The Dynamics of the Trojan Asteroids

The state of the art in the dynamics of the Trojan asteroids has progressed rapidly, since it has been possible to perform numerical integrations of many orbits for millions of years. Accurate proper elements are now computed by the synthetic method, that is from the output of a numerical integration; their stability, at least for time spans of a few million years, is good. This has allowed identification of Trojan families with an automated procedure closely mimicking the one used in the main belt. Although the families identified in a reliable way are only four, the occurrence of significant collisional evolution, not unlike that of the main belt, can be confirmed. The dynamical structure of the Trojan cloud, including the location of the main secular resonances, can be deduced from the proper elements and frequencies by a simple fit. However, many problems are not solved: the origin of a significant percentage of chaotic orbits showing no indications of instability; the location of the stability boundary of the Trojan cloud; the origin of the high inclination of most Trojans. We also do not know if there are “Trojans” for some other planets beside Jupiter: only one Mars Trojan has been found.