Applications of Computer Algebra in the Study of the Two-Planet Problem of Three Bodies with Variable Masses

Alexander N. Prokopenya, M. Zh. Minglibayev, Saule Shomshekova

2019

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DOI 10.1134/s0361768819020087
Data confidence 70 medium
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Abstract

Abstract The classical two-planet problem of three bodies of variable masses is studied in the general case when the body masses vary anisotropically at different rates. Differential equations of motion in terms of osculating elements of aperiodic motion along quasi-conic sections are derived. An algorithm for computing the perturbation function in the form of power series in small parameters and the derivation of differential equations determining the secular perturbations of the orbital elements are discussed. All symbolic computations are performed using Mathematica.