Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111549
Title: Behaviour of a Two-planetary System on a Cosmogonic Time-scale
Authors: Kholshevnikov, K. V.
Kuznetsov, E. D.
Issue Date: 2004
Publisher: Cambridge University Press
Cambridge University Press (CUP)
Citation: Kholshevnikov K. V. Behaviour of a Two-planetary System on a Cosmogonic Time-scale / K. V. Kholshevnikov, E. D. Kuznetsov // Proceedings of the International Astronomical Union. — 2004. — Vol. 2004. — Iss. IAUC197. — P. 107-112.
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). © 2005 International Astronomical Union.
Keywords: ANALYTICAL
CELESTIAL MECHANICS
JUPITER
METHODS
NUMERICAL
PLANETS AND SATELLITES
SATURN
URI: http://hdl.handle.net/10995/111549
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 84864460246
ISSN: 1743-9213
metadata.dc.description.sponsorship: This work was partly supported by the RFBR, Grant 02-02-17516, and the Leading Scientific School, Grant NSh-1078.2003.02.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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