An exploration of the Kozai resonance in the Kuiper Belt.

The Kozai resonance of Kuiper Belt objects is explored using a model of a circular-restricted three-body problem. We use an analytical approach to find the topological structure of the plane of the eccentricity and the argument of perihelion. We find that objects inside the 2:3 and 1:2 resonances can be inside the Kozai resonance, with their arguments of perihelion ω librating around 90° or 270°. This is consistent with the fact that Pluto is inside both the 2:3 resonance and the Kozai resonance. Furthermore, objects outside the mean-motion resonances are also found to be inside the Kozai resonance. We discover that there are stable equilibrium points of ω at 90° and 270°, but not at 0° and 180° as was shown in the work of Thomas & Morbidelli. To verify our results, numerical experiments are carried out with various longitudes of the node and mean anomalies. In these experiments, some test particles are found to be in the Kozai resonance around 90° for one billion years, and the libration amplitudes of their arguments of perihelion are small. This is in agreement with our analytical results. No particles are found to stay inside the Kozai resonance around ω= 0° or 180°, although some particles exist temporarily in the Kozai resonance around ω= 0° or 180°. We conclude that the Kozai resonance around ω= 90° or 270° exists both inside and outside the mean-motion resonance for Kuiper Belt objects. [ABSTRACT FROM AUTHOR]