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How long will a 400 km wide 30 km deep pit (trench or crater) with a relatively shallow (for stability) gradient of slope of 20 degrees from the edge to the surface of the planets crust be expected to last on Mars before geological & climate processes close it.

Rock plasticity under the weight & pressure of the rocks above is one potential concern that's been identified for me, I think only 30 km depth may avoid that but I'd like to be sure.

I'd prefer 41 km deep (as that should give us an atmospheric pressure roughly equivalent to a height of 6 km on Earth where our highest plants grow) & with an average crust thickness of 50 km thought that should be OK .. until it was suggested to me anything lower than 30 km would slowly fill back up from the bottom to a depth of 30 km, but at least 30 km should still put us below the Armstrong limit.

How long could we expect the structure to remain viable & retain a depth of at least 29 km?

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    $\begingroup$ At what point is the structure not considered "viable"? When it's 29km deep? When it's 1km deep? When all traces that it was ever there have vanished? At a very pedantic level, a 30km deep hole isn't 30km deep as soon as some Martian dust settles at the bottom, but that's probably not what you're looking for. $\endgroup$ – Nuclear Wang Nov 27 '19 at 16:04
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    $\begingroup$ @overlord-ReinstateMonica : Because the more left of centre questions tend to get a better reception here & I'm reasonably comfortable in this forum :) but yes Physics might be an appropriate venue (& maybe I should have gone to have a look see if it is b4 posting) but I'm pretty sure Astronomy isn't. $\endgroup$ – Pelinore Nov 27 '19 at 16:09
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    $\begingroup$ I guess it is quite literally building a world... $\endgroup$ – thanby - reinstate Monica Nov 27 '19 at 16:18
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    $\begingroup$ This question is on the edge for me between worldbuilding and physics/engineering of the real world. I voted to close it, but it is on edge. It is exactly the kind of question that I want to encourage moving to other SE sites because there it will be among more similar questions. But the specific question is one that it is hard for me to propose another SE site. $\endgroup$ – SRM Nov 27 '19 at 18:25
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    $\begingroup$ I do want to say that anything we build on any other world tends to have its lifetime limited some by nature but more by how long it takes for some other of us to destroy it. The hole will last until someone else fills it in! $\endgroup$ – SRM Nov 27 '19 at 18:26
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Since nothing exactly like this exists on Mars, let's look at the best real-life example of what you're describing: A crater.

On Mars

Hellas Planitia is one of the oldest and largest craters on Mars. It was formed during the Late Heavy Bombardment, which started around 4.1 BYA. At more than 7 km deep, it's one of the deepest craters in the solar system.

This crater has survived nearly all of Mars' volcanic history, atmospheric conditions, erosion from wind and water, has even been dumped into by a few volcanoes, and is still this large after billions of years. Assuming you maintain a similar grade (maybe even steeper depending on your timeframe), your pit could theoretically last as long as the history of the planet.

Since you also mentioned atmospheric pressure, it's worth noting that at the bottom of the crater the atmosphere is already 103% more dense than at the surface of the surrounding topology.

Edit based on comments: Since nothing of the dimensions described exists in the solar system, let's check out some examples of rock slopes here on earth.

Above Ground

Trango Towers in Pakistan is home to some of the steepest rock faces in the world. They range up to more then 7 km tall, and have nearly-vertical drops, so the downward pressure of gravity is much more significant than the outward pressure of the rock. That being said, you're talking about something below the surface, so let's look at perhaps a closer example.

Below Ground

The Mariana Trench dips down to 11 km below sea level, over a third of the value we're targeting, so it should be a decent model for how these things work on a large scale. According to studies of the trench, the deepest parts still maintain an incline of up to 34 degrees in places. Consider that the trench is entirely submerged, is subjected to massive erosive currents, and violent earthquakes, and it has survived for 180 million years and counting.

In Summary

As long as you stick to a gradient of ~30 degrees (to be very very safe), I think any depth that does not break the crust would be fine. Just be careful to also consider temperature at that depth, as you'll be getting close to the mantle.

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    $\begingroup$ We can certainly use the Hellas Planitia as plausible argument for erosion from weather events & infilling with dust to be an unlikely problem but it's only 7 km (less than 25% of the target depth), so less useful for saying rock @ the bottom of the crater wall won't be squeezed into it like putty by the weight of all the rock above it. $\endgroup$ – Pelinore Nov 27 '19 at 16:50
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    $\begingroup$ I expanded the answer a bit to cover that for you. It's difficult to give an exact answer, because nothing like this exists, so I did the best I could to extrapolate from what we do know. $\endgroup$ – thanby - reinstate Monica Nov 27 '19 at 18:38
  • $\begingroup$ There is a difference between 11km and 30km - mantle pressure. The main problem here is 400km width - the center would rise or have a large vulcano for shure. Mars is not that hard on this, but 10-20 km heght difference with avarage is a max even for it. $\endgroup$ – ksbes Nov 28 '19 at 7:10
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    $\begingroup$ @ksbes Do you have some kind of source for your information? Part of the problem I had was finding any examples of a hole that deep, let alone what would happen to it. $\endgroup$ – thanby - reinstate Monica Nov 28 '19 at 13:22
  • $\begingroup$ @I've read some papers on "hard" geology (in russian) about plate movements and why planets are spherical. Since I am not a specialist - almoust all I can undestand is in my comment - planets can't go away from spherical shape on large scale. By definition of a planet. $\endgroup$ – ksbes Nov 29 '19 at 6:44
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Valles Marineris reaches a depth of 11 km, while Olympus mons reaches 25 km of height, together they make the gap you envision.

