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The enormous shield volcano that this question was based on was held up by magic or God. It presented some very interesting conditions for alternate worlds so I thought I would develop that train of thought to see if something similar could actually exist without the intervention of Gods or magic.

Assume an Earth-like world with standard atmospheric pressure, except with 95% of the water missing (less water arrived when the planet formed). So a desert world, but still inhabited as there is still some water.

Let’s be a little more conservative than the original question was. Can we have volcanoes extending 25 miles up into the stratosphere? If not, why and, if we can, roughly how high might they reasonably be expected to get (rough estimate)?

Edit: assume 25 miles above the mean planetary surface level

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  • $\begingroup$ This is not a duplicate of worldbuilding.stackexchange.com/questions/96872/… because in this question the mountain must be formed and supported naturaly not by magic. $\endgroup$
    – Slarty
    Nov 8, 2017 at 17:35
  • $\begingroup$ Is it a duplicate of this one? worldbuilding.stackexchange.com/questions/92205/… Because if not I am going to paste my answer calculating possible heights for mountains made of sapphire and diamond. Maybe my diamond mountain image too! $\endgroup$
    – Willk
    Nov 8, 2017 at 17:41
  • $\begingroup$ @Will no I don't think so. That question was asking what such a mountain would look like. I want to know if it could actualy exist. I am also suggesting a desert world because I suspect such a mountain would not be possible on an earth clone world. I would be interested to see your answer, but remember that other than the very much diminished oceans this is an earth like world $\endgroup$
    – Slarty
    Nov 8, 2017 at 17:57
  • $\begingroup$ Mountains on Earth are measured from sea level which doesn't make sense in this context. Island volcanoes are much taller if you measure from the sea floor. I think weathering plays a huge role on Earth in limiting the sizes of mountains, I don't think it's impossible for a mountain much larger than Olympus Mons to exist on an alien world. $\endgroup$
    – A. C. A. C.
    Nov 8, 2017 at 18:03
  • $\begingroup$ @A.C.A.C. Yes thank you I have added a note to the effect that it is 25 miles above the mean surface level. There probably would be a very much reduced sea level as 5% of the oceans remain, but the mean surface level makes more sense. $\endgroup$
    – Slarty
    Nov 8, 2017 at 18:07

3 Answers 3

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Here is my answer from How would a 30-kilometer tall mountain on an Earthlike planet look?

This is reminding me of your scheme for islands floating in the mantle because that is pretty much where this one ends - the ginormous diamond mountain would sink down until it displaced its weight in whatever denser material constitutes the mantle.

I found this fine math laden site which shows the maximum height for a mountain made of granite.

https://talkingphysics.wordpress.com/2011/09/08/how-high-can-mountains-be/

The density of granite is ρ = 3 g/cm3 (actually, the densities of most liquids and solids are close to 1. Lead is only about 11 g/cm3 and gold is 19.3 g/cm3). The total weight of the mountain is just the volume times density times g so: Weight W≈ ρgr2h To see when the rock will start to break, we’ll compare the stress of the weight of the mountain to the compressive strength of granite. (Most mountains aren’t made out of granite, but it should give us a good upper limit on mountain heights). The weight of the mountain is spread out over an area of roughly (ignoring constants such as π): A ≈ r2 so the stress σ the mountain exerts on the ground underneath it is: σ ≈ W/A ≈ (ρ g r2h)/r2 ≈ ρgh The compressive strength of a material is the maximum compressive >stress a material can withstand before it starts to deform.
For granite the compressive strength is σC = 200 megaPascals = 2 × 108 N/m2 so the rock beneath the mountain will start to compress when: σ = σC or ρghmax = σC. Rearrange this equation to solve for hmax yields: hmax ≈ σC/(ρg) The max height for a mountain works out to be:

hmax ≈ 2×108 N/m2/(3×103 kg/m3 ˙ 10 m/s2 )≈ 104 m = 10 km

So a granite mountain can only be 10 km. A mountain on earth which was 30 km must be made of material that is less dense, or which has a higher compressive strength.

Less dense is a nonstarter because granite is not that dense at 3, and less dense materials have markedly less compressive strength.

More compressive strength is a tall order because granite is the best among stones at 200. So not stone.

Sapphire.

Sapphire is more dense than granite at 3.98 (we will use 4) instead of 3 g/cc. But the compressive strength is 2 GPa - that is 2000 MPa or an order of magnitude greater than granite.

