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H. Scholl (Observatoire de la Cote d'Azur), F. Marzari (Univ. of Padova)
Do Saturn, Uranus, and Neptune have Trojans? Only a few observational surveys have been devoted to this problem and negative results have been obtained until now. The Trojans of these planets would be intrinsically faint and deep surveys are required to detect them. It is not clear if Trojans formed out there and also the sizes of the stable regions of these Trojans over timescales comparable to the age of the Solar System are not well known. The discovery of Trojans could provide clues concerning the formation of bodies in the outer solar system. In this paper, we concentrate on the problem to determine the sizes of the stable Trojan regions which can serve as a basis for discovery programs. In the case of Saturn Trojans, the 5:2 mean motion resonance with Jupiter and a mixed secular resonance are major sources of instability. Recently, Melita and Brunini (2001) showed that there are small regions which are stable over timescales of the order of the age of the solar system. Which mechanism protects bodies from crossing the resonances and becoming unstable? We found in numerical models that a particular locking of the perihelion longitude of a Trojan seems to be prevent the resonance crossing and favour long term stability. Examples will be shown.
In the case of Uranus and Neptune Trojans, stable regions over 20 Myrs were found by Holman and Wisdom(1990). We extended the integrations over up to 500 Myrs. Taking into account the evaporation rate of Uranus Trojans, the expected stable Trojan region appears to be very small. On the other hand, the comparatively large sizes of the stable Neptune Trojan regions are encouraging for discovery programs. Our results concerning the Neptune and Trojan regions appear to be in good agreement with results obtained independently by Nesvorny (2001, private communication) who integrated over 4 Byrs.
Our results serve as a basis to search for Trojans on images provided by ESO's ASTROVIRTEL Project.