Hybrid Gradient Descent Method for Galactic Modelling Using the Enhanced Newtonian Dynamics Framework

The study of galactic dynamics remains fragmented across three competing paradigms—Dark Matter (ΛCDM), Modified Newtonian Dynamics (MOND), and Yukawa-type modifications. This work relies on Enhanced Newtonian Dynamics (END), a parameter-free gravitational framework that derives rotational velocities exclusively from observable baryonic mass distributions and geometric configurations. Applying END to 39 high-quality galaxies from the SPARC database via a three-oblate spheroid composite model (core, bulge, and disc), we achieve mean velocity errors below 3% for 71.79% of the sample, with a median χ2=1.77. The fundamental END relation, MT2=κV (where κ≈1.4121×1011kgm3s2), successfully reproduces observed rotation curves without invoking non-baryonic dark matter haloes or modified gravity interpolation functions. Notable exceptions (e.g., IC2574, χ2=51.56) arise from geometric mismatches between the assumed exponential decay profiles and the actual density structures of dwarf irregular systems. Classical Newtonian Dynamics, applied to identical mass distributions, accounts for only 20% of observed velocities, suggesting the “missing mass” problem reflects limitations in how gravitational law relates enclosed mass to orbital motion rather than unseen matter. END’s zero-parameter architecture renders it strictly falsifiable, offering a parsimonious alternative to parameter-heavy competing models while requiring future iterations to incorporate adaptive geometric baselines for morphologically diverse galaxies.