Thursday, February 5, 2009

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= Gm1m2
Fe= keq1q2
Fe = ke
q1q2
r2r2FgGm1m2
Constants
ke = 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
G6.67428·10-11 kg-2

Electron mass and charge
me = 9.10938215(45)·10−31 kg
qe = −1.602176487(40)·10−19 C
Electron Electron
Fe = 1.34659·1020−1.60218·10−19 × −1.60218·10−19 = 4.16562·1042
Fg9.10938·10−31 × 9.10938·10−31

Proton mass and charge
mp = 1.672621637(83)·10−27 kg
qp = 1.602176487(40)·10−19 C
Proton Proton
Fe = 1.34659·10201.60218·10−19 × 1.60218·10−19 = 1.23556·1036
Fg1.67262·10−27 × 1.67262·10−27

Electron Proton
Fe = 1.34659·1020−1.60218·10−19 × 1.60218·10−19 = -2.26867·1039
Fg9.10938·10−31 × 1.67262·10−27


Neutron mass and charge
mn = 1.67492729(28)·10−27 kg
qn = 0 C
Neutron Neutron
Fe = 1.34659·10200 × 0 = 0
Fg1.67493·10−27 × 1.67493·10−27

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