An Upgrade of Universal Gravitation: A New Theory Incorporating Newton’s Gravitational Equation and Reproducing MOND Effects in Disk Galaxies Without Requiring Dark Matter

This paper proposes a new gravitational framework derived from Newton's law of universal gravitation, incorporating the superposition principle and geometric boundary effects in non-spherical systems. The theory reduces to classical Newtonian dynamics in spherical configurations—consistent with solar system tests—while predicting a∝1/r acceleration dependence in flattened disk systems, naturally yielding flat rotation curves without dark matter. This replicates the empirical success of MOND but is rigorously derived from classical physics and respects fundamental conservation laws. The framework reveals a deep link between gravity and geometry, showing that gravitational effects depend on the surface area associated with mass distributions, and predicts that the gravitational "constant" G is actually a shape-dependent effective parameter G'. Key predictions include: (1) spherical systems follow Newtonian dynamics; (2) disk galaxies exhibit flat but modulated rotation curves; and (3) vertical stellar oscillations through the galactic plane induce periodic fluctuations in rotational velocity—consistent with observed ripples in real rotation curves. These results suggest that galactic-scale gravitational anomalies may stem not from unseen matter, but from the intrinsic geometric dependence of classical gravity in realistic astrophysical structures, offering a dark matter-free paradigm rooted in classical physics.