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

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

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.

Язык оригиналарусский
Страницы (с-по)337-350
Число страниц14
ЖурналAstronomy Letters
Том44
Номер выпуска5
DOI
СостояниеОпубликовано - мая 2018

Предметные области Scopus

  • Астрономия и астрофизика
  • Космические науки и планетоведение

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

В: Astronomy Letters, Том 44, № 5, 05.2018, стр. 337-350.

Результат исследований: Научные публикации в периодических изданияхстатья

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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

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KW - disturbing function

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