Electrostatic to Gravitational Force Ratio

For charged subatomic particles the electrostatic force dominates the gravitational force at least on the order of 10³⁶. A billion is 10⁹, and 10³⁶ = 10⁹⁴ or a billion times a billion times a billion times a billion. Here are the mathematical derivations using the equations for the electrostatic force and the gravitational force.

Gravitational Force			Electrostatic Force			Force Ratio
Fg= G	m1m2		Fe= ke	q1q2		Fe	=	ke		q1q2
	r2			r2		Fg		G		m1m2

Constants
k_e = 8.987551787·10⁹ N m² C^-2
G = 6.67428·10^-11 N m² kg^-2

ke	=	8.987551787·109 C-2	= 1.34659·1020 kg2 C-2
G		6.67428·10-11 kg-2

Electron mass and charge
m_e = 9.10938215(45)·10⁻³¹ kg
q_e = −1.602176487(40)·10⁻¹⁹ C

Electron Electron
Fe	= 1.34659·1020	−1.60218·10−19 × −1.60218·10−19	= 4.16562·1042
Fg		9.10938·10−31 × 9.10938·10−31

Proton mass and charge
m_p = 1.672621637(83)·10⁻²⁷ kg
q_p = 1.602176487(40)·10⁻¹⁹ C

Proton Proton
Fe	= 1.34659·1020	1.60218·10−19 × 1.60218·10−19	= 1.23556·1036
Fg		1.67262·10−27 × 1.67262·10−27

Electron Proton
Fe	= 1.34659·1020	−1.60218·10−19 × 1.60218·10−19	= -2.26867·1039
Fg		9.10938·10−31 × 1.67262·10−27

Neutron mass and charge
m_n = 1.67492729(28)·10⁻²⁷ kg
q_n = 0 C

Neutron Neutron
Fe	= 1.34659·1020	0 × 0	= 0
Fg		1.67493·10−27 × 1.67493·10−27