Surface Motion Relative to the Irregular Celestial Bodies

TL;DR

This paper analyzes the motion and equilibria of surface grains on irregular celestial bodies, considering various surface conditions and forces, and identifies stable regions through simulations on asteroid 6489 Golevka.

Contribution

It introduces a detailed linearized model of grain motion on irregular bodies, including stick-slip effects, damping, and spring forces, and applies it to real asteroid data.

Findings

Stable surface equilibria are mainly on concave and flat regions.

Maximum hopping height can exceed the previous height after bounce.

Simulations show different motion types: orbital, impact, and surface motion.

Abstract

We study the motion and equilibria of the grains on the surface of the irregular celestial body (hereafter called irregular bodies). Motions for the grains on the smooth and unsmooth surfaces are discussed, respectively. The linearized equations of motion relative to a surface equilibrium point and its characteristic equations are presented. Considering the stick-slip effect, the damping forces and the spring forces for the grain are calculated, then the linearized equations of motion and the characteristic equations relative to the surface equilibrium points are derived. The number of non-degenerate surface equilibria is an even number. We compute the motion of a grain released above three different regions relative to the irregular asteroid 6489 Golevka, including the flat surface, the concave region, and the convex region. Following the grain release and initial bounce, three kinds of motions exist, the orbital motion, the impact motion and the surface motion. We find that the maximum height of the next hop may be bigger than the maximum height of the current hopping. We also used Monte Carlo simulations to calculate 100 grains hopping motions, the results shows that the stable surface equilibria are on the concave region and flat surface of the asteroid.