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Right now the Earth rotates around the y-axis so East and West replace one another. What would the affect be on Earth's seasons if it rotated on either other axis?

The first is the Z axis, pointing from Earth to the sun so that South and North swap places by going through East and West. The second option is the X axis, a tangent on Earth's orbit. This has North and South flipping over the Equator.

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Just curios, is the Moon tilted too? – Hohmannfan Feb 4 at 1:08
    
@Hohmannfan If it matters, sure. – Vulcronos Feb 4 at 3:36
    
FYI there's a related question on EarthScience.SE; the resulting weather will be very extreme. – congusbongus Feb 4 at 7:36
    
You mean like Uranus? – Michael Kjörling Feb 4 at 9:55
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I edited the title of your question, to hopefully make it more clearly summarize the question you are asking. If you disagree, feel free to roll back or edit further. – Michael Kjörling Feb 4 at 9:56
up vote 13 down vote accepted

Your Z-axis and X-axis are actually the same, the axis of the Earth stay fixed in space while Earth orbits the Sun, resulting in an alternating pattern.

  • The Sun is zig-zaging over the sky in circles most places at the Earth, if you are close to the equator, the amplitude is high.
  • All places on Earth would have the Sun in zenith at least once a year.
  • All places except for the equator is going to have a dark season.
  • Midnight Sun at least once a year in all locations, except for the equator that has two seasons of day-and-night twilight.
  • Actually more overall solar insolation of the poles than the equator, making them the warmest region of Earth.
  • Almost all stars are visible from all places on Earth during the year, not just limited to a southern or northern hemisphere.

Illustration of the Sun's motion across the sky:

weird

In other news, the magnetic field is screwed up, so we are going to have aurora and cancer everywhere.

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The pattern of the Sun is even weirder than I thought! – Hohmannfan Feb 4 at 1:21
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I don't agree with the magnetic field being screwed up. The geodynamo is coupled to the axis of rotation of the Earth; averaged over geological timescales (~10000 years), the magnetic dipole is parallel to the axis of rotation. Sure, there's would be a difference to the current magnetic field, but it likely would still protect us from the solar wind. – user15078 Feb 4 at 7:53
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I still don't understand: are you saying that a different orientation of the axis/dipole with respect to the Earth's motion would cause the dipole to flip twice a year with respect to the axis, or are you saying that the magnetic field won't provide any protection at two particular times of year because the dipole is oriented "wrong" with respect to the Sun at those times (presumably when the solar wind is shooting straight down either pole)? Or something entirely different that I'm missing? – Steve Jessop Feb 4 at 14:02
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@magnetometer I was perhaps a little unclear, the poles does not switch place, as you say, but the axis seems to rotate relative to the Sun. That means that the magnetic poles are going to point directly at the Sun twice a year. Not a god idea. – Hohmannfan Feb 4 at 18:48
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Where is your image from? – Samuel Feb 4 at 18:58

Tilting the Earth's axis by 90 degrees will have the same effect on the climate as Uranus, with alternating poles having extended "summers" and "winters" while the equator will be in twilight during this time. In the "spring" and "fall", the poles will be dark while the equatorial regions will be in sunlight.

Uranus orbital path

Overall, because of the size and orbital period of the Earth, I think this will suppress the formation of ice caps and polar regions. Since there will be sunlight 3/4 of the year striking both poles, the period of total darkness will be rather short, and the Earth's atmosphere and oceanic currents will probably provide enough heat to keep the region simply covered in snow rather than ice caps.

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The other two answers address the "rolling" scenario quite well, but I'd like to point out one glaring error you made in your reasoning: the Earth isn't rotating along the Y-axis. It's rotating on an angle.

Now, of course, you know that. But the important point is that this causes the seasons. If Earth was rotating exactly around the Y-axis (with respect to the orbital plane), there would be no difference in climate due to orbital position.

As you let the rotation axis fall away from the Y-axis, you get more and more seasonal weather, up to the point where the rotation is aligned with the orbital plane (it doesn't matter in which direction - that's just an offset to when each season starts, but the effect is the same).

For additional points, changing the rotation rate can give you more to work with. If a day takes half a year, it's going to have a huge effect on the seasonal variations - it might be interesting to explore a scenario where the rotation is a bit more tilted and slowed down. Venusian weather and climate is pretty interesting, in part due to its slow rotation and massive atmosphere; while the planet's day is longer than its year, the clouds make the trip around in measly four Earth days.

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I guess life would be pretty much constrained to the equator regions. However, during the periods when the poles points towards the sun, the very hot sunward climate will very violently clash with the very cold climate on the other hemisphere. This is unlike the current polar climates - while we currently (in real life) also have a six-moth summer period at each pole, the shallow angle at which the sun provides heat and illumination is about nothing compared to the situation where the pole points directly at the sun. Imagine tropical climate there, but not for half a day with a cooldown in the night, but with heat building up increasingly for several months.

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