In section 2, we stated that the gravitational force between fundamental particles is weaker than the coulombic force between them. Now we have the equations and most of the numbers we need to verify this. Let's calculate the gravitational and coulombic force between a proton and an electron at 0.05 nm = 5 x 10^-11 m separation (the approximate distance in the H atom).

GRAVITY
F_grav = G m₁ m₂ / r²
F_grav = (6.7 x 10^-11 nt m² / kg²) (9.12 x 10^-31 kg) (1.67 x 10^-27 kg) / ( 5 x 10^-11 m )² = 4.1 x 10^-47 nt

COULOMBIC
F_coul = (1/4πε₀) q₁ q₂ / r²
F_coul = (9 x 10⁹ nt m² / C²) (1.6 x 10^-19 C) (1.6 x 10^-19 C) / ( 5 x 10^-11 m )² = 9.2 x 10^-8 nt

This is not a small difference—it's nearly 40 orders of magnitude.