Binary Emergent Gravity Applied to Wide Binary Stars: Predictions for Gaia DR3/DR4 and the Gravitational Boost

We extend Binary Emergent Gravity (BEG — companion paper)

to the wide binary star regime (d_bin = 500–30 000 AU),

where gravitational accelerations are in the range

g_N ~ 0.05–500 a₀. BEG predicts a gravitational boost

γ_g = G_eff/G_N ≈ 1.077, constant across all separations

— a signature qualitatively distinct from MOND (which

predicts no effect in the high-acceleration regime where

g_N > a₀). A theorem of invariance establishes that this

boost arises exclusively from the entropic cross-term,

not from any radial potential modification.

Comparison with Gaia DR3 Bayesian orbit measurements

(Chae 2025) shows agreement at <2σ. The discriminating

test — Γ at g_N > 10 a₀ with σ_Γ < 0.005 — requires

~600 pairs with 3D velocities, accessible to Gaia DR4.

Companion paper to BEG Article 1.