Behaviour of a two-planetary system on a cosmogonic time-scale / Kholshevnikov K.V., Kuznetsov E.D. // Proceedings of the International Astronomical Union. - 2004. - V. 2004, l. IAUC197. - P. 107-112.

ISSN:

17439213

Type:

Conference Paper

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.

Author keywords:

Analytical; Celestial mechanics; Jupiter; Methods; Numerical; Planets and satellites; Saturn

Index keywords:

нет данных

DOI:

10.1017/S1743921304008567

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84864460246&doi=10.1017%2fS1743921304008567&partnerID=40&md5=0429606aaef14cabcbe0b6235d5b9bee

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Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84864460246&doi=10.1017%2fS1743921304008567&partnerID=40&md5=0429606aaef14cabcbe0b6235d5b9bee
Affiliations	Sobolev Astronomical Institute, St.Petersburg State University, Universitetsky pr.,28, St.Petersburg, Stary Peterhof, 198504, Russian Federation; Astronomical Observatory, Urals State University, Lenin pr., 51, Ekaterinburg, 620083, Russian Federation
Author Keywords	Analytical; Celestial mechanics; Jupiter; Methods; Numerical; Planets and satellites; Saturn
References	Brumberg, V.A., (1995) Analytical Techniques of Celestial Mechanics, , Springer, Heidelberg; Charlier, C.L., (1927) Die Mechanik des Himmels, , Walter de Gruyter & Co., Berlin und Leipzig; Greb, A.V., (2002), PhD thesis, St. Petersburg State University, St. Petersburg; Ivanova, T.V., (1996) Dynamics, Ephemerides and Astrometry of the Solar System, p. 283. , S.Ferraz-Mello, B.Morando and J.-E.Arlot (eds.) , IAU Symp. 172, (Kluwer Academic Publishers; Ivanova, T., (2001) Cel. Mech. Dyn. Astron., 80, p. 167; Kholshevnikov, K.V., (1991) Astron. Zh., 68, p. 660; Kholshevnikov, K.V., (1997) Astron. Rep., 41, p. 135; Kholshevnikov, K.V., (2001) Astron. Rep., 45, p. 577; Kholshevnikov, K.V., Greb, A.V., Kuznetsov, E.D., (2001) Solar System Res., 35, p. 243; Kholshevnikov, K.V., Greb, A.V., (2001) Solar System Res., 35, p. 415; Kholshevnikov, K.V., Greb, A.V., Kuznetsov, E.D., (2002) Solar System Res., 36, p. 68; Kuznetsov, E.D., Kholshevnikov, K.V., (2004) Solar System Res., 38, p. 147; Laskar, J., Robutel, P., (1995) Cel. Mech. Dyn. Astron., 62, p. 193; Michtchenko, T.A., Ferraz-Mello, S., (2001) Icarus, 149, p. 357; Robutel, P., (1993) Cel. Mech. Dyn. Astron., 56, p. 197; Robutel, P., (1993) Cel. Mech. Dyn. Astron., 57, p. 97; Robutel, P., (1995) Cel. Mech. Dyn. Astron., 62, p. 219; Rom, A., (1971) Celest. Mech., 3, p. 331; Smart, W.M., (1953) Celestial Mechanics, , . (Longmans Green and Co., London, New York, Toronto; Subbotin, M.F., (1968) Introduction to Theoretical Astronomy, , Nauka, Moscow
Correspondence Address	Kholshevnikov, K.V.; Sobolev Astronomical Institute, St.Petersburg State University, Universitetsky pr.,28, St.Petersburg, Stary Peterhof, 198504, Russian Federation; email: kvk@astro.spbu.ru
Publisher	Cambridge University Press
Language of Original Document	English
Abbreviated Source Title	Proc. Int. Astron. Union
Source	Scopus