Rudolf Dvorak1 and Kleomenis Tsiganis1,2 1 Intitute of Astronomy - University of Vienna, Austria 2 Section of Astrophysics, Astronomy & Mechanics - University of Thessaloniki, Greece
We integrate numerically the orbits of 12 Trojan asteroids (6 at L4 and 6
at L5), which are known to belong to the class of ASCs(=asteroids
in stable chaos) and have Lyapunov times of the order of 104
years. For each object a
group of 5 nearby orbits are integrated for 50 Myrs in the model of the outer
solar system (OSS=Jupiter-Neptune). The integrations are performed twice,
using different integration methods. About 50 % of the orbits present large
instabilities in the inclination within the integration time-span; two escapes
are also recorded. Secular resonances involving the nodes of the outer planets
are found to be responsible for these variations. In contrast to these
unstable orbits, no low order resonance is found to be responsible for the
observed chaotic behavior. In some cases, orbital
stability depends critically on the choice of the initial conditions and,
thus, these objects can be regarded as being on the edge of strong chaos.
As most of these orbits are concentrated in a specific region of the
Trojan belt, where the population is sparce, it may be the case that
secular resonances have sculpted some sort of `gap' in this
dynamical neighborhood.