This paper re-examines the anomalous perihelion precession of Mercury within a Newtonian framework, incorporating finite-speed gravitational propagation, gravitational aberration effects, and galactic motion corrections. Using updated astrophysical parameters, a classical explanation for the observed 43 arcseconds per century precession is derived without invoking spacetime curvature. The analysis emphasizes transparent methodology, reproducibility of calculations, and extensions of Newtonian mechanics under contemporary physical understanding.