Effective stability of the Trojan asteroids

¹ Research Center for Astronomy, Academy of Athens, 14 Anagnostopoulou Str., 106 73 Athens, Greece
² School of Pharmacy, University of Athens, Panepistimiopolis, 157 71 Zografos, Athens, Greece

Corresponding author: Ch. Skokos, hskokos@cc.uoa.gr

Received: 19 October 2000
Accepted: 5 December 2000

Abstract

We study the spatial circular restricted problem of three bodies in the light of Nekhoroshev theory of stability over large time intervals. We consider in particular the Sun-Jupiter model and the Trojan asteroids in the neighborhood of the Lagrangian point L₄. We find a region of effective stability around the point L₄ such that if the initial point of an orbit is inside this region the orbit is confined in a slightly larger neighborhood of the equilibrium (in phase space) for a very long time interval. By combining analytical methods and numerical approximations we are able to prove that stability over the age of the universe is guaranteed on a realistic region, big enough to include one real asteroid. By comparing this result with the one obtained for the planar problem we see that the regions of stability in the two cases are of the same magnitude.