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There is a physical limit to the height of mountains on earth
- Thread starter Wandering Monk
- Start date
Darkforbid
Well-Known Member
Mount Everest is 8.848km
Wandering Monk
Well-Known Member
Hmm. Guess the math doesn't work in the OP.
I heard some physicist talking about this. Had to do with the mass of the mountain and the strength of the foundational rock on which the mountain rests. At some point the mountain base crumbles IIRC.
Wandering Monk
Well-Known Member
Looking into this a little more, the 5 km limit is in relation to the local elevation (prominence); it is not related to sea level.
julianalexander745
Active Member
Who cares?
Mauna Kea is over 10km from base to peak.
most of it is under water
most of it is under water
exchemist
Veteran Member
This looks bogus to me. I can't find any other reference to Weisskopf having made this calculation and the logic does not look at all convincing.
For a start, how can you know whether or not rock will get hot enough to melt, unless you can calculate where the heat will be liberated, a rate of heat release and a rate of conduction and convection (i.e. heat loss mechanisms).
Furthermore, if a floating object sinks, the potential energy released does not go into melting anything, it goes into raising the potential energy of the fluid in which it is floating, by displacement. So, if Mt Everest sinks a bit, it raises the level of the rest of the rocks in which Mt Everest floats, so there is no reason why energy need go into melting anything, so far as I can see.
But Subduction Zone may know the geophysics of this better than I do.
P.S. The idea of a latent heat of fusion for silica looks suspect to me as well. Silica forms a glass, without a defined melting point. I'm not sure it even has a latent heat of fusion at all!
Last edited:
Shad
Veteran Member
Subduction Zone
Veteran Member
I am sure that there is a limit. But the math in the OP appears to have been refuted. This reminds me of Desertphile's original gravity rant. Planets are round due to gravity and there will be some sort of natural limit on the height of mountains. The math in the OP may have been off by a factor of two, which is not too bad for a first estimate.
exchemist
Veteran Member
Thanks very much for this.
Unfortunately I can't seem to get access to the relevant pages. I must confess that at the moment I do not understand how this calculation can be valid, for the reasons I have given. Perhaps if I were able to read the whole thing I might get it.
exchemist
Veteran Member
Do you follow the logic of the basic argument, though? This is what bothers me. I'd have thought sinking of the mountain would be an isostatic readjustment and would not necessarily involve any melting of anything.
Subduction Zone
Veteran Member
I have not touched the math on this. But the concept of isostasy is not new:
Isostasy - Wikipedia
In reality it is quite complex since strata under high heat and pressure can bend and move without breaking. A full melt or even partial one is not necessary. This would be a problem for a structural geologist. Which reminds me of fossils. Creationists quite often try to argue that sedimentary rocks with folds and bends had to be done while soft. That is belied by the fact that fossils themselves show that they were distorted. Fossils tend to be even more brittle and fragile than the sedimentary rock that surrounds them and yet they clearly are often deformed. Structural geologists jokingly refer to fossils as only "strain markers" at times. They are not concerned so much of them as indicators of relative ages. They use them to study how the rock has been deformed. A fossil is often represented as a circle that has been distorted, but for a practical example fossils that one is familiar with make this obvious. This is my favorite picture of two trilobites:
One is almost parallel to the direction of compression and is much shorter, and the other is elongated by that same strain.
A trilobite at an angle to the strain could look like this one:
And of course there are other factors to consider. When mountains are formed the compression not only forces the mountains higher. They also get deeper. Mountains float on top of the mantle with roots extending even deeper in mountain ranges. Continental crust is twenty five to seventy kilometers thick while oceanic crust varies much less and is much thinner at seven to ten kilometers. Mountains are also a product of erosion. The higher the elevation the higher the gravitational potential energy and that results in a higher erosion rate. Though the crust does sink down a bit as mountains are formed the mountains themselves are eroded. And since plate tectonics is a motion horizontally as fast as one's fingernails grow the vertical growth rate will be a fraction of that.
Bottom line, the article in the OP is oversimplified and is going to have quite a few problems with it. Melting was the incorrect mechanism to use.
exchemist
Veteran Member
Yes the height of a mountain is determined by the thickness of the crust supporting it. So I would have thought if there were a maximum height for mountain it would be determined by the maximum crustal thickness that can be achieved by tectonic processes.
