High School How many electrons to make a stable gravitational object?

[Feynstein100]

I was wondering if we could have an object made up of only electrons. Normally, that wouldn't be possible because electrons repel each other. However, this repulsion can be overcome using gravity. So my question is, how many electrons would you need to have their gravitational attraction overcome the electromagnetic repulsion and form a stable object? Or perhaps is the charge-to-mass ratio of the electron such that the electromagnetic repulsion will always be higher than the gravitational attraction and thus preclude such an object?
Of course, an object like that would not form naturally since the electromagnetic force has the tendency to self-limit via neutralization. So for our purposes, we assume that there aren't any positively charged particles nearby to neutralize our object. There are only electrons.

 

[berkeman]

So my question is, how many electrons would you need to have their gravitational attraction overcome the electromagnetic repulsion and form a stable object?

What did you find when you did your Google searches to compare the electrostatic force to the gravitational force at typical atomic lattice distances?

 

[Feynstein100]

What did you find when you did your Google searches to compare the electrostatic force to the gravitational force at typical atomic lattice distances?

That the electromagnetic force is 23 orders of magnitude stronger than gravity.

Or perhaps is the charge-to-mass ratio of the electron such that the electromagnetic repulsion will always be higher than the gravitational attraction and thus preclude such an object?

So I guess this is the answer?

 

[berkeman]

That the electromagnetic force is 23 orders of magnitude stronger than gravity.

Boom!

 

[Feynstein100]

Boom!

I'll take that as a yes But not so fast. We've still got neutrinos. They don't have charge. So I know you can make a gravitational object out of them So, indulge me. How many would it take?

 

[berkeman]

Neutrinos don't like crowds, so that would not work. They also hate to be anthropomorphized, so I'll have to tie off this thread now before they get their neutrino union involved...