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I am trying to design a world where one pole is very cold, and the other is very hot. I don't mean that there would be instant death in either, but it is colder than our South Pole on one end and warmer than our equator on the other. I don't know if this is possible. Is there a way (maybe incorporating $n$ stars) that this situation could be possible? Any ideas?

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    $\begingroup$ Welcome to the site, Alex. By chance, have you heard of Uranus? Might be a good starting place. $\endgroup$ – Frostfyre Mar 31 '16 at 21:03
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    $\begingroup$ Does it have to be the poles? Have you considered a tidally locked planet? That would have the same effect — one side of the planet always significantly warmer than the other. worldbuilding.stackexchange.com/questions/358/… $\endgroup$ – ghoppe Mar 31 '16 at 22:53
  • $\begingroup$ Wouldn't that be like our planet. The average temperature at the South Pole is -76F in winter and -18F in summer - that is cold. The average temperature at the North Pole is -40F in the winter and 32F in the summer (relatively warm) $\endgroup$ – emory Apr 1 '16 at 1:16
  • $\begingroup$ @emory, that planet isn't like anything our planet has ever seen. On Earth, the tropics stay in pretty much one band around the earth. On this planet, the tropics are continually migrating as are the arctic zones. It's really trippy. $\endgroup$ – Green Apr 1 '16 at 3:36
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    $\begingroup$ @Alex, I found this question/answer over on EarthScience.SE. It appears to address most of the climate questions for this kind of planet. earthscience.stackexchange.com/questions/2498/… $\endgroup$ – Green Apr 1 '16 at 21:56
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Make the axial tilt of the planet be parallel to its orbital plane

Uranus does this already with an axial tilt of about 97 degrees off orbital plane though this isn't a great example because Uranus is just cold all the time. All it's a gas giant while the OP is implying a rocky planet.

Torque required to keep the hot pole pointing towards the star

The trade-off to this approach is that without a source of torque to keep the hot pole pointing towards the star, the poles will alternate between extreme heat and extreme cold as the planet orbits the star. While this sounds a bit counter-intuitive, try it with a gyroscope. Pick an object to represent the sun. Spin up the gyroscope then suspend it from string. Walk all the way around the "sun". You'll notice that the gyroscope continues to point in the same direction, not towards the sun. To get it to always point towards the sun, you'll need to move it by hand.

Temperature Profiles

This is going to be a very interesting planet to build an ecosystem on. The sun will always move from North to South.

The North and South hemispheres will always alternate between extreme hot and extreme cold. Just like on earth, the equator will always receive sunlight though being on the border between the two temperature extremes will make for very interesting living. How fast the planet rotates along its axis will have a huge influence on the ambient temperature. Too slow and everything freezes in the winter. Too fast causes other problems.

There is no comparable climate zone on earth to what this planet will experience. In some respects it is close to the Arctic climate zone in that there are wild temperature swings between summer and winter but different in that summer at the poles will get the equivalent of equatorial solar radiation for the entire day.

The sun is always up until it dips below the horizon, thus bringing on winter. Astronomers on this planet will notice the gentle spiral of the sun as the year goes by.

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    $\begingroup$ or you could have like with the moon and Earth, the rotation of the planet being exactly the time it takes to orbit around the sun $\endgroup$ – Auberon Vacher Mar 31 '16 at 21:18
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    $\begingroup$ @Jim2B Tidal locking, by definition, means that a satellite's rotational period is the same as its period of revolution. Therefore, a planet with ~90° of axial tilt cannot become tidally locked with its sun. $\endgroup$ – ghoppe Mar 31 '16 at 22:43
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    $\begingroup$ @oberron Do we consider the moon to have poles? If so, is one of them pointing at the earth? I would think that since it's tidally locked, we'd consider it either to have no poles (because it's not rotating around its axis), or for the poles to be oriented pretty much the same as the earth's (since it's rotating around them every 28 days to keep one side pointing at earth). $\endgroup$ – BrettFromLA Mar 31 '16 at 23:20
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    $\begingroup$ @AlexJohnson Making this a water giant would actually be very helpful. On earth, the Hadley cells that move equatorial heat towards the poles depend largely on water temperature. If your planet has lots of water then there's plenty of opportunities for heat distribution. There isn't any such thing as a permanently cold pole on this planet as the axial tilt makes each pole alternate between hot and cold. The equatorial regions would be a better place to put habitable land masses as the temperatures will be more moderated but don't forget that everywhere on this planet has 6 months of darkness. $\endgroup$ – Green Apr 1 '16 at 14:12
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    $\begingroup$ @AlexJohnson Tidal locking can't occur in a scenario with this much orbital tilt. If you want to make it habitable, tidal locking makes your job much harder. $\endgroup$ – Green Apr 1 '16 at 14:29
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Have you considered a Sitnikov planet?


Image courtesy of Scholarpedia user Christoph Lhotka under the Creative Commons Attribution-ShareAlike 3.0 License.

A Sitnikov planet moves on an axis, perpendicular to the orbital plane of two binary stars. It oscillates along this axis, gradually moving up and down. While it's on one half of the journey, one pole faces the two stars while one faces away, and while it's on the other half of the journey, the poles experience the opposite temperatures.

Here's the planet's height above the orbital plane as a function of time:


Image courtesy of Scholarpedia user Christoph Lhotka under the Creative Commons Attribution-ShareAlike 3.0 License.

