Mechanisms of capture in external resonances

Anne Lemaitre
FUNDP, Namur, Belgium


The quasi discovery of planets orbiting around other stars than our Sun, in a nebular cloud, has given a new motivation to the development of models combining resonances and drag forces. In this context we develop a very simplified model, similar to the second fundamental model of resonance, but including the asymmetric equilibria present in some of the external mean motion resonances. The calculation of critical ares and probabilities of capture can explain how and why the orbits are captured in resonances, and by which paths they escape. On the other hand, on a more quantitative point of view, we use the three-dimensional Schubart-like integrator developped by M. Moons for all the mean motion resonances, completed by the addition of the averaged contributions of the drag forces; following the same idea as the initial integrator, we calculate closed forms, without any expansion in series of the eccentricity or the inclination, for the drag terms. This integrator is a fast tool for simulations and tests. We compare our results (especially in two dimensions) with other papers on the same topic, as Beaugé and Ferraz-Mello, Gomes, Liu and Jackson, etc.

Download this abstract as [tex] or [html]