 Komsomolskaya St., 620049 Ekaterinburg, Russia
    Academic Department of Information Technologies and Control Systems, Ural Federal University, 19 Mira St., 620049 Ekaterinburg, Russia)

  • 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

This article is devoted to the study of the stability of movement of a satellite of finite size around the natural satellites of the planets in the solar system, using the new concept of ER3BP with variable eccentricity. This concept was introduced earlier for the variable spin state of a secondary planet correlated implicitly to the motion of the satellite for its trapped orbit near the secondary planet (which is involved in the Kepler duet “Sun-planet”). But it is of real interest to explore another kind of this problem, plane ER3BP “planet-moon-satellite”. Here, we consider two primary celestial bodies, a planet and a moon, the latter revolves around its common barycenter in a quasi-elliptical orbit in a fixed plane (invariable plane) around the planet with a slowly varying eccentricity on a large time scale due to tidal phenomena. This study presents both new theoretical and numerical results for various cases of the “planet-moon-satellite” trio.

Suggested Citation

  • Sergey Ershkov & Dmytro Leshchenko & E. Yu. Prosviryakov & Elbaz I. Abouelmagd, 2023. "Finite-Sized Orbiter’s Motion around the Natural Moons of Planets with Slow-Variable Eccentricity of Their Orbit in ER3BP," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3147-:d:1195737
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    References listed on IDEAS

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    1. Sahar H. Younis & M. N. Ismail & Ghada F. Mohamdien & A. H. Ibrahiem, 2021. "Effects of Radiation Pressure on the Elliptic Restricted Four-Body Problem," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-9, November.
    2. Meena, Poonam & Kishor, Ram, 2021. "First order stability test of equilibrium points in the planar elliptic restricted four body problem with radiating primaries," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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