We present a rigorous, non-circular derivation of surface gravity within Structured Vacuum Theory (TVS), demonstrating that gravitational acceleration emerges universally from quantum vacuum structure. The work provides: First-principles derivation of the gravitational constant G=κme28πℏcα21G=8πℏcκme2α21 from fundamental quantum constants Independent validation using lunar and martian gravity without parameter fitting Universal predictions accurate to 0.6% using independently measured planetary parameters Circularity-free framework where all inputs are determined from spectroscopic and geodetic data This work establishes TVS as a viable framework for emergent gravity, connecting quantum vacuum structure to macroscopic gravitational phenomena through a mathematically rigorous approach that eliminates traditional circular dependencies in gravitational theory.