We propose that the compactification radius in 5D Kaluza-Klein theory is set by the Roche limit: R5 = dRoche/2. Using Einstein's constant kappa = 8πGN/c⁴, we derive dRoche = (1/M) sqrtħc/πGN kappa (ρP/ρ) ^1/4 with no free parameters. For black holes this predicts dRoche = rₛ = 2GN M/c², unifying tidal and horizon scales. The relation is validated with <0. 3% error from Earth-Moon to GW170817 and extended to the observable universe gives t0 = 14. 6 Gyr. This suggests gravity and electromagnetism unify at R5 ~ lₚ, when dRoche ~ rₛ ~ λC.
Demicheri et al. (Tue,) studied this question.