ASTROPHYSICS Effective stability of the Trojan asteroids

Realistic Estimations of the Effective Stability Region of the Trojan Asteroids

The usual approach in analytical studies of the stability of the Trojan asteroids is to consider simple models for the system such as the two dimensional (2D) planar, and the three dimensional (3D) spatial restricted three body problem (RTBP) (Giorgilli et al., 1989; Simó, 1989; Celletti and Giorgilli, 1991; Celletti and Ferrara, 1996). As an example of a more complicated model for the problem ...

On the stability of the Trojan asteroids

We reconsider the problem of stability of the triangular Lagrangian equilibria of the restricted problem of three bodies.We consider in particular the Sun–Jupiter model and the Trojan asteroids in the neighbourhood of the point L4. In the spirit of Nekhoroshev’s theory on stability over exponentially large times, we are able to prove that stability over the age of the universe is guaranteed on ...

On the construction of the Kolmogorov normal form for the Trojan asteroids

In this paper we focus on the stability of the Trojan asteroids for the planar Restricted Three-Body Problem (RTBP), by extending the usual techniques for the neighbourhood of an elliptic point to derive results in a larger vicinity. Our approach is based on the numerical determination of the frequencies of the asteroid and the effective computation of the Kolmogorov normal form for the corresp...

Stability of the Trojan asteroids

Effective stability of the Trojan asteroids

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 i...