Galactic Gravitational Field Measurements Part 1: An Extension of Emergent Gravity Through Modulation-Based Field Theory

Galactic rotation profiles have challenged conventional gravitational theory since Rubin and Ford’s groundbreaking spectroscopic analysis of Andromeda in 1970 revealed that stars maintain unexpectedly constant velocities regardless of their distance from galactic centers. This phenomenon, later systematically cataloged across various spiral systems in Sofue and Rubin’s landmark 2001 review, created a fundamental crisis in astrophysics that led to the development of the dark matter hypothesis to reconcile the significant discrepancy between observed gravitational effects and visible mass distribution.This paper presents an alternative approach, extending Verlinde’s emergent gravity theory through a modulation-based field framework. We demonstrate how energy emanating from supermassive black holes propagates through the auxiliary modulation coordinate, creating structured energy flow patterns that sustain space-time curvature throughout galaxies.