A person is falling toward the sun. Is there a distance at which the sun would warm their body to a comfortable temperature such that they could survive at least the temperature part if they were naked? (I’m assuming that the radiation would be a serious problem, if not immediately fatal, and obviously they would have to have an oxygen source.)
Follow-up question: with no atmosphere to radiate the heat, would the part of their body facing the sun be nicely warm, but their back be frozen solid?
Very simple answer: if you move from a distance at which received radiation is insufficient to keep you warm to one where it’s excessive, you pass through one where it’s just right.
An atmosphere distributes heat by conduction and convection, but not much by radiation.
You’d have to be a very long way away just to prevent overheating. Further away than the earth, at least - imagine you’re naked on the beach in the full sun on a summer’s day, but without any convection to get rid of the heat. And no cold beers, either.
We can use the Stefan-Boltzmann law to calculate this, at least approximately. Let’s say that we want our astronaut’s surface temperature to be about 30 C. As noted above, the answer is going to depend on whether our fearless astronaut is rotating or not. If he’s not rotating, then his Sun-facing side will come to an equilibrium temperature of 30 C when he’s about 1.7 AU from the sun. (His back-facing side, meanwhile, will be pretty damn cold.) On the other hand, if he’s rotating, then he loses energy to radiation much more quickly, and so he needs to be closer to the sun; assuming the ratio of his total area to cross-sectional area is about 3, he’d actually be pretty comfortable around Earth’s orbit.
IIRC, the temperature at about Earth orbit away from the sun is about 300K, so you’re already at about the right place-temperature wise. If you spin to make sure you heat evenly, you’ll be okay.
Of course., you’ll be getting lots of UV, including hard UV from the sun – that’s usually filtered out by the atmosphere. Plus particles from the solar wind that the magnetosphere usually takes care of, and cosmic rays from all directions. Then there’s that whole vacuum thing.
But as far as the temperature goes, you’ll be just fine!
Would that matter that much? Radiating heat is the slowest way to get rid of heat. Indeed a problem for spaceships (e.g. the Space Shuttle) is to get rid of excess heat rather than freezing out there. I think a human would lose heat faster in cold air than they would in space.
Which should hardly be a surprise, since that’s where we are, after all. The Earth is an object which gains (essentially) all of its heat input from the Sun and loses energy exclusively through radiation.
Well thank you for your replies! Ignorance fought. My assumption was that at 1 AU the cold of space would suck the heat from you faster than the sun would heat you up, so I assumed you’d have to be much closer to the sun than that.
So let me get this straight - if you emerged from the the orbiting Space Shuttle buck naked, in full sunlight, you would die of a lot of things, but freezing to death isn’t one of them? (As long as you had the 1920s style rotisserie?)
Wearing a reflective surface will cause you to eventually overheat, at any distance, because if you can’t absorb radiation, you can’t emit it, either, so your body heat will just build up until it’s too much.
There should be some material that reflects and radiates just the right amount of energy to keep you at nice room temperature while you die of asphyxiation and decompression hemoraging. Assuming steps were taken to maintain an pressure and oxygen, a material with the proper thermal conductivity should allow you maintain any position relative to the sun so that the cosmic rays can kill you more slowly, or turn you into a potential member of the Fantastic Four (Five?).
You can tweak the thermal conductivity, yes — but you’re essentially talking about insulating our fearless/hapless hero. It’s not possible to maintain an arbitrary temperature indefinitely solely by tweaking the amount of reflection and the amount of radiation from the outer surface; the two quantities are related. Specifically, they’re equal due to Kirchoff’s law of thermal radiation. So an object that absorbs less sublight will also radiate its heat less quickly, and an object that absorbs more sunlight will radiate its heat more quickly. The two effects cancel out, and the equilibrium temperature ends up being independent of the surface properties. All you can do is delay the inevitable for longer & longer.
What you can do is to have a nonuniform surface: Something that’s highly reflective on the side facing the Sun, but black (across a wide spectral range including infrared) on the side away from the Sun. In principle that could keep you at a comfortable temperature at any distance, though obviously there will be practical limitations (you can’t make a perfectly reflective surface, for example).
