Planetary commensurabilities driven by accretion and dynamical friction

Numerical integrations of a three-body problem, consisting of the Sun and two planets under the influence of both accretion and dynamical friction forces, evolve into planetary resonance when the inner body is more massive. After a transient, the ratio of the periods oscillates closely about a commensurable value; the semimajor axes of both bodies decay, and the eccentricities, which are initially damped, remain constant after the resonance is established. The inclinations are rapidly damped to the mean plane. Although not all the parameters used in this model represent a strictly realistic situation, this work shows that this mechanism could explain the near-commensurable relations found between the periods of the major planets.