The Hydrodynamic Theory of g as the Pressure Gradient of the Celestial Plenum

This paper presents a complete fluid-dynamical derivation of gravitational acceleration (g) that eliminates Newton's gravitational constant (G) from the foundational equations of celestial mechanics. By modelling the interplanetary vacuum as a viscous, compressible quantum foam (the celestial plenum) with bulk density ρ0 ≈ 8.854 × 10−12 kg/m3 numerically coincident with the SI permittivity of free space, gravity is recast as the inward centripetal pressure gradient of a Keplerian vortex impressed upon the plenum by every rotating massive body. The Plenum Influence Parameter Φ = ve2 · r is shown to be the invariant specific kinematic torque of this vortex, yielding the vacuum law g = Φ/r2. To bridge laboratory and geophysical regimes, the paper introduces a Coefficient of Density Cρ, derived ab initio from the geometric cross-section of atomic electron clouds and the Specific Interactive Volume Siv. The unified law g(r) = Φ0 / [Cρ(r) · r2] reproduces (i) the latitude-dependent surface gravity to better than 0.1 percent, (ii) the residual decay of Low Earth Orbit satellites described as Quantum Foam Braking, (iii) the empirical Preliminary Reference Earth Model sub-surface gravity profile including the 10.68 m/s2 peak at the Core-Mantle Boundary, and (iv) a finite, non-singular zero-drag equilibrium at the geometric centre of the planet (the Eye of the Storm), permanently resolving the classical r = 0 singularity. The framework also predicts a previously unrecognised mid-mantle Hydrodynamic Dip near 1,250 km depth, offering a falsifiable laboratory for high-precision borehole gravimetry.