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Equation of Motion of a Particle in a Gravitation Field
From Visual Physics Wiki

Contents
Intro
Hopefully, by comparing the classical and the "Special Relativistic" equation we will be able to derive the shape of spacetime curvature that produces gravitation.
Classical Equation of Motion of a Particle in Gravitation Field as a Function of Time
"Special Relativistic" Equation of Motion of a Particle in Gravitation Field as a Function of Time
(Based on the definition of acceleration in Special Relativity)