36th DPS Meeting, 8-12 November 2004
Session 35 Extrasolar Planets
Poster II, Thursday, November 11, 2004, 4:15-7:00pm, Exhibition Hall 1A

## [35.10] Long-term Orbital Evolution of Planetary Systems

K. Zhang, D. P. Hamilton (University of Maryland)

Some extrasolar hot Jupiters'' (Jupiter-size planets very close to their sun) have been observed to have non-zero eccentricities. Small eccentricities are expected in multi-planet systems due to forcing from other planets. We are currently undertaking an investigation of the secular (long-term) perturbations in a system of two planets, where the solar tides are strong enough to circularize the inner planet's orbit in a timescale less than the age of the system. We have found, both numerically and analytically, that in such a system the orbits of the two planets evolve very quickly into either an apsidal aligned (\tilde{\omega}1\approx \tilde{\omega}2) or an anti-aligned (\tilde{\omega}1- \tilde{\omega}2\approx±80o) state. The evolution rate is approximately the same as the tidal damping rate of the inner planet. This agrees with the findings of Wu and Goldreich (2002). After the apsidal alignment, the two orbits are circularized simultaneously on a much longer timescale, which is a function of the masses and semimajor axes of the two planets. Our analytic derivation assumes that the semimajor axis of the inner planet does not change, which is valid for the small eccentricities considered here. We are currently seeking to describe how the system responds to an imposed change of the semimajor axis of either object utilizing adiabatic invariants. If one planet is much more massive than the other so that it is not disturbed, we have shown that the free eccentricity of the planet remains constant, as long as the semimajor axes change very slowly. We hope to generalize this to all mass ratios so that our results may be applied to systems in which orbits are disturbed by arbitrary external forces. Important applications include tidal damping and perturbations from an external disk.

The author(s) of this abstract have provided an email address for comments about the abstract: kzh@astro.umd.edu

Bulletin of the American Astronomical Society, 36 #4
© 2004. The American Astronomical Soceity.