Extrasolar Planetary Dynamics with a Generalized Planar Laplace-Lagrange Secular Theory

Details Extrasolar Planetary Dynamics with a Generalized Planar Laplace-Lagrange Secular Theory Extrasolar Planetary Dynamics with a Generalized Planar Laplace-Lagrange Secular Theory

Oct 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dps....39.6006v&link_type=abstract

American Astronomical Society, DPS meeting #39, #60.06; Bulletin of the American Astronomical Society, Vol. 39, p.537

Astronomy and Astrophysics

Astronomy

Scientific paper

The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the traditional Laplace-Lagrange (LL) secular theory in analyses of the motion. We analytically generalize this theory to fourth-order in the eccentricities, compare the result with the second-order theory and octupole-level theory, and apply these theories to the likely secularly-dominated HD 12661, HD 168443, HD 38529 and upsilon Andromedae multi-planet systems. The fourth-order scheme yields a multiply-branched criterion for maintaining apsidal libration. Numerical results indicate that the primary difference the second and fourth-order theories reveal is an alteration in secular periodicities, and to a smaller extent amplitudes of the planetary eccentricity variation. Comparison with numerical integrations indicates that the improvement afforded by the fourth-order theory over the second-order theory sometimes dwarfs the improvement needed to reproduce the actual dynamical evolution.

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