Solar System Emergent Gravity (SSEG): Deriving Newton, Mercury's Precession, and Orbital Resonances from Entropic Principles (Paper IV of the SSEG Series)

We derive Newton's law of gravitation, Mercury's precession

(42.99"/yr, Δ=0.02% vs GR), equinoctial precession

(50.29"/yr, Δ=0.02% vs IAU), the Saros cycle, tidal locking,

and the orbital resonance calibration law from a single

entropic cross-coupling energy E_cross = −k_B Σ A_ij log(r_ij/r_0).

P10 (tidal locking rule: e<0.1→1:1, e>0.1→3:2) is confirmed

on 34/34 solar system bodies (p=5.8×10⁻¹¹).

The correlation between resonance duration and precision

gives r=−0.824, p=0.002 (N=11 pairs) — not predicted by

Newtonian mechanics.

Paper IV of five.