Thersites: a `jumping' Trojan?

In this paper, we examine the dynamical evolution of the asteroid (1868) Thersites, a member of the Trojan belt. Thersites is librating around the Lagrangian point L_4, following, however, a chaotic orbit. The equations of motion for Thersites as well as for a distribution of neighboring initial conditions are integrated numerically for 50 million years in the Outer Solar System model (OSS), which consists of the Sun and the four giant planets. Our results indicate that the probability that this asteroid will eventually escape from the Trojan swarm is rather high. In fact, 20% from our initial distribution escaped within the integration time. Many of the remaining ones also show characteristic `jumps' in the orbital elements, especially the inclination. Secular resonances involving the nodes of the outer planets are found to be responsible for this chaotic behavior. The width of libration and eccentricity values that lead to grossly unstable orbits are calculated and compared with previously known results on the stability of the Trojans. Finally, a very interesting behavior has been observed for one of the escaping asteroids as he `jumped' from L_4 to L_5 where he remained performing a highly inclined libration for ~ 2 Myrs before escaping from the Trojan swarm.

According to Homer, Thersites was not only the ugliest of all Greeks that took part in the Trojan war, but also had the most intolerable personality. His nasty habit of making fun of everybody cost him his life, as the last person for whom he spoke ironically about was Achilles, the mightiest warrior of all Greeks, who killed Thersites with just one punch!