Simple Gravity IV: Refined Particle Dynamics and Full Perihelion Precession

This work refines the dynamical sector of the Simple Gravity framework by introducing an effective test-particle Lagrangian consistent with the nonlinear scalar field structure. The resulting orbital equation is derived and analyzed in the weak-field regime. The theory naturally produces perihelion precession, and a general condition on the dynamical coefficients is obtained. Under this condition, the full observed perihelion shift is exactly recovered: Δθ = 6πGM / (a(1−e²)c²), without invoking spacetime curvature. This result demonstrates that the missing factor in previous formulations originates from the dynamical sector rather than the gravitational field itself. This is the fourth paper in the Simple Gravity series.