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Evolution equations of the multi-planetary problem with variable masses

Published online by Cambridge University Press:  16 August 2023

A.B. Kosherbayeva Open the ORCID record for A.B. Kosherbayeva [Opens in a new window]  and
M.Zh Minglibayev
A.B. Kosherbayeva
Affiliation:
Al-Farabi Kazakh National University, Almaty, Kazakhstan
M.Zh Minglibayev
Affiliation:
Al-Farabi Kazakh National University, Almaty, Kazakhstan
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Abstract

We investigated the influence of the variability of the masses of planets and the parent star on the dynamic evolution of n planetary systems, considering that the masses of bodies change isotropically with different rates. The methods of canonical perturbation theory, which developed on the basis of aperiodic motion over a quasi-conical cross section and methods of computer algebra were used. 4n evolutionary equations were obtained in analogues of Poincare elements. As an example, the evolutionary equations of the three-planet exosystem K2 − 3 were obtained explicitly, which is a system of 12 linear non-autonomous differential equations. Further, the evolutionary equations will be investigated numerically.

Keywords

celestial mechanicsvariable massanalogues of Poincare elementsmulti-planetary systemsecular perturbation.
Type
Poster Paper
Information
Proceedings of the International Astronomical Union , Volume 17 , Symposium S370: Winds of Stars and Exoplanets , August 2021 , pp. 283 - 284
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of International Astronomical Union

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References

NASA Exoplanet Exploration, Last update: September 28, 2022, url: https://exoplanets.nasa.gov/ Google Scholar
Minglibaev, M. Zh., 2012, Dynamics of Gravitating Bodies with Variable Masses and Dimensions, LAP LAMBERT Academic Publishing, 224 Google Scholar
Prokopenya, A. N., Minglibayev, M. Zh., Kosherbaeva, A. B., 2022, Derivation of Evolutionary Equations in the Many-Body Problem with Isotropically Varying Masses Using Computer Algebra, Programming and Computer Software, 48, 2, 107–115, DOI: 10.1134/S0361768822020098 10.1134/S0361768822020098CrossRefGoogle Scholar