Solution of Newton's Gravitational Field Equation of a Static Homogeneous Oblate Spheroidal Massive Body
Nura Yakubu, S. X. K. Howusu, Williams Lucas Lumbi, N. Ibrahim · International Journal of Theoretical and Mathematical Physics · 2016
It is well known that Newton's dynamical gravitational field equation and Einstein's geometrical gravitational field equation were derived based upon the Euclidean geometry. In this paper, we used a golden metric tensor for all gravitational fields in nature to develop Riemannian Laplacian field equation which is assumed to be more general than the Euclidean geometry in order to derive Riemann's dynamical gravitational field equation for a static homogeneous oblate spheroidal massive bodies due correction terms of all order c -2 that is not found in Newton's gravitational field equation and also in this paper we derived the solution of Newton's gravitational field equation for a static homogeneous oblate spheroidal massive body. In the last six decades, the theoretical study of gravitational fields in Newton's dynamical gravitational field equation was treated under the assumption that massive bodies are perfectly spherical in nature. In the same way, Einstein's Geometrical gravitational field equation was treated under the assumption that the sun is exclusively a perfect sphere as seen in Schwarzschild's solution to Einstein's Geometrical gravitational field equation. It is well known that Newton's dynamical gravitational field equation and Einstein's geometrical gravitational field equation were derived based upon the Euclidean Laplacian operator. Recently, research has shown that all rotating bodies example the planets, sun, stars and the galaxies in the universe are either oblate spheroidal or prolate in shape (1, 2, 9, 10, 13). In Newton's mechanics, the motion of particles (such as projectile, satellites and pendulli) in earth's atmosphere is treated under the assumption that the earth is a perfect sphere (14). Similarly, in the solar system the motion of bodies (such as planets comets and asteroids) is treated under the assumption that the Sun is a perfect sphere (3, 12). Also in Einstein's theory, the motion of bodies (such as planets) and particles (such as photons) are treated under the