This paper presents an alternative hydrodynamic framework for modeling the dynamics of the solar system and astrodynamical anomalies using the unified Vortex-Sink (Z4DP) equation. In the proposed approach, space is modeled as a compressible superfluid vacuum, where central sinks and their rotation naturally form macroscopic vortices (e.g., the ecliptic plane). The predictive capability of the model is empirically tested on two independent phenomena. First, it demonstrates a >99% match with the observed secular perihelion precession of the inner planets purely by applying a nonlinear continuum compression gradient (3(v/c)^2). Second, it provides an exact analytical solution for unexplained flyby anomalies. By applying transverse momentum transfer via the entrainment parameter K and an exponential vacuum compression profile (n=5.63) derived independently from GNSS satellites, the model predicts the anomalous acceleration of the NEAR Shoemaker spacecraft with absolute precision (+13.44 mm/s predicted vs. +13.46 mm/s measured by NASA). The paper further analyzes long-term orbital stabilization and the cosmological implications of the 60° ecliptic tilt relative to the galactic continuum flow.