Secular Interactions of Coorbiting Objects
Résumé
We study the dynamics of the three-body problem when two objects are in the 1:1 mean motion commensurability and can experience close encounters. Three orbit families are relevant to the dynamics: horseshoe orbits, passing orbits, and retrograde satellite orbits. The latter two families are present only when the relative eccentricity of the two objects is large in comparison to the width of their coorbital region. In the planar case, the three families are disjoint because the guiding center of the motion is stationary with respect to secular perturbations; as a result, collisional orbits are unstable. Orbit transitions between different families occur in three dimensions owing to the secular variations of the eccentricity and argument of pericenter omega_r. Potentially colliding horseshoe orbits transit via eccentric retrograde satellite orbits in a secular mechanism where omega_r librates around +/-90 deg. Coorbital passing orbits are located at the Kozai resonances with 2omega_r librating around either 0 deg or 180 deg. The former resonance is a dominant feature of the dynamics once passing orbits exist. The latter is found only at large values of the Jacobi constant. Large amplitude librations around the Kozai resonances involve the transition from a passing orbit to an association of horseshoe and retrograde satellite orbits and the secular periodic reversal of the relative semimajor axis of the passing orbit. The stability of these structures supports the existence of coorbiting material with the planets, especially Mercury, and favors a coorbital origin of the retrograde natural satellites.