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In the Chronicles of the Riddick there was planet Crematoria. Temperature during the day there was 372°C and during night −182°C. There is not much information about about this planet avaiable. Link to wikia

I think of a planet with similar condition. Let's say:
Planet radius would be around 9'000 km (Earth's is ~6'300 km)

Mass of the planet also somewhat similar to earth,so the gravity is not much higher than normal.

Planet size also will make not all surface burning during day and freezing during night, but only central part of it, since it is most affected by solar activity.

1 full day on this planet will last 96 hours. (This parameter is not strictly set)

Closer to planet poles there will be Temperate-cold climate, that allow life to exist.

Is this type of planet is possible?

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    $\begingroup$ Is the lack of atmosphere an option? If so, we might have a great chance. $\endgroup$ – John Dvorak Jul 16 '17 at 15:25
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    $\begingroup$ -182ºC is pretty cold though. $\endgroup$ – John Dvorak Jul 16 '17 at 15:26
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    $\begingroup$ I take it back. We don't have any real chance, even without atmosphere. $\endgroup$ – John Dvorak Jul 16 '17 at 15:50
  • $\begingroup$ cap of temperature at +372ºC and -182ºC can only be reached at equator. Climate could be less harsh further from equator $\endgroup$ – Markus Jul 16 '17 at 16:14
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I'm going with yes and no. Pushing the maximum temperature is easy. Pushing the minimum temperature is much harder.

I'll note some discrepancies with Crematoria first

  • Wiki quotes the top temperature of +372 degrees Celsius. But the gallery also shows that the surface is lava. Silicate lava is a little hotter than 372 degrees Celsius - by about 200 degrees.
  • On the same note, if the temperature at mid-day is 372 degrees, it won't be so early in the morning. The image shows that the edge between lava and not-lava is as thin as the terminator line, however.
  • Wiki also states a rotation speed - I'm assuming surface velocity at equator - of 5000 mph and rotation period of 52 hours. Quick math tells us that the equator is 400 000 km. That is ten times more than that of Earth. If the planet is of similar density as Earth (it would probably be even denser), the surface gravity is 10G. The reason Crematoria prisoners aren't able to escape isn't they'd be scorched before they reach the surface. It's because they would be unable to sit or stand under their own weight, and they probably have trouble breathing even when lying flat on the floor. Luckily, your planet isn't as harsh as Crematoria in this respect, it's only slightly worse than an elevator that's constantly accelerating upwards.

For our first estimate, let us look at Earth's moon. Space.com states:

When sunlight hits the moon's surface, the temperature can reach 253 degrees F (123 C). The "dark side of the moon" can have temperatures dipping to minus 243 F (minus 153 C).

Note three things:

  • The temperature range is half of what we're looking for at Crematoria.
  • In case of the Moon, we are not even looking at the temperatures of the same spot. Note that it's not one of those places that never get sunlight - those get even colder. The article later says:

    The Lunar Reconnaissance Orbiter measured temperatures of minus 396 F (minus 238 C) in craters at the southern pole and minus 413 F (minus 247 C) in a crater at the northern pole.

  • The Moon day lasts 28 Earth days. On Crematoria it's 2.

Atmosphere is pretty good at redistributing heat. Your planet shouldn't have any. I'm sorry to say, your planet won't have any life of its own, even at the poles, unless someone arrives in a spaceship. You better give them a pretty good reason - and if "scorching hot, occasionally" is your primary selling point, the humans are going to go visit Venus first. Much closer and much more scorching. Sulphuric acid in the atmosphere and a pressure of 20 Earth atmospheres complicates your prisoners' escapes even further.

So, what can you do to improve on Moon's efforts on achieving the temperature difference stated?

First a quick talk about black-body radiation, because that's your primary method your planet would be losing heat. One thing to note is that the amount of energy a bit of black-body material radiates out is given solely by its temperature. You can try to increase the surface area but then the material will be shining on itself, and it won't lose heat any faster. Real materials also aren't perfect black-bodies, so they won't be radiating as fast. The amount of energy is given by the Stephan-Boltzmann law and says that the amount of radiation is proportional to the fourth power of temperature above absolute zero.

If we look at a small patch of thermally insulated black-body material at the surface of your planet at night-time, its temperature will be governed by the differential equation $dT = c T^4 dt$ where $c$ depends on the material in question. Wolfram Alpha tells us that the temperature over time will follow the inverse cube root curve - the material cools down the much slower the cooler it is. Note that this assumes your planet doesn't melt in the sunlight - that would account for even more energy to dump as the material solidifies.

Let's pick some value of $c$, let's say 1/3, and see when certain temperatures are reached, with t=0 being set to the time when the temperature is infinite.

-182 C |  89 K | 1.41850209016283×10^-6 T | coldest temperature on Crematoria
-153 C | 120 K | 5.78703703703704×10^-7 T | coldest temperature on Moon
   0 C | 273 K | 4.91487026929606×10^-8 T | melting point of water at standard pressure
 123 C | 396 K | 1.61032836270057×10^-8 T | highest temperature on Moon
 372 C | 645 K | 3.72666930328520×10^-9 T | hottest temperature on Crematoria

Observation: getting from infinite temperature to 0 degrees celsius is ten times faster than reaching the coldest temperature on Moon. It also takes 2.4 times longer to reach -182 C than to reach -153C.

