On the stability of high inclined \(\mathbf L_4\) and \(\mathbf L_5\) Trojans
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 \(L_4\).
scientific article; zbMATH DE number 2139791