In classical electromagnetism, Coulomb's constant is derived from Gauss's law. The result is:(adsbygoogle = window.adsbygoogle || []).push({});

k_{e}= 1/4πε = μc^2/4π = 8987551787.3681764 N·m^{2}/C^{2}

Where ε is the electric permittivity of free space, μ is the magnetic permeability of free space, c is the speed of light in a vaccuum, and 4π is because of how Coulomb's constant is calculated (εEA=Q and F=qE ergo F=qQ/εA, and since A=4πr^{2}then F=1/4πε * Qq/r^{2}).

(on an unrelated side note, the symbol for pi looks funny and I'm not sure if I like it, it's not majestic enough and it looks awkward if I use itex tags to do it... okay, back to topic at hand)

The equations for electrostatics and gravity have been compared with almost no end. Even Tesla went so far as to attempt to attribute gravity to electromagnetism (though I don't think he ever published his theory, he just mentioned it). What I'm most interested in is the gravitational constant, G. Working backwards from G, could we perchance find the permeability/permissivity of a vacuum with respect to gravitation just as k_{e}does for electromagnetism?

Starting with G and assuming that G = 1/4πε, we find that 1/4πG = ε. The result is 1.1924*10^{9}kg s^{2}/ m^{3}. Now since ε = 1/μc^{2}, that means 1/εc^{2}= μ. The result for this is 9.3314*10^{-27}m / kg.

What interests me the most is if this could split classical gravitation into two forces that act as one, just as magnetism and electricity do to form electromagnetism.

Thoughts? Or am I barking up the wrong tree? This thought just occurred to me and I ran straight here to ask about it. :)

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# Concerning the Classical Electromagnetism and Gravitation Constants

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