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Behaviour of a two-planetary system on a cosmogonic time-scale. / Kholshevnikov, Konstantin V.; Kuznetsov, Eduard d.
In: Proceedings of the International Astronomical Union, Vol. 2004, No. IAUC197, 01.08.2004, p. 107-112.

Research output: Contribution to journal › Conference article › peer-review

Harvard

Kholshevnikov, KV & Kuznetsov, ED 2004, 'Behaviour of a two-planetary system on a cosmogonic time-scale', Proceedings of the International Astronomical Union, vol. 2004, no. IAUC197, pp. 107-112. https://doi.org/10.1017/S1743921304008567

APA

Kholshevnikov, K. V., & Kuznetsov, E. D. (2004). Behaviour of a two-planetary system on a cosmogonic time-scale. Proceedings of the International Astronomical Union, 2004(IAUC197), 107-112. https://doi.org/10.1017/S1743921304008567

Vancouver

Kholshevnikov KV, Kuznetsov ED. Behaviour of a two-planetary system on a cosmogonic time-scale. Proceedings of the International Astronomical Union. 2004 Aug 1;2004(IAUC197):107-112. doi: 10.1017/S1743921304008567

Author

Kholshevnikov, Konstantin V. ; Kuznetsov, Eduard d. / Behaviour of a two-planetary system on a cosmogonic time-scale. In: Proceedings of the International Astronomical Union. 2004 ; Vol. 2004, No. IAUC197. pp. 107-112.

BibTeX

@article{dc3c626b62804c79ad97c5354c5138fa,
title = "Behaviour of a two-planetary system on a cosmogonic time-scale",
abstract = "The orbital evolution of planetary systems similar to our Solar one represents one of the most important problems of Celestial Mechanics. In the present work we use Jacobian coordinates, introduce two systems of osculating elements, construct the Hamiltonian expansions in Poisson series for all the elements for the planetary three-body problem (including the problem Sun–Jupiter–Saturn). Further we construct the averaged Hamiltonian by the Hori–Deprit method with accuracy up to second order with respect to the small parameter, the generating function, the change of variables formulae, and the right-hand sides of the averaged equations. The averaged equations for the Sun–Jupiter–Saturn system are integrated numerically over a time span of 10 Gyr. The Liapunov Time turns out to be 14 Myr (Jupiter) and 10 Myr (Saturn).",
author = "Kholshevnikov, {Konstantin V.} and Kuznetsov, {Eduard d.}",
year = "2004",
month = aug,
day = "1",
doi = "10.1017/S1743921304008567",
language = "English",
volume = "2004",
pages = "107--112",
journal = "Proceedings of the International Astronomical Union",
issn = "1743-9213",
publisher = "Cambridge University Press",
number = "IAUC197",

}

RIS

TY - JOUR

T1 - Behaviour of a two-planetary system on a cosmogonic time-scale

AU - Kholshevnikov, Konstantin V.

AU - Kuznetsov, Eduard d.

PY - 2004/8/1

Y1 - 2004/8/1

N2 - The orbital evolution of planetary systems similar to our Solar one represents one of the most important problems of Celestial Mechanics. In the present work we use Jacobian coordinates, introduce two systems of osculating elements, construct the Hamiltonian expansions in Poisson series for all the elements for the planetary three-body problem (including the problem Sun–Jupiter–Saturn). Further we construct the averaged Hamiltonian by the Hori–Deprit method with accuracy up to second order with respect to the small parameter, the generating function, the change of variables formulae, and the right-hand sides of the averaged equations. The averaged equations for the Sun–Jupiter–Saturn system are integrated numerically over a time span of 10 Gyr. The Liapunov Time turns out to be 14 Myr (Jupiter) and 10 Myr (Saturn).

AB - The orbital evolution of planetary systems similar to our Solar one represents one of the most important problems of Celestial Mechanics. In the present work we use Jacobian coordinates, introduce two systems of osculating elements, construct the Hamiltonian expansions in Poisson series for all the elements for the planetary three-body problem (including the problem Sun–Jupiter–Saturn). Further we construct the averaged Hamiltonian by the Hori–Deprit method with accuracy up to second order with respect to the small parameter, the generating function, the change of variables formulae, and the right-hand sides of the averaged equations. The averaged equations for the Sun–Jupiter–Saturn system are integrated numerically over a time span of 10 Gyr. The Liapunov Time turns out to be 14 Myr (Jupiter) and 10 Myr (Saturn).

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=84864460246

U2 - 10.1017/S1743921304008567

DO - 10.1017/S1743921304008567

M3 - Conference article

VL - 2004

SP - 107

EP - 112

JO - Proceedings of the International Astronomical Union

JF - Proceedings of the International Astronomical Union

SN - 1743-9213

IS - IAUC197

ER -

ID: 44462094