Inertial Buoyancy of Vacuum and the Constant Kβ: A Novel Predictor of Atmospheric Stability and Multi-Scale Cosmological Applications

This paper introduces the updated formulation of the inertial constant Kβ, defined as: Kβ=Mπ⋅R2⋅v2K_β = \frac{\sqrt{M}}{π·R²·v²}Kβ=π⋅R2⋅v2M where MMM is the planetary mass, RRR the radius, and vvv the orbital velocity of the satellite or atmosphere. The Kβ constant acts as a predictive indicator of atmospheric stability across celestial bodies. The new analysis confirms a predictive accuracy of 88.9% across nine celestial objects, and a remarkable match of 101.6% with the Hubble constant when accounting for the inertial resistance of vacuum. The paper proposes that vacuum behaves as an active inertial fluid, exerting a directional drag on matter at large scales. This hypothesis offers alternative explanations for: The persistence and geometry of galactic filaments (95.3% accuracy), The discrepancy in H₀ measurements, The potential existence of a critical inertial threshold below which no atmosphere can be sustained. Applications include trajectory optimization, exoplanet atmosphere prediction, and a reinterpretation of dark energy as a manifestation of the gradient ∇Kβ across spacetime. This version refines the original V1 by introducing: A clearer dimensional analysis, An expanded corpus of celestial validation cases, And a reformulated expression of vacuum dynamics applicable from planetary to cosmological scales.