Open Earth Polar Model v3: A Gauge-Invariant Framework for Galactic Dynamics Without Dark Matter

This paper reinterprets the landmark 1980 study by Vera C. Rubin, Kent Ford, and Norbert Thonnard on the rotation curves of 21 Sc galaxies. While the original paper inferred the existence of dark matter due to flat galactic rotation profiles, this work shows that the data can be explained through the Open Earth Polar Model (OEPM)—a geometric field theory where gravity emerges from energy density gradients in a scalar field, Ψ(r, θ, t). Through mathematical derivations and energy-field modeling, the OEPM framework demonstrates that Newtonian gravity does not hold at galactic scales and provides a falsifiable, parameter-free explanation for the observed phenomena without invoking dark matter halos Keywords: OEPM, Rubin, galactic rotation, dark matter, Newtonian gravity, energy geometry, scalar field theory, astrophysics, polar coordinates License: CC BY-NC-ND 4.0 (Attribution–NonCommercial–NoDerivatives)