An Analytic Mathematical Model to Explain the Spiral Structure and Rotation Curve of NGC 3198

This archive presents the source code, data, and full paper for a mathematical model explaining both the spiral morphology and flat velocity rotation profiles of disk galaxies. The model is derived from a transformation within general relativity, applied to rotating polar coordinate systems in a metric-preserving manner. It demonstrates that the observed flat rotation curves and spiral structures are natural products of relativistic frame dynamics—without invoking non-baryonic dark matter.

The model has been tested against 878 galaxy rotation curves, primarily in the Southern Hemisphere, using datasets compiled by Salucci and others. Derived mass and angular momentum estimates are cross-validated with distance moduli from Cepheid variables, water masers, and Tully-Fisher relations. We show that the morphology of NGC 3198 aligns with a rotating geodesic and suggest that such galaxies are gravitationally viscous and self-bound systems.

This archive includes the full text of the paper, raw and processed rotation curve data, Matlab source code, and README documentation for reproducibility.