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Secular evolution of exoplanetary systems and close encounters

Published online by Cambridge University Press:  01 October 2007

M. Šidlichovský  and
E. Gerlach
M. Šidlichovský
Affiliation:
Astronomical Institute, Academy of Sciences of the Czech Republic, Boĉní II 1401, 141 31 Prague email: sidli@ig.cas.cz
E. Gerlach
Affiliation:
Technical University, Institute for Planetary Geodesy, Lohrmann Observatory, Dresden, Germany email: enrico.gerlach@tu-dresden.de
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Abstract

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We investigate the secular evolution of non-resonant exoplanetary systems consisting of a central star and two co-planar planets using a semi-numerical averaging method of the first order in planetary masses (in this case equivalent to “averaging by scissors” or simply dropping the fast periodic terms). The resulting Hamiltonian level curves for different exoplanetary systems were compared to those obtained by direct numerical integration. Studying the dependence of the reliability of the averaging method (as well as chaoticity of numerically integrated trajectories) upon the initial conditions, we found that the averaging methods fails even for Hill stable systems. Based on the Hill stability criterion we introduced empirically a more restrictive stability condition, that enabled us to give an estimate for the region of validity of the averaging method in the plane of initial conditions.

Keywords

Celestial mechanicsexoplanetsstability
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 3 , Symposium S249: Exoplanets: Detection, Formation and Dynamics , October 2007 , pp. 479 - 484
Copyright
Copyright © International Astronomical Union 2008

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