Relativistic Newtonian Dynamics under a central force

Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Clock Hypothesis, an explicit description of this influence is derived. We present a new relativity model by incorporating the influence of the potential energy on spacetime in Newton's dynamics for motion under a central force. This model extends the model used by Friedman and Steiner (EPL, 113 (2016) 39001) to obtain the exact precession of Mercury without curving spacetime. We also present a solution of this model for a hydrogen-like atom, which explains the reason for a probabilistic description