How would a 30-kilometer tall mountain on an Earthlike planet look?

Question

Let us take an earthlike planet. Approximately same radius, atmosphere and climate.

Now let us create an approximately circular, paleovolcanic mountain approximately 30 kilometers in height and 150 kilometers in radius, not dissimilar from Olympus Mons. The crater's radius is 20 kilometers and its depth is 10 kilometers. The mountain is located in a temperate continent similar to Europe, surrounded by grasslands, forests, hillscapes and normal mountain ranges similar to the Alps. It borders the ocean to the south.

My question is:

How would such a mountain look from orbit and from the surface? What vegetation and climate zones would exist? Is it true that there would be no snow above 15 kilometers due to lack of water?

Answer 1

This mountain will look... unrealistic.

There is a limit to how high a mountain can be in a certain level of gravity how high can mountains be For Earth, this limit is less than 10 km.

(The basic idea is as follows. Take a column of rock; it will exert a certain hydrostatic pressure on its base, proportional to its height. At a certain point this pressure will reach the maximum which can be supported by the material; any attempt to make the column higher will make the material at the base flow sideways. Granite has a density of about 2.7 grams/cubic centimeter and a compressive strength of about 200 MPa or 2 million grams-force/square centimeter; simple arithmetic gives a maximum height of about 7.5 km. Real mountains are not columns, so they can be a little higher because the core of the mountain is propped laterally by the sides and because the mountain is not all granite.)

However, if your planet has Mars-like lower gravity, your mountain can be higher.

If, for argument's sake, we allow this mountain to exist, it will look like big round glacier with naked top, probably with some glaciation inside the crater. Atmospheric conditions in stratosphere do not support glaciation (boiling point of water drops to -50-60C).

Answer 2

To be clear: this is not a question about whether a 30km mountain on an earth like planet could exist. It is a question about how it would look.

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. So here it how it would look.

https://orig08.deviantart.net/a5c2/f/2014/021/f/a/crystal_mountain_by_elbardo-d734c7a.jpg

Except for those birds. Nothing is flying up there. At all. Also I object to that curly mountain at the side. But the principle stands.

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ADDENDUM 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.

So 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.

This also gives insight into how this diamond iceberg mountain would look. There would be no plants on it and no ice or snow. 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.

my own assembly. mount hood with uncut diamond

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Answer 3

It depends on where from space really. As @Alexander had said, it is quite unrealistic too. If viewed from the moon it would be visible(if not completely by the naked eye). It is bigger than Switzerland:

Secondly, for your question of "Can it snow above 15km?". I am not sure, correct me if I am wrong, but it can't snow if it is too cold so it wouldn't snow at that altitude.

Paradoxically, just as the air can be too cold to generate much snow, it can also be too hot to generate much rain. The reason is partly because record-high temperatures generally coincide with high-pressure systems that feature plenty of sunshine and stable air.