Hydrodynamic Density of the Substratum: Exact Calculation of Solar and Galactic Vacuum Density and the Resolution of the Dark Matter Problem

Standard cosmological models face a fundamental crisis known as the “Missing Mass” problem, necessitating the introduction of hypothetical non-baryonic “Dark Matter.” This paper proposes a definitive solution within the framework of Substratum Hydrodynamics, developed in our previous studies (Papers I-V). Based on the concept of matter as a “condensed phase” of the vacuum and the derivation of the Schwarzschild metric as an acoustic metric, we postulate that the physical vacuum is a ponderable fluid with variable density. By treating massive bodies as condensation nodes, we utilize the Hill Sphere boundary to calculate the effective background density of the Substratum required to confine planetary vortices. Our calculations reveal a strict density gradient in the Solar System, dropping from ~10⁻² kg/m³ (near Mercury) to ~10⁻⁸ kg/m³ (near Neptune). Extrapolating this hydrodynamic attenuation to the galactic scale, we yield an intergalactic background density of ρ ≈ 10⁻²⁴ - 10⁻²⁷ kg/m³. This value precisely matches the critical density of the universe and the dynamic requirements of galactic halos, thereby solving the Dark Matter enigma without resorting to exotic particles.