The Trojan asteroid belt: Proper elements, stability, chaos and families

  title={The Trojan asteroid belt: Proper elements, stability, chaos and families},
  author={Andrea Milani},
  journal={Celestial Mechanics and Dynamical Astronomy},
  • A. Milani
  • Published 1 October 1993
  • Geology, Physics
  • Celestial Mechanics and Dynamical Astronomy
I have computed proper elements for 174 asteroids in the 1 : 1 resonance with Jupiter, that is for all the reliable orbits available (numbered and multi-opposition). The procedure requires numerical integration, under the perturbations by the four major planets, for 1,000,000 years; the output is digitally filtered and compressed into a “synthetic theory” (as defined within theLONGSTOP project). The proper modes of oscillation of the variables related to eccentricity, perihelion, inclination… 
On the Stability Regions of the Trojan Asteroids
The orbits of fictitious bodies around Jupiter’s stable equilibrium points L4 and L5 were integrated for a fine grid of initial conditions up to 100 million years. We checked the validity of three
The Dynamics of the Trojan Asteroids
The state of the art in the dynamics of the Trojan asteroids has progressed rapidly, since it has been possible to perform numerical integrations of many orbits for millions of years. Accurate proper
A Semianalytical Model for the Motion of the Trojan Asteroids: Proper Elements and Families
In this paper we develop a semianalytical model to describe the long-term motion of Trojan asteroids located in tadpole orbits around the L4 and L5 jovian Lagrangian points. The dynamical model is
Formal Integrals and Nekhoroshev Stability in a Mapping Model for the Trojan Asteroids
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
Trojans in Stable Chaotic Motion
The orbits of 13 Trojan asteroids have been calculated numerically in the model of the outer solar system for a time interval of 100 million years. For these asteroids Milani et al. (1997) determined
The dynamics of Neptune Trojans – II. Eccentric orbits and observed objects
In a previous paper, we presented a global view of the stability of Neptune Trojans (NTs hereafter) on inclined orbits. As the continuation of the investigation, we discuss in this paper the
Stable Chaos in the Asteroid Belt
Abstract Most asteroids are characterized by positive Lyapounov Characteristic Exponents (LCE), which means that their orbits are chaotic. Indeed, the striking fact is that for many of them the
Proper Elements and Stability of the Trojan Asteroids
Up to now ∼ 400 asteroids are known which move close to the Lagrangian equilibrium points L 4 (246) and L 5 (167) of Jupiter. In this investigation the orbits of all known Trojans were integrated
Dynamics of Planet-Crossing Asteroids
A small, but by no means negligible, fraction of the small bodies of the Solar System is on planet-crossing orbits, including Earth-crossing ones. The dynamics of planet-crossing asteroids/comets is
Asteroid Proper Elements : The Big Picture
Four perturbation theories presently used to compute asteroid proper elements are reviewed, and their results are briefly discussed (Milani and Kneževic, 1990, 1992, 1994, for low to moderate


Secular perturbation theory and computation of asteroid proper elements
A new theory for the calculation of proper elements, taking into account terms of degree four in the eccentricities and inclinations, and also terms of order two in the mass of Jupiter, has been
An example of stable chaos in the Solar System
MANY planets have been shown to have chaotic instabilities in their orbital motions, but the long-term significance of this is not fully understood1. The eccentricity of Mercury, for example, changes
Secular perturbations of asteroids in secular resonance
When the precessional rate of the orbital plane of an asteroid is nearly equal to that of Jupiter, the orbital inclination of the asteroid changes quite largely due to this near equality of their
Integration error over very long time spans
The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error.
Long periodic perturbations of Trojan asteroids
The motion of the Trojan asteroids is studied in the elliptic restricted three-body problem of the Sun-Jupiter-asteroid system. Long periodic perturbations of the orbital elements are discussed.
An application of Labrouste's method to quasi-periodic asteroidal motion
In an earlier paper the authors have applied Labrouste's method to single orbital elements in order to isolate periodicities. However, in practice the investigation of two-dimensional vectors, where
The 1977 Palomar-Leiden Trojan survey
Une etude d'observations photographiques d'asteroides a permis de trouver 1491 asteroides dont les elements orbitaux peuvent etre determines (publies dans Mina Planet Circulars, 12536-12560, 5