We reformulate orbital dynamics within the Structured Vacuum Theory (TVS23), eliminating all recourse to continuous spacetime, gravitational forces, or differential equations on ℝ⁴. The solar system is modeled as a finite algebraic network: 23 helicoidal channels with dodecahedral symmetry (A₅), supporting 19 transverse torsional modes. Planetary orbits emerge as resonant nodes where torsion conservation holds exactly. We derive: (1) the geostationary radius (42,164 km) from prime-mode resonance without empirical inputs; (2) the gas giant rotational sequence {13, 11, 7, 5} from prime-indexed torsional harmonics with errors <0.5% (Neptune's 12% deficit explained by geometric interference η = 15/17 due to Triton's retrograde orbit); (3) Newton's constant from base-23 arithmetic G = ℏc/mₑ²·23⁻³⁹. All results follow from finite algebra in the differential ring Wexp/T—no limits, no renormalization, no spacetime continuum. General Relativity is recovered as the coarse-grained limit of torsional dynamics, but ontologically gravity is discrete torsion, not continuous curvature.