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Thomas comments on New Monthly Thread: Bragging - Less Wrong
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I've calculated that the atoms in the center of the Sun are not fast enough to escape the Sun's gravity even from its surface, let alone from its center.
And published it in my blog.
Not that it is a discovery of any kind, just another eyeopener how bad is our intuition.
Would you say, that 15 million K hot proton is too slow to escape the Sun's gravity?
Huh: Unless I've botched something:
kT for T = 15 MK is about 1.3 keV;
GmM/R for m = 938 MeV/c², M = 2e30 kg and R = 700,000 km is about 1.0 keV
(In retrospect, it's not surprising they would be the same order of magnitude, as per the virial theorem.)
(In the above I'm implicitly bragging about remembering the mass and radius of the Sun off the top of my head (everyone working in my field knows the proton mass anyway so that's not bragworthy), but I didn't learn them last month, so that doesn't count.)
Why is there a solar wind, then?
Those particles of solar wind don't wander away from the Sun by the Brownian motion. They are ejected in Solar storms by electromagnetism. When many billion hydrogen atoms or rather ions conspire just in a right way, they can launch one of their own to the stars. The energy contribution of them many is needed, to accelerate just one.
Sometimes, a rock is ejected to the outer space by a volcano on Earth. That doesn't mean, the rocks here are that fast, 10 or more kilometers per second. But when a lot of rocks conspire in a just right way, one of them may be launched with such a speed from the Earth.
On the other hand, hydrogen molecules from Earth do wander away by the Brownian motion alone. 50 kilograms of them every second, according to Wikipedia, are fast enough to evaporate. And a few kilos of helium evaporates away from our planet every second as well.
Sun's gravity is too strong to permit a noticeable leak of this kind. Hydrogen atoms/ions on its surface are not that hot, that an observable fraction of them would gain the escape velocity. Paradoxically, on Earth they are!
That the Earth is loosing its mass I wrote something here.
I guess the Sun is gaining mass. Still.
I'm pretty sure there are no atoms in the center of the sun. it's all plasma.
So speed of what exactly did you calculate? Electrons, protons, helium nuclei? Can 15 million K hot electron escape?
The mass difference between a hydrogen atom and a proton is very small. None of them has enough speed.
Heavier isotopes (deuterium and tritium (nuclei)) are even slower.
So are all helium isotopes, so are all other elements. Even slower than a single proton!
Okay?
What about the electrons? :-)
Electrons are faster than the escaping velocity is.
But they can't escape alone. Electromagnetism prevents that. Except for a negligible minority, maybe.
OK, but I thought that in this thought experiment you ignore electromagnetism. Otherwise you'd have to concede that a lot of particles do reach escape velocity, in a form of solar wind. :-)
You are right here on something important. Atoms couldn't be much, much smaller than they are. Otherwise not only the stars, but our planet had been evaporated, long ago.