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Analysis of the Stability of a Planetary System on Cosmogonic Time Scales. / Mikryukov, D. V.

In: Astronomy Letters, Vol. 46, No. 5, 05.2020, p. 344-358.

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Mikryukov, D. V. / Analysis of the Stability of a Planetary System on Cosmogonic Time Scales. In: Astronomy Letters. 2020 ; Vol. 46, No. 5. pp. 344-358.

BibTeX

@article{e53b0b25f3e84e7c907decc665a94de6,
title = "Analysis of the Stability of a Planetary System on Cosmogonic Time Scales",
abstract = "Abstract: We consider the dynamical evolution of planetary systems whose structure is nearly circular and coplanar. The analysis is performed by the Hori–Deprit averaging method within the theory of the first order in planetary masses. A convenient set of canonical elements and a rarely employed variety of astrocentric coordinates are used to derive the equations of motion. Owing to the use of the chosen system of canonical elements, the expansions of the right-hand sides of the averaged equations contain a relatively small number of terms. Compared to other widespread coordinate systems, the astrocentric coordinates used by us allow a more convenient representation of the disturbing function to be obtained and do not require its expansion into a series in powers of a small parameter. On time scales ∼105-107 years we have studied the long-term evolution of the planetary systems HD 12661, υ Andromedae, and some model systems by numerical integration of the averaged equations. Possible secular resonances have been revealed in the systems considered.",
keywords = "astrocentric coordinates, averaging method, disturbing function, Hamiltonian, heliocentric coordinates, Hori–Deprit method, Laplace coefficients, N-body planetary problem, Poincar{\'e} canonical elements, Poisson series, secular resonances, Poincare canonical elements, Hori-Deprit method, ELEMENTS, EVOLUTION, EXPANSION, POISSON SERIES",
author = "Mikryukov, {D. V.}",
note = "Funding Information: I thank K.V. Kholshevnikov for supervising the work and V.S. Shaidulin for his help in preparing the figures. I also express my gratitude to the anonymous referee for the fruitful comments and useful suggestions on the manuscript. All our computations were performed using the equipment of the Computing Center in the scientific park of the St. Petersburg State University. This work was financially supported by the Russian Science Foundation (project no. 19-72-10023). Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = may,
doi = "10.1134/S1063773720050059",
language = "English",
volume = "46",
pages = "344--358",
journal = "Astronomy Letters",
issn = "1063-7737",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "5",

}

RIS

TY - JOUR

T1 - Analysis of the Stability of a Planetary System on Cosmogonic Time Scales

AU - Mikryukov, D. V.

N1 - Funding Information: I thank K.V. Kholshevnikov for supervising the work and V.S. Shaidulin for his help in preparing the figures. I also express my gratitude to the anonymous referee for the fruitful comments and useful suggestions on the manuscript. All our computations were performed using the equipment of the Computing Center in the scientific park of the St. Petersburg State University. This work was financially supported by the Russian Science Foundation (project no. 19-72-10023). Publisher Copyright: © 2020, Pleiades Publishing, Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5

Y1 - 2020/5

N2 - Abstract: We consider the dynamical evolution of planetary systems whose structure is nearly circular and coplanar. The analysis is performed by the Hori–Deprit averaging method within the theory of the first order in planetary masses. A convenient set of canonical elements and a rarely employed variety of astrocentric coordinates are used to derive the equations of motion. Owing to the use of the chosen system of canonical elements, the expansions of the right-hand sides of the averaged equations contain a relatively small number of terms. Compared to other widespread coordinate systems, the astrocentric coordinates used by us allow a more convenient representation of the disturbing function to be obtained and do not require its expansion into a series in powers of a small parameter. On time scales ∼105-107 years we have studied the long-term evolution of the planetary systems HD 12661, υ Andromedae, and some model systems by numerical integration of the averaged equations. Possible secular resonances have been revealed in the systems considered.

AB - Abstract: We consider the dynamical evolution of planetary systems whose structure is nearly circular and coplanar. The analysis is performed by the Hori–Deprit averaging method within the theory of the first order in planetary masses. A convenient set of canonical elements and a rarely employed variety of astrocentric coordinates are used to derive the equations of motion. Owing to the use of the chosen system of canonical elements, the expansions of the right-hand sides of the averaged equations contain a relatively small number of terms. Compared to other widespread coordinate systems, the astrocentric coordinates used by us allow a more convenient representation of the disturbing function to be obtained and do not require its expansion into a series in powers of a small parameter. On time scales ∼105-107 years we have studied the long-term evolution of the planetary systems HD 12661, υ Andromedae, and some model systems by numerical integration of the averaged equations. Possible secular resonances have been revealed in the systems considered.

KW - astrocentric coordinates

KW - averaging method

KW - disturbing function

KW - Hamiltonian

KW - heliocentric coordinates

KW - Hori–Deprit method

KW - Laplace coefficients

KW - N-body planetary problem

KW - Poincaré canonical elements

KW - Poisson series

KW - secular resonances

KW - Poincare canonical elements

KW - Hori-Deprit method

KW - ELEMENTS

KW - EVOLUTION

KW - EXPANSION

KW - POISSON SERIES

UR - http://www.scopus.com/inward/record.url?scp=85091294719&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42964158

U2 - 10.1134/S1063773720050059

DO - 10.1134/S1063773720050059

M3 - Article

AN - SCOPUS:85091294719

VL - 46

SP - 344

EP - 358

JO - Astronomy Letters

JF - Astronomy Letters

SN - 1063-7737

IS - 5

ER -

ID: 70304888