The Hermes Equation: Galaxy Rotation Curves from Age and Density with No Free Constants

Abstract

In many galaxies, stars orbit faster than their visible mass can explain. This gap is traditionally attributed to dark matter or to modified gravity laws like MOND. We propose a third explanation: the gap is not permanent. It decays as galaxies age. We present a single equation that predicts each galaxy’s gravity gap from two measurements: its age and its peak baryonic acceleration. The equation’s constants, derived from staged tests on galaxy subsets, turn out to match known mathematical constants involving pi, Euler’s number, and the speed of light. No constants are adjusted per galaxy. No per-galaxy fitting is performed. We tested the equation on 133 galaxies from the SPARC database with verified stellar ages from 77 independent published sources. The equation achieves a median fit score of 1.312, comparable to MOND, while producing substantially fewer catastrophic failures: 84% of galaxies score below 5.0, compared to 71% for MOND. Beyond fitting rotation curves, the equation predicts how galaxies should change as they age: young galaxies should retain large gravity gaps, old galaxies should lose them, and structural properties like gas content, central concentration, and bulge size should all track the same decay variable. The data confirm every one of these predictions, including a sharp transition near 7 billion years. Two galaxies fail badly, but the failures are consistent with incomplete input data for those specific systems rather than with problems in the equation itself. These results support the conclusion that the gravity gap in disk galaxies is not a permanent property but a changing quantity that decays at a rate set by fundamental constants.