Olympus mons is thought to be 200 million years old, while Valles Marineris should count 3 billion years. Therefore the lower limit for existence of such a height difference seems to be at least 200 million years.

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    $\begingroup$ OP seems to be worried about atmospheric pressure at the bottom of the pit. Unfortunately a mountain next to a valley won't increase the pressure at the bottom of the valley. $\endgroup$ – thanby - reinstate Monica Nov 27 '19 at 16:08
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    $\begingroup$ The most recent lava flows on Olympus Mons are only ~2 million years old, so I don't think you can really count the time period when the mountain was still growing for the longevity of a static hole. $\endgroup$ – Nuclear Wang Nov 27 '19 at 16:11
  • $\begingroup$ I understood the Valles Marineris to be 'up to' 7 km deep & Olympus mons to be 'nearly' 22 km high? $\endgroup$ – Pelinore Nov 27 '19 at 16:55
  • $\begingroup$ @NuclearWang : It was formed 'during Mars's Hesperian Period' that ended (@ least) 2000 million years ago & "By some estimates" the most recent eruption was 25 million years ago is what I got with a few searches? : We've only been around as a species 300,000 years or less, so 25 million would do nicely I think (any more would do very nicely), even your 2 million would do in a pinch if I couldn't get more. $\endgroup$ – Pelinore Nov 27 '19 at 18:57
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    $\begingroup$ But they're not next to each other so I can't put them together & use that to claim rock with 39 km of rock sitting on top of it won't be squeezed into any available space like so much damp putty .. the Olympus Mons on it's own can be used to show that with an adequately shallow gradient a structure of up to 22 km deep is feasible on Mars & should last for many millions of years, 8 km shy of my target but still good :) $\endgroup$ – Pelinore Nov 27 '19 at 21:00
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What I should have been looking at is the Geoid of Mars & the depth from it to the mantle

The thickness of the crust varies between 50 km & 22 km due to the Geography & features (rock layers) above the Geoid while the distance from it to the mantle should be reasonably uniform.

I presume the putative Geoid of Mars is the altitude used for measuring atmospheric density.

According to some sources the crust of Mars is 10 km thick at its thinnest points which is presumably to be found in those places furthest below the Geoid like the Hellas Planitia .. which means the mantle is around 17 km below the Geoid & may mean we can't go much deeper than 7 km without lava flows.

So the crust beneath the Hellas Planitia is probably only 10 km thick.

I found this KSP compatible Mars Heightmap

enter image description here

& this map of the topography of Mars (useful as you can zoom in & out on features)

The Interactive Mars map at the bottom of WikipediA's 'Atmosphere of Mars' page is also useful as it names features you hover the cursor on & links you directly to their page if you click on them.

What I think this means is a 30 km deep hole either pops straight through the crust into the mantle or will be just fine almost indefinitely, depending on where you dig it.

It also means we probably can't achieve a depth below the standard atmospheric pressure of Mars of much more than a few kilometers beyond 7 km without being in danger of getting magma .. the 0.168 PSI of Hellas Planitia (air pressure at the summit of Mount Everest (the highest point on Earth) is 4.89 PSI) is probably not that far from as good as we can get on Mars by digging holes .. not what I hoped.

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  • $\begingroup$ Mars has a mantle? I thought it had frozen all the way through, which is why it doesn't have a magnetic field or any plate tectonics anymore? $\endgroup$ – nick012000 Nov 30 '19 at 10:04
  • $\begingroup$ @nick012000 : iirc the lack of magnetic field is from a lack of an inner core interacting with the outer core? $\endgroup$ – Pelinore Nov 30 '19 at 19:54
  • $\begingroup$ @nick012000 Hot or cold at a certain depth the rocks should have some plasticity & eventually semi fluidity & higher temperature simply due to the weight & pressure of the rock above, if you go below a certain depth it means the rocks below will be squeezed up into any hole or crater to refill it from the bottom like so much damp putty welling into a bucket with a hole in the bottom, I'm presuming this begins at around 7 km below the Geoid in part because there is nothing deeper on Mars & so many craters near this depth seem to have volcanoes in the middle (where they're deepest). $\endgroup$ – Pelinore Nov 30 '19 at 20:37
  • $\begingroup$ @nick012000 : Also see answers to this Astronomy SE question "What is the temperature 55 km beneath the surface of Mars?" 330° C according to the OP's chosen answer, admittedly the coolest molten rock lava you'll find flowing on earth is probably 700° C so actual lava may not result? & I should perhaps edit it, but that aside Mars is not cold all the way through, models suggest a very hot molten iron core. $\endgroup$ – Pelinore Nov 30 '19 at 20:38
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A possible side effect: displacing such huge amount of material could perceptibly shift the planet's rotation axis. It is believed to have actually happened on our Moon due to volcanism moving the material.

So it should not be done haphazardly. If this causes the artificial crater to end up closer to pole after the excavation, it will have colder climate than planned. Even worse, if the rotation axis is destabilized and starts to precess, large temperature variations. I'm not sure if planetary precession with short period of ~few years is mathematically feasible but in a story, why not.

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