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They say, Mercury polar areas have temperatures of around 0C.

What other areas in the Solar System (on the planets or on the moons, on the surface or under) in what seasons have temperatures suitable for human beings?

Let's say, within the range of -50C to +80C, for the duration no less than a week. Let's say the pressure is within the range of 0 to 100MPa (1000 atm).

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    $\begingroup$ I think that the main missing ingredient with this questions is not defining environmental pressure limits. E.g. there might be liquid water pockets on Europa, Enceladus, and possible saltwater ocean 200 km below Ganymede's surface. $\endgroup$ – TildalWave Aug 28 '13 at 1:46
  • $\begingroup$ Okay, since the question comes up, I added a range for the pressure. $\endgroup$ – horsh Aug 28 '13 at 15:34
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I think the best answer here doesn't even rely on specifics of planets and other bodies. The basic radiative physics of the universe do the job. So let's look at the different ways we could produce room-temperature elsewhere in the solar system.

Criteria 1: Rotating blackbody in sun orbit

If something (like an asteroid) is rotating fast enough, then the temperature is pretty well evenly distributed over its surface. So if you could burrow just under the surface (strange hypothetical, I know), then the temperature you see there will be dictated by the equation for a blackbody's temperature in orbit around the sun. My version of this equation:

$$ T_s = \left( \left( \frac{R_S}{4 R} \right)^2 T_S^4 \right)^{1/4} $$

Here capital S is the sun and lowercase s is for the surface values. R is the distance from the sun.

I can walk you through the logic behind this in more detail if needed. But basically, you assume the temperature of space is zero, which covers the majority of the sphere around the body. Then the fraction of area the sun covers is the visual area of the sun divided by the area of the sphere on which the sun lies, which is where the factor of 4 comes from.

The value of this equation is about -78 degrees Celsius for Earth's location. Now, if I set this equation to be equal to room temperature I can get a distance from the sun. I find that at about 0.44 AU from the sun the surface temperature will be equal to room temperature.

That means that it'll be difficult to be cool enough to be livable closer than about 1/2 AU from the sun. That can only happen with constant shielding. I don't believe that any bodies exist which are truly tidally locked with our sun, so that limits it to polar caps.

Criteria 2: Internal heat production

According to the question, any place even inside a body is sufficient. Internal heat production keeps the insides of large bodies toasty even if its far from the sun. You could derive the equation for the internal temperature, but I'm lazy, so I'm copying from a book. Here, $a$ is the radius of the body (which we assume is spherical), and this is the equation for the temperature inside it.

$$ T(r) = T_0 + \frac{\rho H }{6 k } \left( a^2 - r^2 \right) $$

$$ T(0) \approx \alpha a^2$$

If I assume any other body is made of the same stuff Earth is, then it has the same thermal conductivity and heat production term. That means I can just use values for Earth to find that coefficient and not worry about the specifics. See, I am a very lazy physicist. Note that the temperature of the center of the Earth is the same as the temperature of the surface of the sun.

$$ \alpha = \frac{ 5700 K }{ R_E^2 }$$

If something is far from the sun, we can use this to find the minimum size needed to have a livable center temperature.

$$ R = \left( \frac{293}{5700} \right)^{1/2} R_E = 1,500 km$$

So any moon or asteroid with a radius larger than this has some room temperature area inside it. The pressure would be too high though.

How many are there

http://en.wikipedia.org/wiki/List_of_Solar_System_objects_by_size

According to that, there are 14 objects that meet criteria 2.

Criteria 1 includes basically all asteroids around Venus orbit. That could be a million, because there are lots of small asteroids. I hope you weren't expecting a list!

If you combine both criteria it will be many more. The pressure requirement given combined with temperature is simply way to complicated to address as a blanket query. You can ask specifically for each body.

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