Determination of the value for the bending angle of the light deflection and the impact parameter in Einstein’s theory

Abstract

The gravitational deflection of the ray of light is one of the famous demonstrations that space-time is curved in the General Theory of Relativity predicted by A Einstein, and later demonstrated by different astronomical experimental observations in solar eclipses. In this work, the deflection of light and the impact parameter in the gravitational field of the Sun are calculated through the solutions to the geodesic equations by the methods of the elliptic functions of Jacobi and Weierstrass, around a central gravitational mass, using the solution found by Schwarzschild to the equations of the gravitational field in the General Theory of Relativity. The results obtained were subjected to a comparative study of the deflection of the light ray experimentally. From this analysis, it is demonstrated that the theoretical results obtained by the Weierstrass and Jacobi methods are in the range of the experimental results calculated during the eclipses of the years 1919 to 1973, demonstrating once again the validity of the General Theory of Relativity that all gravitational mass curves space-time.