Contributed Oral Parallel Session, Tuesday, October 12, 1999, 8:30-10:00am, Sala Plenaria

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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 (i_{M}) between
Saturn and the test particle from 0^{o} to 88^{o} with a
step of 2^{o}. I have found that there is stable behaviour
of the test particle only when i_{M}\le 26^{o} in the case of
L_{4} and when i_{M}\le30^{o} in the case of L_{5}, while if
i_{M} 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