Planetary and Light Motions From Newtoinian Theory: An Amusing Exercise
  We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor as a tool for grasping Einstein's General Relativity. Though the exercise is understandable by readers at large, it is especially recommended to the teachers of Relativity for an appreciative understanding of its peculiarity as well as its pedagogical value in the teaching of differential equations. 
K.K. Nandi, N.G. Migranov, J.C. Evans, and M.K. Amedeker