Fel & Fg Interaction: Electron Count for Balance

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Praestrigiator
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I did the math and figured that Fel between two protons at 1 mm is 2.307E-22 N, and the Fg at the same distance is 1.867E-36 obviously these values change with the number of protons, and distance. this is an issue because I'm trying to imagine a hypothetical object as charged as possible while still held together by gravity. Assuming uniform distribution of protons and electrons, how many electrons are needed to make The repulsive force of Fel less than the attractive force of gravity on an object primarily comprised of protons? What about an object comprised of electrons?
 

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The biggest problem i see is that in replacing protons with electrons reduces both repulsive Fel and attractive Fg
 
Praestrigiator said:
The biggest problem i see is that in replacing protons with electrons reduces both repulsive Fel and attractive Fg

Atoms and molecules aren't held together by gravity. The force exists, of course, but is negligible compared to the other forces present. They are held together by the electromagnetic force at one level, and the nuclear force (extremely important) at another. Gravity is too weak to be considered here, don't you think? Protons are held together in nuclei not because "surrounding electrons reduce the repulsion between them causing gravity to become more prominent", but because of the strong nuclear force which binds the nucleons together. It is much stronger than the repulsive force between protons.
 
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Praestrigiator said:
I did the math and figured that Fel between two protons at 1 mm is 2.307E-22 N, and the Fg at the same distance is 1.867E-36 obviously these values change with the number of protons, and distance. this is an issue because I'm trying to imagine a hypothetical object as charged as possible while still held together by gravity. Assuming uniform distribution of protons and electrons, how many electrons are needed to make The repulsive force of Fel less than the attractive force of gravity on an object primarily comprised of protons?
Let nP be the number of protons and nE be the number of electrons. Write down an expression for the gravitational force from nP+nE, and an expression for the electrostatic force. Set them equal.

You now have one equation in two unknowns, so you cannot solve. But you can solve for nE/nP