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Investigation of the restricted problem of three bodies of variable masses using computer algebra

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Abstract

The classical restricted three-body problem for bodies with variable masses is discussed for the case when the masses of two bodies vary isotropically at different rates and their sum varies according to the joint Meshchersky law. Within the perturbation theory in Hills’s approximation, differential equations determining the secular perturbations of the orbital elements are obtained and it is shown that they are integrable under arbitrary laws governing the mass variations satisfying the joint Meshchersky law. The influence of the variations of the body masses on the evolution of the orbital parameters is comparable with the perturbations created by massive bodies. All symbolic computations are performed in Wolfram Mathematica.

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Authors and Affiliations

  1. Warsaw University of Life Sciences, ul. Novoursynovska 159, Moscow, 02-776, Poland

    A. N. Prokopenya

  2. Innovation High School Collegium of Mazovia, ul. Sokolowska 161, Siedlce, 09-110, Poland

    A. N. Prokopenya

  3. Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan

    M. Zh. Minglibayev, G. M. Mayemerova & Zh. U. Imanova

  4. Fesenkov Astrophysical Institute, Almaty, 050020, Kazakhstan

    M. Zh. Minglibayev

Authors
  1. A. N. Prokopenya
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  2. M. Zh. Minglibayev
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  3. G. M. Mayemerova
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  4. Zh. U. Imanova
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Correspondence to A. N. Prokopenya.

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Original Russian Text © A.N. Prokopenya, M.Zh. Minglibayev, G.M. Mayemerova, Zh.U. Imanova, 2017, published in Programmirovanie, 2017, Vol. 43, No. 5.

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Prokopenya, A.N., Minglibayev, M.Z., Mayemerova, G.M. et al. Investigation of the restricted problem of three bodies of variable masses using computer algebra. Program Comput Soft 43, 289–293 (2017). https://doi.org/10.1134/S0361768817050061

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  • DOI: https://doi.org/10.1134/S0361768817050061

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