Investigation of the restricted problem of three bodies of variable masses using computer algebra
- Authors: Prokopenya A.N.1,2, Minglibayev M.Z.3,4, Mayemerova G.M.3, Imanova Z.U.3
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Affiliations:
- Warsaw University of Life Sciences
- Innovation High School Collegium of Mazovia
- Al-Farabi Kazakh National University
- Fesenkov Astrophysical Institute
- Issue: Vol 43, No 5 (2017)
- Pages: 289-293
- Section: Article
- URL: https://journals.rcsi.science/0361-7688/article/view/176540
- DOI: https://doi.org/10.1134/S0361768817050061
- ID: 176540
Cite item
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.
About the authors
A. N. Prokopenya
Warsaw University of Life Sciences; Innovation High School Collegium of Mazovia
Author for correspondence.
Email: alexander_prokopenya@sggw.pl
Poland, ul. Novoursynovska 159, Moscow, 02-776; ul. Sokolowska 161, Siedlce, 09-110
M. Zh. Minglibayev
Al-Farabi Kazakh National University; Fesenkov Astrophysical Institute
Email: alexander_prokopenya@sggw.pl
Kazakhstan, Almaty, 050040; Almaty, 050020
G. M. Mayemerova
Al-Farabi Kazakh National University
Email: alexander_prokopenya@sggw.pl
Kazakhstan, Almaty, 050040
Zh. U. Imanova
Al-Farabi Kazakh National University
Email: alexander_prokopenya@sggw.pl
Kazakhstan, Almaty, 050040