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F. T\'eger (ELTE)
Several papers have been written recently investigating the stability of Saturn's Trojans. Most of these papers treated low inclination orbits, only Zhang and Innanen (1989c) considered orbits with high inclination. However, they used an idealised model and their integration time was smaller than 100000 year, though we know that the triangular Lagrangian points of Saturn become unstable after 100000 year. Thus the question is, how the orbits will evolve at high inclination if we integrate these orbits for more than 100000 year.
I studied the evolution of about 2000 test particles distributed near the Lagrangian points of the Saturn for intervals up to 300000 year in the model of the Sun-Jupiter-Saturn-Asteroid system using a 4th order symplectic mapping method described by Wisdom and Holman (1991). The initial semimajor axis (a) of the test particle was varied from 9.08 to 9.96[AU] with a step of 0.04. I also varied the mutual inclination (iM) between Saturn and the test particle from 0o to 88o with a step of 2o. I have found that there is stable behaviour of the test particle only when iM\le 26o in the case of L4 and when iM\le30o in the case of L5, while if iM is larger than these values the orbits are unstable. In the case of some unstable orbits, particularly at high inclination, I found a very interesting behaviour of the semimajor axis. While at the beginning the semimajor axis varied in an irregular way, after a few hundred years became stable around the initial value. In order to that the semimajor axis remain in the neighbourhood of its initial value, the eccentricity has to increase to a high value, in general above 0.3. I have integrated these orbits for a time longer than 300000 year, and I found that after a few tens of thousand years they became chaotic. Therefore we can say about these orbits that they are temporarily coorbital. The eccentricity plays an important role in the behaviour of the orbits, in most of the cases the sudden increase of the eccentricity leads to instability, but in a few cases this increasing is accompained by a temporary stability.
The grant OTKA F030147 of the NRF is acknowledged.
The author(s) of this abstract have provided an email address for comments about the abstract: tfeca@innin.elte.hu