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A novel type of ER3BP introducing Milankovitch cycles or seasonal irradiation processes influencing onto orbit of planet

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A Correction to this article was published on 19 November 2022

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Abstract

A developing approach for solving equations of a trapped motion of small satellite near the secondary planet mplanet (Earth) in case of the elliptic restricted problem of three bodies, ER3BP, is presented hereby. In ordinary way, this problem includes consideration of two primaries, MSun and mplanet (mplanet <  < MSun), both are orbiting around their center of mass on Keplerian orbits. Eccentricity of orbit for the aforementioned mplanet is considered to be quasiperiodically variable depending on long-term Milankovitch cycles or various types of seasonal irradiation processes influencing onto orbit of planet (hereafter, Earth). Our aim is first to establish and second to investigate a novel type of ER3BP with variable eccentricity of secondary planet stemming from long-term Milankovitch cycles where in the formulation of above problem, small satellite will always maintain its orbit located near the secondary planet, mplanet. Indeed, Milankovitch cycles govern the dynamics of slow changing the eccentricity of the secondary planet orbit quasiperiodically during a long-time period of secondary planet’s motion around the primary. This planet moves on quasi-stable elliptic orbit with negligible deviations from purely elliptical motion. Semi-analytical solutions and numerical findings with graphical plots are presented accordingly.

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Authors and Affiliations

  1. Plekhanov Russian University of Economics, Scopus Number 60030998, Moscow, Russia

    Sergey Ershkov

  2. Sternberg Astronomical Institute, M.V. Lomonosov’s Moscow State University, 13 Universitetskij Prospect, Moscow, Russia, 119992

    Sergey Ershkov

  3. Odessa State Academy of Civil Engineering and Architecture, Odessa, Ukraine

    Dmytro Leshchenko

  4. Institute of Engineering Science UB RAS, Ekaterinburg, Russia

    E. Yu. Prosviryakov

  5. B.N. Yeltsin Ural Federal University, Ekaterinburg, Russia

    E. Yu. Prosviryakov

Authors
  1. Sergey Ershkov
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  2. Dmytro Leshchenko
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  3. E. Yu. Prosviryakov
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Contributions

In this research, Dr. S.E. is responsible for the general ansatz and the solving procedure, simple algebra manipulations, calculations, results of the article and also is responsible for the search for analytical and semi-analytical solutions. Dr. D.L. is responsible for theoretical investigations as well as for the deep survey of the literature on the problem under consideration. Dr. E.P. is responsible for obtaining numerical solutions related to approximated ones (including their graphical plots). All authors agreed with results and conclusions of each other in Sects. 1–4.

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Correspondence to Sergey Ershkov.

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Ershkov, S., Leshchenko, D. & Prosviryakov, E.Y. A novel type of ER3BP introducing Milankovitch cycles or seasonal irradiation processes influencing onto orbit of planet. Arch Appl Mech 93, 813–822 (2023). https://doi.org/10.1007/s00419-022-02300-4

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