Sobre a dinâmica de rotação de um planeta através de um sistema médio

• Autor(a) principal: Trotta, Leonardo Di Schiavi [UNESP]
• Data de Publicação: 2013
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/121631
• topic: Astronomia; Movimento rotacional; Dinâmica; Perturbação (Astronomia); Planetas - Orbitas; Plutão (Planeta)

Let us consider a non-spherical body (usually a planet C1) which is in a keplerian orbit around C3 (Sun). We still consider a massive satellite (C2) around the target planet (C1). Our main task is to investigate the secular rotational dynamics of C1. As it is well known, among other conditions, the secular dynamics of the equator of a planet is deeply related to the climate and habitability conditions of this planet. Therefore, here we try to present a simplified model to study the behavior of the equator of a planet under these disturbers. In order to derive long period motion of the problem, we use Andoyer variables. This set of variables is very powerful and convenient as it allows the averaged system in a clear and rigorous way. In fact, when C1 is an axisymmetric body, Andoyer variables are automatically action-angle variables of the torque free motion, so that classical canonical perturbation theory can be applied very easily. Basically, the rotation of C1 is disturbed by C3 and C2. While C3 is in a keplerian orbit, for the translational motion of C2 we have to consider the perturbation of C3 and also the oblateness effect of the target body. All these details are included in our code through the integration of extra Lagrange´s equations. We tested our secular equations to Pluto- Charon system. Our results for period and amplitude of the variation of the equator are in quite agreement with those obtained previously by Dobrovolskis et al. (1997). We also tested some different initial inclinations for Charon´s orbit. While there appear some variations, they are not so significant for the considered time span. Our model can also be applied to study the variation of the equator of Uranus or Neptune, considering the presence of a massive satellite during the planetary migration. Preliminary simulations show interesting results