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The article summary is as follows:

We can establish a mathematical correspondence between the classical Lagrangian approach and geodesic analysis as suggested by the standard general relativity (GR), in finding the nature of planetary orbits:

The question is: Is the classical flat space three-dimensional Lagrangian analysis geometrically superior to the GR analysis of a four-dimensional curved space, in finding planetary orbits, when we can get similar results in a three-dimensional flat space by modifying potential? We can get this expression for the modified potential by rearranging the curved space four-dimensional metric (or the corresponding total energy equation). The flat space analysis will always have a proper geometric support. We already know that, the arrangement of charges in the source and speed of the source modifies the potential function, in electrodynamics.

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