Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: McKay on 13/09/2017 11:14:03
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I mean, regular matter, atoms and molecules, is far, far lighter than, say, a neutron star or a black hole. How weak is gravity if we compare a proton sized black holes gravity to the electromagnetic strength of a proton?
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I mean, regular matter, atoms and molecules, is far, far lighter than, say, a neutron star or a black hole. How weak is gravity if we compare a proton sized black holes gravity hole to the electromagnetic strength of a proton?
Firstly, there is a theoretical minimum amount of mass that can form a black hole. This is the Planck mass which is far larger than a proton. Secondly, if you have to compress a mass into its own event horizon to make a comparison then gravity HAS to be weaker by definition.
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Possibly we need some clarification.
My understanding of “light matter” is that it would be a small amount of matter in a gravitational field. Is this what you mean?
The comparison between a proton sized black hole’s gravity and the electromagnetic strength of a proton seems to be comparing two different forces in two very different situations. E.g. the mass in each case would be very different.
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We crossed over, there, Jeffrey. I think your:
Secondly, if you have to compress a mass into its own event horizon to make a comparison then gravity HAS to be weaker by definition.
addresses my second point, in a more technical way. Would you agree; or is my thinking drifting off the OP/
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We crossed over, there, Jeffrey. I think your:
Juju
Secondly, if you have to compress a mass into its own event horizon to make a comparison then gravity HAS to be weaker by definition.
addresses my second point, in a more technical way. Would you agree; or is my thinking drifting off the OP/
Correct. We are on the same page. ;D
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It would be interesting to calculate the mass required to produce the same gravitational effect as the electrostatic effect of the proton. I'm not sure what that would tell us that would move anything on in terms of any theory.
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My understanding of “light matter” is that it would be a small amount of matter in a gravitational field. Is this what you mean?
Anything, even a planet, is light matter compared to black holes. Sorry, I just didnt know how to describe it better.
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E.g. the mass in each case would be very different.
Sure, the mass would be different, but, then again, gravity is directly tied to the mass - of course it would be different.
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It would be interesting to calculate the mass required to produce the same gravitational effect as the electrostatic effect of the proton. I'm not sure what that would tell us that would move anything on in terms of any theory.
At a distance of 1 meter apart, the electrostatic force between two protons would be ~2.3e-28 Newtons. The gravitational force would be ~1,86e-41 Newtons. In other words, the electrostatic force would be 1.24e14 times greater than the gravitational force. Since both forces follow the inverse square law, this ratio would remain constant over all distance ranges.
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Damit, some admin changed my topics title.. again.
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If by "proton-sized" you mean "the size of the internationally accepted charge radius of the proton", then that would mean a black hole with a radius of 0.8768 femtometers. Such a black hole would have a mass of 590.5 billion kilograms: http://xaonon.dyndns.org/hawking/ (http://xaonon.dyndns.org/hawking/). The resulting force between two such black holes placed one meter apart would be 23.3 trillion newtons: https://www.shodor.org/os411/courses/_master/tools/calculators/gravcalc/gravcalc.html (https://www.shodor.org/os411/courses/_master/tools/calculators/gravcalc/gravcalc.html)
In order to make the gravitational force at 1 meter equal to 2.3 x 10-28 newtons (equal to the electromagnetic force between two protons, as calculated by Janus), the require black hole mass would be 0.000001857 grams, with a corresponding radius of 0.0681 Planck lengths. I don't know if a black hole can even be that small. Physics gets weird below the Planck length (if that even makes sense).
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If it's smaller than the Planck mass then it can't be a black hole. The Schwarzschild radius of the Planck mass is 2 Planck lengths. That is why it is considered the smallest possible black hole.