All this stuff about alleged melting if the mountain were to sink strikes me as very dodgy - not to mention the fact that I am not convinced silica has a latent heat of fusion at all!
But I think I may have found Weisskopf's original version of this, here: Don’t miss this one: “Modern Physics from an Elementary Point of View” « Statistical Modeling, Causal Inference, and Social Science
This makes it clear he is just doing a back of the envelope estimate, to determine the order of magnitude of mountain heights, and comes up with a number of 30km max. It seems he guesstimated a value for the "latent heat of fusion" of silica by taking 10% of the bond energy of the Si-O bond! Flaky or what?
So the whole thing is really just a fun physics game, not to be taken very seriously. It is certainly not rigorous geophysics in any way.
Shad
Veteran Member
Sorry I was just linking the source. You will probably need to use a search engine for a public copy.
Try this link
https://www.astro.princeton.edu/~burrows/classes/542/papers/Patryk.1975_Weisskopf.pdf
exchemist
Veteran Member
Shad
Veteran Member
I found a public copy so put a link in my previous comment.
Subduction Zone
Veteran Member
Knowing the melting point of an object seems more to be in the area of chemistry than geology so I will completely bow out on that. But yeah. My point was that gravity etc. seem to limit the size of mountains. He was right about their being a limit but for the wrong reasons. I know that even tectonic process would eventually fail even if there was no erosion. It would be curious to see how large mountains could get on an exo-Earth without an atmosphere. I like you have serious doubts about his back of the envelope work. I don't think it is quite ready for peer review yetYes the height of a mountain is determined by the thickness of the crust supporting it. So I would have thought if there were a maximum height for mountain it would be determined by the maximum crustal thickness that can be achieved by tectonic processes.
All this stuff about alleged melting if the mountain were to sink strikes me as very dodgy - not to mention the fact that I am not convinced silica has a latent heat of fusion at all!
But I think I may have found Weisskopf's original version of this, here: Don’t miss this one: “Modern Physics from an Elementary Point of View” « Statistical Modeling, Causal Inference, and Social Science
This makes it clear he is just doing a back of the envelope estimate, to determine the order of magnitude of mountain heights, and comes up with a number of 30km max. It seems he guesstimated a value for the "latent heat of fusion" of silica by taking 10% of the bond energy of the Si-O bond! Flaky or what?
So the whole thing is really just a fun physics game, not to be taken very seriously. It is certainly not rigorous geophysics in any way.
exchemist
Veteran Member
Thinking about this some more, I suppose the actual way a mountain range rises is due to crustal compression and thickening, under the constraint of isostatic buoyancy of the crustal block relative to the mantle. So what we really have is the energy of a compressive tectonic force, doing work by acting through a distance as it shortens and thickens the crust. This energy goes partly into heat I suppose, as the crust is deformed, but also into gravitational potential energy, both of the raising of the mountain and the depression of the buoyant mountain root down into the mantle.Knowing the melting point of an object seems more to be in the area of chemistry than geology so I will completely bow out on that. But yeah. My point was that gravity etc. seem to limit the size of mountains. He was right about their being a limit but for the wrong reasons. I know that even tectonic process would eventually fail even if there was no erosion. It would be curious to see how large mountains could get on an exo-Earth without an atmosphere. I like you have serious doubts about his back of the envelope work. I don't think it is quite ready for peer review yet
What would cause this process to reach a limit? If we assume it is not limited by the size of the compressive force available from plate tectonics, then I imagine it will be the mechanical strength of the rocks. The whole tectonic process implies a plastic flow of nominally solid material anyway. If the mass of the mountain - and the corresponding "mass deficiency" of the mountain root, as it is depressed into the mantle - exceed a certain amount, then the the rocks will tend to spread outward as well as being simply forced up - and down.
I suppose one could say that Weisskopf's "latent heat" idea of overcoming the bond energy in the minerals is equivalent to overcoming the energy barrier to inducing plastic flow under pressure.
exchemist
Veteran Member
What an inane remark.