Effective stability of the Trojan asteroids

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 $L_4$. We find a region of effective stability around the point $L_4$ 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.

9 pages, 2 figures, Astronomy & Astrophysics in press

Cited by in corpus (3)

• The resonant structure of Jupiter's trojan asteroids-II. What happens for different configurations of the planetary system
• On the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system
• Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories