Poincaré surfaces of section around a 3D irregular body: The case of asteroid 4179 Toutatis

Abstract

In general, small bodies of the Solar system, e.g. asteroids and comets, have a very irregular shape. This feature affects significantly the gravitational potential around these irregular bodies, which hinders dynamical studies. The Poincaré surface of section technique is often used to look for stable and chaotic regions in two-dimensional dynamic cases. In this work, we show that this tool can be useful for exploring the surroundings of irregular bodies such as the asteroid 4179 Toutatis. Considering a rotating system with a particle, under the effect of the gravitational field computed three dimensionally, we define a plane in the phase space to build the Poincaré surface of section. Despite the extra dimension, the sections created allow us to find trajectories and classify their stabilities. Thus, we have also been able to map stable and chaotic regions, as well as to find correlations between those regions and the contribution of the third dimension of the system to the trajectory dynamics as well. As examples, we show details of periodic (resonant or not) and quasi-periodic trajectories.