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S. Ferraz-Mello (IAG,Universidade de Sao Paulo, Brasil)
The action of a semi-diurnal planetary tidal bulge, on the evolution of a 2-planet system, was studied in several circumstances. The main consequence is the synchronisation of one close planet in a timescale which, for typical values of the tidal time lag, is of the order of 107 years. During this time, the planetary rotation is the only parameter significantly affected. In the case of an isolated planet, the orbit circularizes and the tidal action tends to zero. In 2-planet resonant systems (as Gliese 876), however, the eccentricities are not damped by the tides, and the tidal bulge oscillates around the noon direction. This oscillation and an imperfect synchronisation allow the continuation of the energy dissipation. Since the system can no longer pump energy from the planet rotation, because of the synchronisation, the planet orbit decays. The actual decay is, however, very slow.
The general study of an adiabatically perturbed 2:1-resonant system has shown periastrons alignement (\Delta\pi ~ 0o) and counter-alignement (\Delta\pi ~180o). (As in the case of the 5:2 planetary resonance cf. Michtchenko and Ferraz-Mello, Icarus 149, 357, 2001.) Periastrons alignement happens roughly when e1 > 0.1 and counter-alignement when e1 < 0.1. However, these cases are not the only possible stationary solutions in the 2:1 resonance. When the innermost planet is more massive than the outermost one, for a wide range of eccentricities, stationary solutions are found where the distance between the periastrons is fixed, but at values of \Delta\pi which are not 0o or 180o. In these asymmetric libration states, \Delta\pi takes a value between 0o and 180o, which depends on the ratio of the planet masses and on the eccentricities. These new solutions result from a bifurcation of the stable stationary orbit and occur in pairs, one on each side of 0o (or 180o).
Acknowledgements: FAPESP and CNPq.
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Bulletin of the American Astronomical Society, 34, #3< br> © 2002. The American Astronomical Soceity.