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From this calculation (http://uk.answers.yahoo.com/question/index?qid=20080724101956AA4zed1), two protons seperated by the distance of one atom feel the electromagnetic force repelling them 1.239*10^36 stronger than the gravitational force attracting them.

This means that for gravity to be able to bring hydrogen atoms together to make stars, their overall charge must have to be PERFECTLY neutral. Is this level of symmetry surprising? Does it show protons and electrons were cut from the same cloth?

Qmechanic
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Amphibio
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The effects of gravity are really only observable to us on a macroscopic (large) scale. When a large enough number of (perfectly neutral) Hydrogen atoms come together they will gravitate towards each other. That sets things in motion for the Hydrogen to heat up. Once they reach a high enough temperature and density, they will ionize and the protons can approach each other close enough for the strong nuclear force to act. This force is approx. 2000 times stronger than the coulomb repulsion between the protons. Even with conditions found in our sun, the reaction rate for forming Deuterium is only about 5 * 10^(-18)/sec per proton. What keeps our sun radiating is the enormous number of reacting protons, on the order of 10^56, making the total reaction rate of the order of 10^38/sec. What’s astonishing to me is that the weakest force, gravity, can crush these particles together and create stars, neutron stars and even black holes.