Averaging the Equations of a Planetary Problem in an Astrocentric Reference Frame

Standard

Averaging the Equations of a Planetary Problem in an Astrocentric Reference Frame. / Mikryukov, D. V. .

In: Astronomy Letters, Vol. 44, No. 5, 05.2018, p. 337-350.

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

BibTeX

@article{ead5b1249b134ffaae57724657a2e112,

title = "Averaging the Equations of a Planetary Problem in an Astrocentric Reference Frame",

abstract = "A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincar{\'e}canonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems.",

keywords = "astrocentric coordinates, averaging, disturbing function, Hamiltonian, heliocentric coordinates, Hori–Deprit method, Laplace coefficients, N-body problem, Poincar{\'e} canonical elements, Poisson series, SYSTEM, Poincare canonical elements, Hori-Deprit method, ELEMENTS, EXPANSION, POISSON SERIES",

author = "Mikryukov, {D. V.}",

note = "Mikryukov, D.V. Averaging the Equations of a Planetary Problem in an Astrocentric Reference Frame. Astron. Lett. 44, 337–350 (2018). https://doi.org/10.1134/S106377371805002X",

year = "2018",

month = may,

doi = "10.1134/S106377371805002X",

language = "English",

volume = "44",

pages = "337--350",

journal = "Astronomy Letters",

issn = "1063-7737",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "5",

}

RIS

TY - JOUR

T1 - Averaging the Equations of a Planetary Problem in an Astrocentric Reference Frame

AU - Mikryukov, D. V.

N1 - Mikryukov, D.V. Averaging the Equations of a Planetary Problem in an Astrocentric Reference Frame. Astron. Lett. 44, 337–350 (2018). https://doi.org/10.1134/S106377371805002X

PY - 2018/5

Y1 - 2018/5

N2 - A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincarécanonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems.

AB - A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincarécanonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems.

KW - astrocentric coordinates

KW - averaging

KW - disturbing function

KW - Hamiltonian

KW - heliocentric coordinates

KW - Hori–Deprit method

KW - Laplace coefficients

KW - N-body problem

KW - Poincaré canonical elements

KW - Poisson series

KW - SYSTEM

KW - Poincare canonical elements

KW - Hori-Deprit method

KW - ELEMENTS

KW - EXPANSION

KW - POISSON SERIES

UR - https://link.springer.com/article/10.1134/S106377371805002X

UR - https://www.elibrary.ru/item.asp?id=35514365

UR - https://elibrary.ru/item.asp?id=34885993

U2 - 10.1134/S106377371805002X

DO - 10.1134/S106377371805002X

M3 - Article

AN - SCOPUS:85047500562

VL - 44

SP - 337

EP - 350

JO - Astronomy Letters

JF - Astronomy Letters

SN - 1063-7737

IS - 5

ER -

ID: 32711844