The application of Newton’s laws of motion in gravitational fields has been restricted to the fields of perfectly spherical bodies. In this paper the gravitational fields due to a Spheroidal body is derived to open the way for the extension of Newtonian mechanics from the fields of spherical bodies to these Spheroidal bodies. The results showed that Newton’s gravitational field equations for a Spheroidal body are linear and separable and can be solved in terms of the well known special functions of mathematical physics, the Legendre functions. We also obtained gravitational intensity field of the body and its corresponding unit vectors in components forms. We further obtained general acceleration vector its associated acceleration vector components forms. We finally obtained the components of the equation of motion for a particle of non zero rest mass in the gravitational field exterior to an oblate spheroidal massive body. The Newton’s universal gravitational field equations for a homogeneous oblate Spheroidal body with the exact and complete results are available for mathematical analysis and hence physical interpretation and experimental investigation for all bodies in the universe.
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