(untitled) (Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2025)
This study reveals the unified geometric origin of the gravitational constant G and the speed of light c. By introducing the rotational scaling length , defining the helical divergence strength and the space–mass coupling relation , we establish a one-to-one correspondence between mass and geometric scale. Under the unique bridging law , we rigorously derive the invariant This result demonstrates that G and c are not independent constants but are jointly fixed by the space–mass coupling constant and geometric structure. Using observational data from solar redshift, light deflection, planetary perihelion precession, and both Jupiter’s satellites and the white dwarf Sirius B, we verify the universality and cross-modal consistency of this relation. Geometric scaling not only explains the origin of G but also establishes a unified theoretical framework for future high-precision astronomical observations and constant metrology. This offers a more geometric expression than general relativity and proposes testable metrological predictions.