Study of Secular Perturbations in the Restricted Three-Body Problem of Variable Masses Using Computer Algebra
Ibraimova A.T. Minglibayev M.Z. Prokopenya A.N.
January 2023Pleiades Publishing
Computational Mathematics and Mathematical Physics
2023#63Issue 1115 - 125 pp.
Abstract: A nonstationary restricted three-body problem for variable masses is considered taking into account the reactive forces arising due to anisotropic variation of masses of the bodies. It is assumed that the bodies are spherically symmetric and interact in accordance with Newton’s law of gravitation. On the basis of the equations of motion of the bodies in the relative system of coordinates, differential equations of aperiodic motion along quasi-conic sections in terms of osculating elements are derived. Equations determining the secular perturbations of the orbital elements are derived in the case of small eccentricities and inclinations of orbits. All symbolic computations are performed using Wolfram Mathematica.
equations of motion , restricted three-body problem , secular perturbations , variable mass
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Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Fesenkov Astrophysical Institute, Almaty, 050020, Kazakhstan
Warsaw University of Life Sciences, Warsaw, 02-776, Poland
Al-Farabi Kazakh National University
Fesenkov Astrophysical Institute
Warsaw University of Life Sciences
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