Dinâmica secular rotacional de corpos tri-axiais: expansão de V em ressonâncias de primeira ordem

• Autor(a) principal: Amorim, Diego Soares [UNESP]
• Data de Publicação: 2015
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/131809; http://www.athena.biblioteca.unesp.br/exlibris/bd/capelo/2015-10-22/000852702.pdf
• topic: Astronomia; Movimento rotacional; Mercurio; Planetas

Consider a finite body of mass m (C1) with moments of inertia A, B and C. This body orbits another one of mass much larger M (C2), which at first will be taken as a point, even if it is not completely spherical. The body C1, when orbit C2, performs a translational motion near a Keplerian. It will not be a Keplerian due to external disturbances. We will use two axes systems: fixed in the center of mass of C1 and other inertial. The C1 attitude, that is, the dynamic rotation of this body is know if we know how to situate mobile system according to inertial axes system. The strong influence exerted by C2 on C1, which is a flattened body, generates torques on C1, what affects its dynamics of rotation. We will obtain the mathematical formulation of this problem assuming C1 as a planet and C2 as the sun. Also applies to case of satellite and planet. In the case of Mercury-Sun system, the disturbing potential that governs rotation dynamics, for theoretical studies, necessarily have to be developed by powers of the eccentricity. As is known, such expansions are delicate because of the convergence issue. Thus, we intend to make a development until the third order (superior orders are not always achievable because of the volume of terms generated in cases of first-order resonances). By defining a modern set of canonical variables (Andoyer), we will assemble a disturbed Hamiltonian problem. The Andoyer's Variables allow to define averages, which enable us to discard short-term effects. Our results for the resonant angle variation of Mercury are in full agreement with those obtained by D'Hoedt & Lemaître (2004) and Rambaux & Bois (2004)