A precessão do periélio de Mercúrio: da dinâmica Kepleriana às correções relativísticas

Abstract

The constant questioning about the phenomena of nature led to the emergence of science, especially physics. Newton's laws and the Law of Gravitation accurately portray the orbits of celestial bodies by considering gravity as a force that depends on the masses involved. However, the planet Mercury eluded the explanations provided by Newtonian dynamics, which failed to account for the discrepancy between observational and theoretical values. This work aims to analyze Mercury's orbital motion under two approaches in physics: Classical Mechanics and the Theory of General Relativity (GR). The first part presents the fundamentals of Classical Mechanics, addressing Newton's Laws and the Law of Universal Gravitation, the principle of conservation of energy and angular momentum, and the equations of motion in central potentials. Next, Kepler's laws are reviewed. From this framework, perturbations in planetary motion are examined using Binet's equation to model the planet's orbit. The discrepancy between the value predicted by Newtonian mechanics and observational data regarding Mercury’s perihelion precession reveals the theory’s limitations. The second part of the work deals with the fundamentals of GR, presenting the postulates that govern this theory and the curvature of spacetime caused by the presence of mass and energy. Einstein's equations were analytically solved for a spherically symmetric, static, and uncharged body. From this solution of the field equations, known as the Schwarzschild metric, the equation of motion that describes Mercury's orbit in curved spacetime was derived. The results obtained are compared with observational data, highlighting the precision of relativistic theory in explaining the observed precession. Finally, the historical relevance of this problem for the validation of GR is discussed.