Behavior of apsidal orientations in planetary systems

A widely considered characteristic of extrasolar planetary systems has been a seeming tendency for major axes of adjacent orbits to librate in stable configurations. Based on a new catalog of extrasolar planets (Butler et al.) and our numerical integrations, we find that such small-amplitude oscillations are actually not common but in fact quite rare; most pairs of planets' major axes are consistent with circulating relative to one another. However, the new results are consistent with studies that find that two-planet systems tend to lie near a separatrix between libration and circulation. Similarly, in systems of more than two planets, many adjacent orbits lie near a separatrix that divides modes of circulation.