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Can I have a glacier on a tidally-locked shallow-sea planet?

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I have a planet that is tidally locked to its sun.

The ocean is shallow (a few hundred meters) and was artificially created in the past by harvesting the system's Oort cloud or outer-system ice asteroids (machines that autonomously operated over centuries to re-direct ice bodies at the planet) "“ a terraforming process I'll call "ice bombardment".

Backstory: This world was created for a utility purpose (1 of hundreds), and over the centuries has been abandoned (political or economic powers have long-since shifted). The pretext is that large interstellar ships were sea-vessels, as opposed to "parking" in orbit. It is not hard sci-fi, but the biggest "handwavium" in the story is economics (the Great Wall and the Pyramids were built even though the economics don't make sense). None of this backstory will be discussed.

I realize a tidally locked planet will have a low magnetic field (if any), and this ocean will eventually evaporate. I need water covering the planet, except for a glacier on the "north" pole. The glacier is large enough that its weight has uplifted a scattered ring of small islands.

Is a glacier possible on a tidally-locked, shallow-sea planet? What kind of atmosphere/weather conditions would the planet allow on the sunny side? I have researched tidally-locked, ice, shallow-sea, and "eyeball" planets, but I'm not sure I can have mostly ocean and a glacier too (it seems logical to me but I'd rather be sure).

Bonus question: could I allow for bio-engineered oxygenation? I don't want a perfect atmosphere, it is intended to be an artificial world in decline.

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This post was sourced from https://worldbuilding.stackexchange.com/q/128596. It is licensed under CC BY-SA 4.0.

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Can I have a glacier on a tidally-locked shallow-sea planet?

Yes.

One of the outer system planets, somewhat like a large Jupiter could be a small star:

It takes a little over .08 of a solar mass for a hydrogen-burning star to form

That's roughly 80 times the mass of Our Jupiter, which itself is 320 or so Earth masses. It has an orbital perion of just on 12 Earth years see here.

If every year (or so) your planet was in a position to be slightly warmed on it's dark side for a few months by enough to kick off the cycle of evaporation and re-deposition - then yes it would seem possible by this means.

As to (Bio-) engineered oxygenation - I'd add the possibility of harnessing geothermal energy on the dark or light side - wherever it's available, cracking the water, using the hydrogen as a fuel or locking it up in plastics production - freeing the oxygen.

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