In this case, the eccentricity of the stars' orbits is 0.3, the initial height is 2, and the initial velocity is 0.

The oscillations will also be evident in the changes in heat on each pole. The equatorial regions will also experience oscillations, but not as extreme as at the poles.

Some things to know about the Sitnikov problem:

  • It's relatively unstable.
  • It's unlikely to form in nature.
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  • $\begingroup$ While cool, I don't see how this solves the OP's question any better than a simple sideways axial tilt like Uranus has. $\endgroup$ – Ilmari Karonen Apr 1 '16 at 3:14
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    $\begingroup$ @IlmariKaronen It's not better, but it's still a valid alternate solution. $\endgroup$ – HDE 226868 Apr 1 '16 at 12:49
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Are you going to measure the temperature at the planet's surface? It is required for your planet's pole to be warmer than OUR equator but not ITS OWN equator? If so, maybe this could work for you.

You don't need any special orbit for your rocky planet, just make it closer to its star. This way both poles will be warmer. In fact, the whole planet will become warmer, so now we have to work on freezing one of the poles.

VOLCANOS

Yes they are boiling magma fountains which can heat up the surrounding nearest area, but hey throw something more valuable to your interests: ASHES

Place a super-active volcanic area in that pole and make your volcanos to throw up to the air tons and tons of ashes for centuries or even millennia. This way, you will get a NUCLEAR WINTER that will block the star's light and cool down the surface's temperature.

Make sure that both your volcanos throw up enough ashes (continuously or cyclicly) and your winds flow sustain those ashes in the air and near the pole to get an quasi-permanent effect and don't spread the ashes to the rest of the planet.

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A Celestial body can have a complex rotation, in other words Earth rotates on its axis but there's a phenomenon called the precession of the equinoxes. The direction that the North Pole points actually rotates over time but very slowly.

I'm not a physicist but my guess is that in order for this to work on something like a yearly scale with one pole always pointing toward the solar body firstly the procession would have to exactly match the length of the year which is almost completely unlikely unless it was engineered somehow and the mass of the planet would need to be much different then a normal planet. Perhaps it would work with something like a black hole which spins very quickly and Could Have A procession short enough to be equal to the length of its year.

Note that Earth's precessional cycle take several thousand years.

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Basically, what Green has already stated, but with some modifications in the idea.

Axial Tilt

I guess you are already familiar with the idea of axial tilt, but let me still put it here to reassure it.

enter image description here

Consider that all these planets are circling their stars in a horizontal orbit. The leftmost planet will get equal and very little light on both poles all year round (it would be sunrise forever at one pole and sunset forever at the other pole). For the second (Earth-like) planet, for half the time north pole will slightly face the sun and for the next half, the south pole will face the sun. In the rightmost planet (this is how Uranus is), the poles will undergo extreme seasons. Summers and winters would both last for half a year (just like Earth's poles) but since the poles of this planet would be almost directly facing towards or away from the sun, the day and night (summer and winter) would be very severe.

Green has suggested to make the axial tilt parallel to its orbital plane. This means something like the rightmost planet where the poles face the sun directly at 90°.

If your planet has an axial tilt less than 45° (left and center planets), the pole facing the sun would get less sunlight than the equator. At a tilt of 45°, the pole and the equator would have equal sunlight. For an absolute tilt of 90° (slightly more than the right side planet), the pole would directly face the sun and the equator would be at the twilight zone (eternal morning/evening scenario).

Tidal Locking

Normally when a planet orbits around its star, different sides of it face the star around different times (this is what causes seasons). However, sometimes one side of a planet gets permanently fixated towards the star and there is always mid-day time on this side (the opposite side has an eternal night). This is known as tidal locking.

If you want one of your planet's poles to always face the sun (and the other pole to be always away from the sun) you should consider making your planet tidally locked with your star, with an axial tilt of between 45° and 90°.

However, keep in mind that scientists have only discovered planets orbiting very close to their stars to be tidally locked. Planets further away from their parent stars do not get tidally locked.

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    $\begingroup$ You can't tidally lock a planet that is rotating around an axis in the horizontal plane. The planet is essentially a giant gyroscope. The torque required to keep the pole pointed at the sun is (a) enormous, and has to come from somewhere, and (b) likely to cause the planet to shatter. $\endgroup$ – pojo-guy Apr 1 '16 at 2:49
  • $\begingroup$ @pojo-guy: true that. You can have the planet tidally locked and rotating when the axial tilt is 90°. Yes, for other angles, the rotation would have to stop. $\endgroup$ – Youstay Igo Apr 1 '16 at 2:50
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Make the planet tide locked with its star. There are numerous examples of moons tide locked with their planets. The gas giants in our solar system have many such moons.

I suspect a planet tide locked to a star is a common occurence, especially if the planet is close to the star. If the star is one of the very long lived red dwarfs, the goldilocks habitable zone would be near the dwarf star.

The globe for a tidelocked body has 8 non arbitrary points and 3 non arbitrary great circles:

enter image description here

In this case the hottest region would be the near point and the coldest would be the far point. The North and South Poles as well as the right and left ear would all like on the planet's terminator. (Most call the left and right ears the leading and trailing points) The terminator would be the most temperate region.

I haven't modeled this but I suspect the weather structure would be a torus with air rising from the surface of the Near Point and sinking towards the Near Point. Convection would mitigate temperature extremes at near and far points.

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