Density of the Sun's corona and the "Scale Height"
I am curious science teacher and I wonder "What is the coronal pressure? I mean for example 10 000 km of the photosphere."
Dear Science Teacher
Questions are easy, answers are difficult. I do not know the correct presure "off the top of my head" although I know the number is small. The encyclopaedia on the web says the density of the sun's photosphere is about 1/1000 that of the atmosphere on the ground, and even allowing for a 20 times larger absolute temperature, this is still quite rarefied. At 10,000 kilometers you are in the lower corona, and the answer is harder still.
Since you are a teacher, I will go here into some more detail, maybe your class will be interested. The Sun is not my field, but I should know enough to explain.
Why is the Earth's atmosphere near the ground under pressure? Because it is supporting the weight of all the air above it! You go up 10 kilometers and the pressure is down to 25%, because only 25% of the air is above that level, 75% is below it. In the atmosphere near the ground, pressure goes down by a factor 2 about each 5 kilometers (or by a factor e=2.71828... every 8 kilometers--that is called the "scale height"). The number depends on temperature, so it may go up and down a bit, but you can see it decreases very fast. Above about 100 kilometers the air is so rarefied that molecules and atoms rise up and fall like thrown stones, rather than colliding constantly, and then different rules hold and the decrease is slower.
If the air were 20 times hotter (as in the photosphere of the Sun, 6000 degrees absolute against 300) the pressure would still be the same, because the weight above remains the same. The difference would be that the atmosphere would expand 20 times--"the halving distance" would rise to 100 km--while the density of the air would be only 1/20th. So with density dropping 20 times and temperature rising, the pressure SHOULD be the same.
The same rules hold in the photosphere of the Sun. See:
The gas is indeed has about 20 times hotter, trying to make the "scale height" 20 times larger than ours. However, gravity near the surface of the Sun (or what to the eye looks like one, it's really all gas) is about 28 times the gravity at the surface of the Earth, and that more than counterbalances the higher temperature. Most important, perhaps, is that the photosphere is mostly atomic hydrogen, about 1/30 times lighter than atmospheric molecules, and the scale height is larger by a corresponding factor. If you put all this together (and ignore temperature changes in the photosphere) you get a scale height of the order of 150 km and a "halving distance" of about 100 km.
That is larger than in our atmosphere--but the Sun is much bigger too, and you realize that by the time you reach 10,000 km, something HAS had to change. As a matter of fact, the photosphere is only about 400 km thick. For the next 5000 kilometers you are in the chromosphere--hotter and very uneven, but still decreasing fast in density, and at 10,000 kilometers you are in the lower corona, temperature of about 1.3 million degrees, and who knows what pressure and density!
I have looked for some references and found on the web an article
which claims to observe at 1.03 RS (solar radii; that is, at about 20,000 km above the surface) a density of 180 million electrons per cc (and if that is the density of atoms, that is more rarefied than any laboratory vacuum!) and a "nonthermal" velocity of 33 km/sec. Let me try and check it. Earth is about 200 RS from the Sun and is immersed in the solar wind, density about 10 per cc and velocity about 400 km/sec.
If the flow is the same in all directions, in each second, the flow fills a spherical shell of radius 200 RS and thickness 40 million cm, containing
10 . (12.56 [200 RS]2) . (40 000 000) atoms
= 10 . (12.56 . 40000 RS2) . (40 000 000) atoms
The atoms are of course ionized, and we should really express RS in centimeters, but as will be seen, that is not needed.
If the flow is continuous, and the 33 km/s refers to a radial outflow, the same amount of material leaves each second a spherical shell of thickness 33 km near the Sun, with a radius near 1 RS. If D atoms/cc is the density in that shell , then
10 . (12.56 . 40000 RS2) . (40 000 000) = D . (12.56 . RS2) 3 300 000
Canceling 12.56 . RS2 . 1000 000 (which is why the exact size of RS was not needed!)
16 000 000 = 3.3 D
So D is around 5 million/cc, 36 times smaller than the amount claimed. If the outflowing density is 180 million/cc, the outflow velocity should be 1 km/sec. It is more likely that most of the electron density is contributed by atoms (or rather ions) rising and falling back, like thrown stones. In that case the density D and outflow velocity V remain both uncertain, though the product DV obeys the above equation.
Your message was titled "coronal plumes." If you have not yet seen the 1999 eclipse photograph of the corona, look at
Did Tesla extract free energy from thin air?
This may be a dumb question.....Nikolai Tesla supposedly powered a electric car with a set of vacuum tubes and a antennae set up, which he claimed tapped power from the "aether ." Do you think he actually accomplished such a feat with this kind of set up ? It would seem logical that the massive energy from our planet / universe could be tapped in some way.
Long ago our post office had a sign in its display window: "If something seems to be too good to be true, it probably is."
I do not know too much about Tesla, but he had eccentric ideas, and one of them, I vaguely recall, was to tap energy from the atmospheric electric field. There exist relatively large vertical voltage differences across the atmosphere, the residual effect of atmospheric electric processes in distant storms, the same as are responsible for lightning.
The reason they can persist is that the atmosphere is a very, very good insulator. Electric power companies string their cables in the air and never worry about any leaking away! To get any useful power from that voltage (as Tesla may have wanted) you need a closed circuit, part of which runs in the atmosphere, and the air would not allow it to flow there.
I never heard about an electric car being run from this source. And although, when you stand, the voltage of the air around your head may be (say) 300 volts above the one at the ground, you never feel anything, because the tiny electric charge involved is immediately drained away by your conducting body, essentially short-circuiting the voltage to zero.