Dynamical spreading of small bodies in 1:1 resonance with planets by the diurnal Yarkovsky effect

Abstract

A simple model is introduced to describe the inherent dynamics of Trojans in the presence of the diurnal Yarkovsky effect. For different spin statuses, the orbital elements of the Trojans (mainly semimajor axis, eccentricity and inclination) undergo different variations. The variation rate is generally very small, but the total variation of the semimajor axis or the orbit eccentricity over the age of the Solar system may be large enough to send small Trojans out of the regular region (or, vice versa, to capture small bodies in the regular region). In order to demonstrate the analytical analysis, we first carry out numerical simulations in a simple model, and then generalize these to two ‘real’ systems, namely the Sun–Jupiter system and the Sun–Earth system. In the Sun–Jupiter system, where the motion of Trojans is regular, the Yarkovsky effect gradually alters the libration width or the orbit eccentricity, forcing the Trojan to move from regular regionsto chaotic regions, where chaos may eventually cause it to escape. In the Sun–Earth system, where the motion of Trojans is generally chaotic, our limited numerical simulations indicate that the Yarkovsky effect is negligible for Trojans of 100 m in size, and even for larger ones. The Yarkovsky effect on small bodies captured in other 1:1 resonance orbits is also briefly discussed.