Plugging in these new values hmax ≈ 20×108 N/m2/(4×103 kg/m3 ˙ 10 m/s2 )≈ 754 m = maximum of 75 km

So 30 km is fine. This mountain would not necessarily be a single crystal of sapphire. But that would work.

I was thinking that maybe it is unrealistic to have a giant sapphire crystal. Where would it come from? A mountain of diamond seems so trite, but really it would be better in many respects. Lets get it over with.

Diamond: density of 3.5 and compressive strength of 60 GPA; maximum mountain height is 196 km

These diamonds would have been formed in the atmosphere of a ancient gas giant and then incorporated in the crust of this Earthlike world. I envision this huge, partly fused mountain of diamond extending farther down below the surface than it does above. Despite the huge mass balanced on one point, it does not sink further down because the bottom of the mountain is floating in denser, partly metallic molten materials. The diamond mountain is essentially an iceberg in the crust. Diamond is one of the best thermal conductors there is. With its big bottom side down into the mantle, the entire thing would be very hot.

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    $\begingroup$ A burning hot diamond mountain. If it were a single crystal would it also be illuminated from below, I wonder? +1 $\endgroup$
    – Joe Bloggs
    Nov 8, 2017 at 20:07
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    $\begingroup$ @Joe Bloggs: /illuminated from below/ Yes! Especially at night. I would take a road trip to see that. $\endgroup$
    – Willk
    Nov 8, 2017 at 20:14
  • $\begingroup$ I'm not sure exactly what a mile is, but I think 25 miles would be closer to 40 km. $\endgroup$
    – CJ Dennis
    Nov 8, 2017 at 23:11
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    $\begingroup$ Won’t the compressive strength in the core of the mountain be bolstered by forces pushing in from either side, especially on a shield volcano where the slope is relatively gentle? If the core did “fail” where is it going to go? $\endgroup$
    – Slarty
    Nov 8, 2017 at 23:37
  • $\begingroup$ @CJDennis very close. 6.2 miles per 10k $\endgroup$
    – JohnP
    Nov 8, 2017 at 23:45
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You need a planet with much less gravity to get that high (if at all possible).

Also a much cooler (deeper fluid part) would help... but that would also make volcanoes impractical.

On "standard Earth" a mountain would collapse under its own weight (or sink into the mantle, to the same effect) before reaching 10miles above sea level.

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  • $\begingroup$ I don’t think it would collapse under its weight as it would probably be a shield volcano so not very steep sided. Can you explain why 10 miles in particular? Or is this just your personal estimate. $\endgroup$
    – Slarty
    Nov 8, 2017 at 18:24
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    $\begingroup$ @Slarty: actually it is a "safe margin". Himalaya is already pushing into mantle enough that base is near fusion temperature. In general Mt.Everest is close to the maximum height here on Earth. I strongly doubt a mountain can get to 10 Km, which is sensibly less than 10Mi. A nice explanation is here $\endgroup$
    – ZioByte
    Nov 8, 2017 at 21:25
  • $\begingroup$ Note that there are two overlapping continental plates under Himalayas, so it stands on unusually solid base. Put that same mountain somewhere around Hawaii and it will sink like ...stone. $\endgroup$
    – Congenital Optimist
    Dec 1, 2017 at 9:13
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Water is irrelevant

What drives volcanic formation is the activity of the planets core and tectonics.

Olympus Mons on Mars is 21.9 km

I think the crust would need to be well formed but something needs to keep the planetary core active.

So maybe a gas giant moon that has its own moon which its tidally locked with. Would also be a great explainer for the volcanos size.

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  • $\begingroup$ How can you have a frozen CO2 mountain on a world similar to the earth except for the absence of most of the oceans? It would melt. And why CO2 not water? Also water is very much not irrelevant as it helps drive plate tectonics. $\endgroup$
    – Slarty
    Nov 8, 2017 at 18:16
  • $\begingroup$ Not irrelevant: water allows for plate techtonics and subducted water helps form the volcanoes. $\endgroup$
    – JDługosz
    Nov 8, 2017 at 20:18
  • $\begingroup$ @JDługosz Is there water on IO? If anything water erodes volcanoes so its absence is an implicit advantage. $\endgroup$
    – anon
    Nov 8, 2017 at 20:22

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