Research output: Contribution to journal › Article › peer-review
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.Research output: Contribution to journal › Article › peer-review
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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