On the stability of high inclined \(\mathbf L_4\) and \(\mathbf L_5\) Trojans
type: Item
instance of: scholarly article
title: On the stability of high inclined \(\mathbf L_4\) and \(\mathbf L_5\) Trojans
zbMATH Open document ID: 1147.70308
author: Markus Gyergyovits
author: Rudolf Dvorak
author: Richard I. Schwarz
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 2005-02-28T00:00:00Z
review text: The Trojan group of real asteroids moving near well known Lagrangian triangular points of the Sun-Jupiter-asteroid system on high inclined orbits is investigated from the stability point of view by numerical methods. Several approaches including the Lyapunov characteristic exponents were used to integrate the system of the equations of the dynamical model. As the dynamical model the outer solar system consisting of the Sun and the four outer planets (Jupiter-\-Saturn-\-Uranus-Neptune) was chosen. The orbits of real asteroids around the Lagrangian points \(L_4\) and \(L_5\) with the large inclination (\(i >20^{\circ}\) were integrated for 50 Myrs. To understand the structure of the Trojan belt for high inclination (\(20^{\circ} < i < 55^{\circ}\)) the integration of the orbits of fictitious asteroids around the same equilibrium points were done for \(10^7\) years in the frame of the above mentioned dynamical model. The qualitative behavior of real Trojans fit quite well into the picture of the orbits of the fictitious ones -- they all are lying well inside the numerically found borders of stability. A remarkable difference between the \(L_4\) and \(L_5\) asteroids with large inclinations is found: the stable region around \(L_5\) is considerably smaller than around \(L_4\).
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70F15
zbMATH DE Number: 2139791
zbMATH Keywords: restricted three-body problems
zbMATH Keywords: Lagrangian points
zbMATH Keywords: Trojans asteroids
zbMATH Keywords: high inclination orbits
zbMATH Keywords: stability limits
describes a project that uses: MyRS
MaRDI profile type: Publication
full work available at URL: s10569-004-1007-2
OpenAlex ID: W1995874309
cites work: One to one resonance at high inclination
cites work: Why do Trojan ASCS (not) escape?
cites work: The Trojan problem
cites work: The Lyapunov characteristic exponents-applications to celestial mechanics
cites work: The dynamics of bodies with variable masses
cites work: Trojans in stable chaotic motion
DOI: 10.1007/S10569-004-1007-2
description: scientific article; zbMATH DE number 2139791