Desvio do periélio de Mercúrio na relatividade geral

• Autor(a) principal: Silva, Ana Luiza Bastos Barbosa Guimarães da [UNESP]
• Data de Publicação: 2018
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/203019; http://www.athena.biblioteca.unesp.br/exlibris/bd/capelo/2019-10-16/000918444.pdf
• topic: Relatividade; Astrofisica; Mercúrio; Mercury

This work's objective is to explicit all the steps taken by Einstein so that he could solve the precession of the perihelion of Mercury and find its orbital deflection (the contribution the Special Relativity has given to solve the Newtonian mechanics approach). The first step was to use the Special Relativity, in a plane metric, where the Lorentz Transformations are valid, then define a tensor notation and its properties. While going to the General Relativity, the two body problem approach is made, therefore an accelerated moving reference frame with respect to a steady one are treated in a curve metric, and that will be a Schwarzschild metric approach in this work. Calculations are developed and considerations made to obtain the geodesic curves to the Sun-Mercury sistem from the Euler-Lagrange equations, so that the orbital deflection can be acquired and the exact shape that Mercury's orbit takes in the precession while rotating around the Sun. Finally, the MATLAB platform was used in order to get the numerical solution for the problem, and specific cases were studied to get the validation and a comparison made with the analitical solution