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

Research output

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) 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.

Original languageRussian
Pages (from-to)337-350
Number of pages14
JournalAstronomy Letters
Volume44
Issue number5
DOIs
Publication statusPublished - May 2018

Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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

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