Volume 378, Number 2, November I 2001
|Page(s)||569 - 586|
|Published online||15 November 2001|
Global dynamics of planetary systems with the MEGNO criterion
Observatoire de Bordeaux, UMR/CNRS/INSU 5804, BP 89, 33270 Floirac, France
2 Toruń Centre for Astronomy, N. Copernicus University, Gagarina 11, 87-100 Toruń, Poland
3 Institute of Astronomy, Zielona Góra University, Lubuska 2, 65-265 Zielona Góra, Poland
4 IGPP, LLNL, L-413, 7000 East Ave, Livermore, CA 94550, USA
5 UC Davis, Dept. of Physics, Davis, CA 95616, USA
Corresponding author: K. Goździewski, firstname.lastname@example.org
Accepted: 22 August 2001
In this paper we apply a new technique alternative to the numerically computed Lyapunov Characteristic Number (LCN) for studying the dynamical behaviour of planetary systems in the framework of the gravitational N-body problem. The method invented by P. Cincotta and C. Simó is called the Mean Exponential Growth of Nearby Orbits (MEGNO). It provides an efficient way for investigation of the fine structure of the phase space and its regular and chaotic components in any conservative Hamiltonian system. In this work we use it to study the dynamical behaviour of the multidimensional planetary systems. We investigate the recently discovered υ And planetary system, which consists of a star of and three Jupiter-size planets. The two outermost planets have eccentric orbits. This system appears to be one of the best candidates for dynamical studies. The mutual gravitational interaction between the two outermost planets is strong. Moreover the system can survive on a stellar evolutionary time scale as it is claimed by some authors (e.g., Rivera & Lissauer 2000b). As the main methodological result of this work, we confirm important properties of the MEGNO criterion such as its fast convergence, and short motion times (of the order of 104 times the longest orbital period) required to distinguish between regular and chaotic behaviors. Using the MEGNO technique we found that the presence of the innermost planet may cause the whole system to become chaotic with the Lyapunov time scale of the order of 103-104 yr only. Chaos does not induce in this case visible irregular changes of the orbital elements, and therefore its presence can be overlooked by studying variations of the elements. We confirm explicitly the strong and sensitive dependence of the dynamical behaviour on the companion masses.
Key words: celestial mechanics / stellar dynamics / methods: numerical / methods: N-body simulations / planetary systems / stars: individual: υ And
© ESO, 2001
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