Satellite System Stability and Uranus U-VI Prediction Based on the Hydrodynamic v_L Gravity Model

Abstract: Satellite System Stability and Uranus U-VI Prediction Based on the Hydrodynamic $v_L$ Gravity Model

This paper introduces a deterministic approach to planetary satellite architecture by applying the Space Flow Hydrodynamic Model ($v_L$). Unlike classical N-body simulations, this study treats orbital stability as a result of discrete resonance nodes within a planet’s spatial inflow field. By analyzing "Hill sphere harmonics," the research establishes a predictive framework for the maximum number of stable satellites a celestial body can maintain.

Key Scientific Findings:

• The Nodal Stability Law: The research proposes that the number of primary stable satellites ($N$) is governed by integer harmonics that fit within the effective gravitational radius. The model defines these zones as "flow compensation points" where the $v_L$ vector reaches a local equilibrium.

• Predictive Success: The model demonstrates a 100% correlation with the observed satellite counts and major orbital positions for Earth, Mars, Jupiter, and Saturn, validating the $v_L$ framework as a tool for mapping gravitational capture boundaries.

• Uranus System Discovery (U-VI / "Lelyavin’s Node"): Systematic analysis reveals a missing harmonic node beyond the orbit of Oberon. The $v_L$ equations predict a yet-to-be-confirmed satellite or massive debris ring located at:

  • Orbital Radius: $\approx 840,240$ km.

  • Orbital Period: $\approx 23.26$ Earth days.

  • Nodal Index: $n=6$ (following the quadratic scaling sequence from Oberon).

Conclusion:

The identified "Lelyavin’s Node" represents a critical test for the hydrodynamic gravity theory. This paper provides the mathematical derivation for this orbital position and offers a new method for detecting exomoots and predicting the stability of artificial satellite constellations in complex gravitational fields.