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Take the earth-moon system. Shift the moon's orbital plane about 90 degrees so that it is passes over both poles.

What would the tides on this world look like?

Sub-questions:

  • What would the cycle be near the equator?
  • What would the cycle be at the poles?

Note: While the moon is near the equatorial plane, the tides would be earth-normal, with a 12 hour period.

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It would not make much difference. The ocean is interrupted by land and the bulge can’t just travel around the planet like the common illustration shows. It runs into the land and then what? Note that the tide is not a simple clock at all but takes a complex formula to predict.

The tides are formed by multiple gyres of water sloshing around the oceans, like trying to walk with a cakepan filled with water. It has a natural period and is pumped by the actual tidal force, like a kid's swing toy is pushed once per cycle or pumped by the kid's slight shift in center of gravity.

Making the moon go pole to pole would not change that: the oceans would contain bulges that slosh around and can’t get out, and would develop a pattern of being “pumped” by the daily tidal forces. The details would be different, but I’ll bet the same formulas would apply, just with different parameters measured.

Ah, a difference is that the daily force would shift, and when at right angles would not be affecting that gyre hardly at all. So it will add a monthy intensity cycle, and increase the complexity of the formula at any particular harbor.

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  • $\begingroup$ It's more than just that. If the earth was not rotating, then the motion of the moon would cause the earth to rotate in the same plane as the moon. The complex rotational effects would build over a long time. $\endgroup$ – Lacklub Mar 23 '16 at 18:05
  • $\begingroup$ Right, instead of slowing down as is the real case for us, the friction would make the axis precess! That's the opposite case as now, where the moon keeps the Earth's axis from changing due to outside peturbations. $\endgroup$ – JDługosz Mar 23 '16 at 18:08
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    $\begingroup$ On my initial read, i didn't really agree with your statement. Reading it now though, the "sloshing gyres" description clicked and I see, and agree with, what you are saying. $\endgroup$ – Michael Richardson May 25 '16 at 14:59
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This is not a stable configuration. Starting from a polar orbit, the Moon's orbit around the Earth would be stretched out (its eccentricity would increase to 1) until it collided with the Earth. This is a nice example of the Kozai-Lidov effect (see here: https://en.wikipedia.org/wiki/Kozai_mechanism).

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  • $\begingroup$ A more elaborate version was later posted here. $\endgroup$ – JDługosz Apr 30 '17 at 6:28

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