What is the highest possible mountain on an Earth-like world?

Question

My friend is writing a book, and I volunteered to create a planet for him, one with an epic mountain extending far above the clouds.

The planet features lush jungles in the lower elevations and enormous towering mountains.

If possible, I would like to have a mountain so high it extends well into a typical stratosphere, and possibly even higher. Maybe we can even see the stars in the middle of the day.

Mars has Olympus Mons, at roughly ~ 77,000ft. But Mars may be too small to support life as we know it.

I am aware that there is a planet mass/mountain height correlation.

This brings me to my question:

What is the highest realistic mountain that I can make on a world that can sustain a breathable atmosphere and lush biosphere?

You may choose the mass and density of the planet as long as it is mentioned, and it can reasonably support life.

Answer 1

I would like to take as a starting point the contribution of Anders Sandberg.

The basic assumption there is that the "mountain" is a solid (or near solid) and homogeneous piece of rock. "Near solid" still allows for fissures and cave systems but compared to the total volume of the mountain and the density of the rock, the reduction in overall weight they imply should be very small.

When considering beams, in mechanics, a well known result states that a hollow tube of equal mass to a solid tube (a rod) would resist bending considerably more than its solid counterpart. Other profiles with different "hollowness" are suitable too.

Therefore, without violation of the reasonable assumption that "a pile of solid rock can be so high as to not crumble under its own weight", it could well be that a structure can stand much taller if, for some reason it made "clever use" of its mass.

Yes, it will still break but with a lighter structural pattern, the "accumulation of height" is faster than the accumulation of mass and so it can stand taller before it hits that structural limit imposed by physics.

Examples where something similar to this is found in nature are certain trees, such as the Sequoia and the Baobab. Such trees stand can grow very tall and have hollow interiors. Their trunk does not grow as a solid "tube". This is beneficial for two reasons, it's not only that they are lighter (compared to a typical "solid" tree) but they can also resist bending, because of wind forces (for example), which, as the tree grows taller and taller and inevitably wider too, becomes a considerable force.

Therefore, if you relax the specification that the "mountain" is a solid, homogeneous, "rocky" kind of mountain, then you could end up with a much taller "mountain", in an earth-like planet with possibly an even more interesting (or flexible) narrative.

The key problem here now is how do you grow such a mountain that seems to be taking these principles into account?

1. There is an awful, obvious and quite boring option here, there are living things in the "mountain" and they build it and they interact with the story in mysterious ways until we discover that something is in the mountain and this and that the other.

2. A less boring option is that the "mountain" is one huge composite society of trees, with hollowed trunks, intertwined that grow and expand their base very very slowly. Existing processes accumulate dirt on its sides (by wind for example) and where there is dirt, water and air-born seeds (or carried by birds) there is the potential to form trees, etc. So, from afar, maybe it does look like one incredibly high typical mountain kind of object, but upon close inspection of its behaviour, it could certainly be revealed that it behaves differently.

3. Another option is that the "mountain" grows by crystalisation, maybe aided by the natural day-night cycle and special atmospheric phenomena. Think of it a little bit like constructive 3d printing. The mountain grows by deposition, day by day, in a crystallised profile that allows it to grow so tall.

4. Finally, you can push it even higher by relaxing the specification that the mountain is homogeneous. Maybe it's a combination of the above mechanisms. Maybe the first 15km are rock and another 20km is a "composite tree society" and for another 10km is crystallisation.

Bringing something like this into the story makes it also more flexible, it gives you freedom to talk about other things as well. Maybe the "mountain" "wobbles" continuously because of earthquakes or the flow of wind around it, maybe it allows very fast communications by tapping to its structure.

Hope this helps.

Answer 2

Your question has similarities to this one The current mountains in the Himalayas are at or near the highest that mountains can reach above ground on Earth. Much higher mountains can be achieved on lower gravity worlds, but lower gravity worlds would not tend to be able to hold onto their atmospheres close into the sun where there is a lot of thermal energy to help it leak away into space.

I would suggest that Mars might have once harboured life and may have had a much thicker atmosphere so an Olimpus Mons size mountain (21km) is one candidate. Someone has already done some calculations on this here:

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

One option to reduce the atmospheric loss problem would be to have a lot more of a heavier gas involved in the atmosphere from the start. That way it would be less likely to escape and there would be plenty in reserve if it did slowly leak. Carbon dioxide might be suitable together with some Oxygen. The planet could then be a lot further from its star as it would have a warm Carbon dioxide blanket to keep it warm.

Answer 3

The highest mountain is limited by the strength of rock; a mountain of height $h$ will exert pressure $\rho g h$ on the rock at the base. So assuming earthlike density and rock strength the possible height scales inversely with gravity: a 2G world would have maximal mountains half as tall as Earth, a 1/2 G world can maintain twice as tall mountains.

Calculating the theoretical maximum from first principles is somewhat iffy; Tipler & Barrow's "The Anthropic Cosmological Principle" and Weisskopf gets about 26 km. Doing it using compressive strength of granite gives 10 km.

Now, the height of the atmosphere is set by the scale height, $h=RT/mg$. This is about 8 km for Earth. It also scales as $1/g$. So the 1/G G low gravity world will have an atmosphere declining in pressure half as fast as Earth.

This means that the top of the tallest mountain, unless the rock composition is vastly different, will tend to be about one scale height above the ground. It will be high up in the atmosphere but not above it.