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Planetary equations based upon Newton’s Equations of motion and Newton’s gravitational field of a static homogeneous oblate Spheroidal Sun

J. F. Omonile, D. J. Koffa and S. X. K. Howusu

The expression for the equations of motion for a particle in Cartesian cylindrical and spherical coordinates and their applications in mechanics are well known. It is however, now well known that the planets, the sun and all rotating astronomical bodies are more precisely Spheroidal in geometry and the motions of test particles in them require spheroidal coordinates. Consequently, in this paper we derive the expression for the equations of motion for any test particle in oblate spheroidal coordinates to pave way for the corresponding extension of the well-known mechanics of spherical bodies