### 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 language | Russian |
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Pages (from-to) | 337-350 |

Number of pages | 14 |

Journal | Astronomy Letters |

Volume | 44 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2018 |

### Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

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*Astronomy Letters*, vol. 44, no. 5, pp. 337-350. https://doi.org/10.1134/S106377371805002X

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

Research output

TY - JOUR

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

AU - Mikryukov, D. V.

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

UR - http://www.scopus.com/inward/record.url?scp=85047500562&partnerID=8YFLogxK

U2 - 10.1134/S106377371805002X

DO - 10.1134/S106377371805002X

M3 - статья

AN - SCOPUS:85047500562

VL - 44

SP - 337

EP - 350

JO - Astronomy Letters

JF - Astronomy Letters

SN - 1063-7737

IS - 5

ER -