This gives us a few options:

Making the material darker won't have much effect. Going from regolith to vantablack will give you a 10% speedup. Choosing a material with lower heat capacity also helps, but I can't help with that choice.

Longer days will help. Unfortuately, you probably won't be too happy with a day that lasts as long as a month on Earth. The terminator would still be moving at an appreciable speed, so inhabiting the equator is out of the question, but someone trying to escape from a prison has plenty of time to board their spaceship.

Speaking of which, perhaps your planet is tidally locked? That could yield some pretty nicely extreme temperatures. It doesn't mesh well with the "only poles are inhabitable" part of the question, though.

Going from super-hot to just hot is quick. Going from cold to even colder takes forever. If you relax your -183C requirement a little, you can get slightly less extremely cold temperatures in substantially less time. Humanly sized lengths of days can get you to zero C just fine. This also means that the surface going from minimum temperature to maximum in the matter of a single terminator width may not have been that off, actually.

Maybe the planet is actually just a thin shell supported by a solid layer of vacuum? Less rock = less heat capacity per square meter. Such things don't occur naturally, but there could be a massive network of underground settlements that cover 99% of the sub-surface. Don't forget the "no native life" clause, however. It's also nice if the builders are gone, too, so that they don't vent heat onto our nicely freezing night-side. Fully artificial body that looks like a planet is an option, too, and lets you tweak the critical parameters arbitrarily (max. temperature by tweaking the orbit, min. temperature by tweaking the planet material).

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  • $\begingroup$ Thank you! This is even better answer, then I was hoping to. How do you think, what could be temperature caps for atmosphere to exist? $\endgroup$ – Markus Jul 16 '17 at 18:44
  • $\begingroup$ Not sure. The thinner the better. But note that with temperature differences this big, extreme winds are inevitable. Earth surface varies a couple of degrees and we already get significant amount of wind every once in a while, and it's getting even worse as the oceans get warmer... $\endgroup$ – John Dvorak Jul 16 '17 at 18:50
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Short answer would be no, and short reason would be that an atmosphere is your enemy if you want temperature extremes, but let me take this apart a bit.

  • How does it get so hot during the day? The planet has to be rather close to its primary star, or there must be a thick atmosphere that retains heat and with it probably some serious greenhouse effect, or both.

  • How does it get so cold during the night? The planet has to be rather far from its primary star, or there must be little or no atmosphere capable of retaining heat when the sun sets, or both.

As you see there are conflicting goals here. If a planet has no atmosphere it's not that difficult to achieve such temperature extremes; Mercury, for example, has

surface temperatures that vary diurnally more than on any other planet in the Solar System, ranging from 100 K (−173 °C; −280 °F) at night to 700 K (427 °C; 800 °F) during the day across the equatorial regions.

Having no atmosphere and a night side guarantees extreme cold simply because space is cold.

If a planet has a dense atmosphere, extreme heat is relatively easy to achieve as well; Venus, being farther from the Sun than Mercury, is hotter because of that. But a dense atmosphere prevents heat from escaping during the night, which is why Venus is hot all around.

If your planet has a thin atmosphere it's possible that you might have something a bit like Mars: freezing, sub-Antarctic temperatures on the night side and balmy, temperate spring-like temperatures on the day side (on the equator, at midday, in the summer). If you want to have poles with the same temperature all year round, you could posit that the planet has little or no tilt, thus eliminating seasonal variation.

In any case, as I said, atmosphere is your enemy if you want temperature extremes. It would also work against the idea of a prison or punishment planet, unless it's a crushing, toxic atmosphere like that of Venus.

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Your planet has an average density around 2.9 g/cm3, while Earth is 5.5 g/cm3. This makes the planet even less dense than Mars.

This suggest the content of Iron is pretty low, and therefore almost no iron core can be present. No iron core means no magnetic field, and no magnetic field means gas stripping from stellar wind. On top of this with such high temperatures the gases molecules would have a pretty high velocity, further facilitating the stripping. Lack of atmosphere could justify the extreme temperature differences, though. But atmosphere is needed to support life.

So, such a planet could not exist over time spans sufficiently long to support life development.

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  • $\begingroup$ But it turns out there is a molten aluminum core! 2.7 g/cm3! The magnetic field is back! Keep those gases! How about then, hmm? HMMM?? $\endgroup$ – Willk Jul 16 '17 at 23:14
  • $\begingroup$ @Will you can't have your core less dense than your crust, sorry. It's pretty close, though, so a little tweak might do. $\endgroup$ – John Dvorak Jul 17 '17 at 7:04
  • $\begingroup$ @Jan Dvorak: Si is 1 heavier than Al, but Si always has an entourage of O which reduces the mass of many minerals it comprises (e.g. quartz). Al can hang with that crew too, but can also be a loner, Dottie; a rebel. $\endgroup$ – Willk Jul 18 '17 at 14:20

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