Stability and Dynamics in the Sun-Jupiter System
Stability and Dynamics in the Sun-Jupiter System
"Stability and Dynamics in the Sun-Jupiter System", organizado por CITMAga. Será impartido por Óscar Rodríguez del Río. Departamento de Matemáticas, Universitat Politècnica de Catalunya.
Data: 20 de decembro de 2024.
Hora: 10:00 h.
Duración: 1 hora
Lugar: Aula Magna da Facultade de Matemáticas (USC) e online por MS Teams a través do enlace Teams Meeting.
Abstract:
Hilda group of asteroids consists of over 6,000 asteroids located beyond the main asteroid belt but within Jupiter's orbit. These asteroids are characterized by a 3:2 orbital resonance with Jupiter and follow orbits that appear to approach the three Lagrangian points (𝐿𝐿 3, 𝐿𝐿 4, and 𝐿𝐿 5) of the Sun-Jupiter system.
Our aim is to analyze their behavior from a dynamical systems perspective within the context of both, Sun-Jupiter planar Circular and Elliptical Restricted Three Body Problems (CRTBP and ERTBP), to focus on the role of Jupiter's eccentricity, that acts as a time-periodic perturbation of the CRTBP.
First, we need to develop a non-autonomous transformation of coordinates to those provided by JPL database in order to bring the asteroids into the CRTBP and ERTBP models. Then, we numerically compute the periodic and quasi-periodic orbits(invariant tori) that govern the motion of the Hilda asteroids, as well as their stability, making use of temporal or spatial Poincaré sections.
This is a joint work with Àngel Jorba and Begoña Nicolás.