Simple Gravity III: Orbital Dynamics and Partial Perihelion Shift

This work develops the dynamical sector of the Simple Gravity framework using a Newtonian-type equation of motion in the nonlinear scalar field. The resulting orbital dynamics naturally produce perihelion precession, yielding a value equal to one-sixth of the relativistic prediction. This identifies the need for a refined dynamical description. This is the third paper in the Simple Gravity series.