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General relativistic mechanics in gravitational fields exterior to homogenous spherically symmetric solution is developed using our coordinate displacement approach. In curved Schwarzschild spacetime, the coordinates provide a reference frame for an observer making measurements at an infinite distance from the gravitational source of the Schwarzschild spacetime. The Schwarzschild metric describes the spacetime surrounding a spherical non-rotating mass. However, physical quantities measured by arbitrary observers are not specified directly by these coordinates but rather are computed from the metric. It is well known that Newton’s theory of gravity is an approximation to Einstein’s theory when the curvature of space time is negligible. In this paper, we seek to deduce that in the limit of weak field approximation, Schwarzschild gravitation may be replaced with Newton’s gravitation. Here, we present Schwarzschild gravitation and show its reduction to the classical Newtonian gravitation – using power series expansions.

Determination Of Newtonian Gravitation From The Schwarzschild Spacetime Within The Region Of Spherical Geometry