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Mathematics in Computer Science

Erschienen in:

17.12.2019

Computing Perturbations in the Two-Planetary Three-Body Problem with Masses Varying Non-isotropically at Different Rates

verfasst von: Mukhtar Minglibayev, Alexander Prokopenya, Saule Shomshekova

Erschienen in: Mathematics in Computer Science | Ausgabe 2/2020

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Abstract

The classical problem of three bodies of variable masses is considered in the case when two of the bodies are protoplanets and all the masses vary non-isotropically at different rates. The problem is analyzed in the framework of the planetary perturbation theory in terms of the osculating elements of aperiodic motion on quasi-conic sections. An algorithm for symbolic computation of the disturbing function and its expansion into power series in terms of the eccentricities and inclinations is discussed in detail. Differential equations describing the long-term evolution of the orbital parameters are derived in the form of Lagrange’s planetary equations. All the relevant calculations are done with the computer algebra system Wolfram Mathematica.

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Titel: Computing Perturbations in the Two-Planetary Three-Body Problem with Masses Varying Non-isotropically at Different Rates
verfasst von: Mukhtar Minglibayev
Alexander Prokopenya
Saule Shomshekova
Publikationsdatum: 17.12.2019
Verlag: Springer International Publishing
Erschienen in: Mathematics in Computer Science / Ausgabe 2/2020
Print ISSN: 1661-8270
Elektronische ISSN: 1661-8289
DOI: https://doi.org/10.1007/s11786-019-00437-0

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