Scattered Disk Dynamics: A Mapping Approach

The trans-Neptunian solar system hosts the remnants of a large primordial population of small bodies scattered outward by the giant planets during the early evolution of the solar system. Understanding the orbital evolution of this population over the ensuing billions of years is essential for reconstructing the early history of the solar system. I will describe an approach to treating the dynamics of this population using an area-preserving map. The mapping approach provides accurate analytic predictions for the boundary between regular and chaotic orbits as well as the rate of chaotic semi-major axis diffusion as a function of perihelion distance. The map also provides an integrable model for mean motion resonances of arbitrary order in the high eccentricity regime applicable to much of the trans-Neptunian population. These new analytic results extend previous treatments to smaller perihelion and semi-major axis distances where most observed scattered disk and detached objects reside.