Formal Integrals and Nekhoroshev Stability in a Mapping Model for the Trojan Asteroids

Author: Efthymiopoulos, Christos

Source: Celestial Mechanics and Dynamical Astronomy, Volume 92, Numbers 1-3, April 2005 , pp. 29-52(24)

Publisher: Springer

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A symplectic mapping model for the co-orbital motion (Sándor et al., 2002, Cel. Mech. Dyn. Astr. 84, 355) in the circular restricted three body problem is used to derive Nekhoroshev stability estimates for the Sun–Jupiter Trojans. Following a brief review of the analytical part of Nekhoroshev theory, a direct method is developed to construct formal integrals of motion in symplectic mappings without use of a normal form. Precise estimates are given for the region of effective stability based on the optimization of the size of the remainder of the formal series. The stability region found for t=1010 yrs corresponds to a libration amplitude Dp=10.6°. About 30% of asteroids with accurately known proper elements (Milani, 1993, Cel. Mech. Dyn. Astron. 57, 59), at low eccentricities and inclinations, are included within this region. This represents an improvement with respect to previous estimates given in the literature. The improvement is due partly to the choice of better variables, but also to the use of a mapping model, which is a simplification of the circular restricted three body problem.

Keywords: Nekhoroshev stability; Trojan asteroids

Document Type: Research Article


Affiliations: Research Center for Astronomy, Academy of Athens, Soranou Efessiou 4, 115 27, Athens, Greece, Email:

Publication date: April 1, 2005

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