Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 28/02/2012 17:14:38
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How does the Earth's crust protect us from the heat of the mantle below? And how thick would a crust need to be in order to walk on the surface of the Sun?
Asked by Paul, Woldingham
Visit the webpage for the podcast in which this question is answered. (http://www.thenakedscientists.com/HTML/podcasts/show/20120226/)
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We answered this question on the show...
Dave - The interesting thing about this question is that it doesn’t particularly matter what the crust is made out of. What's really important is how much power is coming out of the Earth every second. The Earth is essentially a body sitting in a vacuum and there’s an equation which relates the temperature of that body to the amount of power it can lose per square metre. The Earth is losing actually only about 0.1 watts per square metre from geothermal sources over the whole of the surface and this means that if it was just sitting in the middle of space with no Sun anywhere near it, you can work out the temperature it should be and it should be at about – 239ºC, but it’s not. That's because the Sun is shining on it and heating it up all the time.
Now you also asked how big the Sun would have to be, how thick a layer of crust it have to be over the Sun in order to get it down to the temperature we could walk on. I used the same equations. I said that you'd probably be able to walk on something at about 60ºC. It might hurt but it’s just about possible. A body at about 60ºC can lose about 664 watts per square metre in one direction. If you work out the size the Sun would have to be to be losing heat about that rate, it’s about 213 million kilometres radius.
Chris - That's way bigger in Sun is at the moment. That’s outside well beyond the orbit of us!
Dave - Yes, so the Sun would have to be enormous and actually, it doesn’t matter what insulation you put in there. If you leave the Sun for long enough, it would be pumping out that heat all the time and that’ll get to the surface. In fact, if you insulated the Sun, it would probably increase the rate of reaction and will get even hotter and increase the power released, so it will actually probably be even hotter and need to be even bigger. So, yes rather inplausible I think!
Chris - In Star Trek, they talk about a Dyson sphere where people create a structure around a star in order to capture all of the energy coming out of the star and do various nefarious things with it. But that would mean you'd basically end up having to contain something that would be 200 million kilometres across then if you allowed it to expand? You'd need something huge!
Dave - Yes. This was, I think invented by Freeman Dyson who was looking at if you took the limit of technology and you were staying in one solar system, what would you do to it? How could you extract all the energy out of the star? If you want to collect all that heat, you then have to get rid of it at a sensible temperature so you would need something out at about the orbit of Mars, radiating outwards. It would be absolutely immense, and an incredible technology needed to do it.
Chris - I wonder how much material you would need to make a sphere as big as that in the first place.
Dave - Immense amounts and just the physical strength of a hollow sphere that size is, I think completely implausible.
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Apart from considerations of temperature walking would be rather difficult as the gravity is 27 times that of the Earth
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There are a few big assumptions here.
One, that the shell is completely engulfs the sun, and thus one can only radiate energy outward.
Consider the Planet mercury. It has a Surface Temperature ranging from −183 °C to 427 °C. (http://en.wikipedia.org/wiki/Mercury_(planet)) The reason it is downright chilly on the side facing away from the sun (slowly rotates), is that much of the heat absorbed by the planet is radiated back on the same side as the sun, rather than absorbing it through the planet.
Our best triple junction solar cells are about 40% efficient, and could effectively reduce the energy received at any one spot by 40%. Of course, electricity generally gets turned back into heat in one way or another. But, one could absorb significant amounts of energy from the sun using solar cells, and thus decrease the distance from the sun.
The last assumption is of a uniformity of the crust.
One could presumably design a shell with a non-uniform distribution of matter. For example, have heat pipes leading away from living quarters, and then insulate with something like silica aerogel (http://en.wikipedia.org/wiki/Aerogel)that would insulate to about 1,200°C or 2,192°F.
Also, keep in mind, that to step anywhere away from Earth, you will need a breathable atmosphere. I.E. a suit... or something which could increase one's protection.
I'd put the maximum temperature of a static structure near the sun as being the melting point of Tantalum hafnium carbide (Ta4HfC5) 4488K (4215°C, 7619°F). Obviously any "shell" would be insulating, and could actually increase the temperature of the sun. But, one could design a structure, probably not that thick that would protect a person from that heat. Maybe a multi-layer heat shield like the JWST. Radiate heat in some directions, just not in all directions.
Also, while one can calculate the radiation of heat per square meter, that is assuming a flat/spherical radiator. To some extent, one could radiate heat with a convoluted heat sink to increase surface area. Would it be effective in a vacuum?
Anyway, calculate the distance from the corona where the temperature reaches 4215°C, and one gets a good approximation of how close a static structure could be. Perhaps a structure with some form of dynamic cooling could get slightly closer.