Under whatever unlikely conditions would be required to generate a super peak. Are there any physical limitations that would keep a mountain under a certain height?
Could a volcano constantly spew lava up and out to create an ever-increasing-in-height mountain?
I don’t have the notes anymore.
But in one graduate level astronomy course we covered this. I recall running the numbers and Mt Everest was nearly as high as something you could get on Earth and Olympus Mons was about as high as you could get on Mars. And probably some other stuff on other planets/moons that I can’t recall at the moment.
I wish I could remember the formula. It wasnt that complicated. And obviously it was more of a rough guide than a precise calculation.
You have to remember that the surface of the earth is a thin crust of solid stuff on top of hot liquid goo. If you spew out a bunch of the goo to form more solid stuff, then eventually the solid part starts to sink into the goo. Then the bottom melts and becomes more goo.
An example of this, though not volcanic, is Greenland. A bunch of ice formed over Greenland, and instead of just making Greenland taller, Greenland instead sank into the Earth’s mantle. Now that global warming is melting the ice, Greenland is rising. Your super-mountain would similarly cause the land it sits on to sink.
You’ve also got the fact that the rock at the bottom has to hold up all of the weight of the rock on top of it. At some point the rock can’t take the extra weight and loses its structural integrity. Then your mountain flattens out and becomes less tall.
From what I have read, when you combine all of these factors, you end up with a limit that is roughly around the height of Everest. You might be able to squeeze one out that is slightly bigger, at least temporarily, but you aren’t going to be able to make something the size of Olympus Mons (the biggest mountain on Mars) here on Earth. Coincidentally (or perhaps not), Olympus Mons is roughly three times the size of Everest, and the gravity on Mars is roughly 1/3rd that of Earth. If you could somehow transport Olympus Mons to Earth, the extra weight caused by the gravity difference would be enough to crush Olympus Mons down to something roughly the height of Everest.
At least that’s what I’ve read. I haven’t tried to plug through the equations myself.
ETA: Beaten to the punch. I must learn to type faster, or not be so wordy.
Yeah, but you gave a much better explanation 
ECG: While your answer is correct, you’ve hit on one of the geologist’s pet peeves – While the interior is hot, there is no consistently liquid layer until you get to the outer core, about 2900 km down.
The solid and (for the most part) brittle layer consists of the crust and the upper mantle, collectively known as the lithosphere (varying in thickness, 100 km is a good approximation). Below lies the asthenosphere (~400 km thick) which, though close to its melting temperature, is below to its melting point over its entire depth: it therefore behaves as an extremely viscous plastic material (localized melting can occur due to changes in pressure or chemistry, such as the addition of water to the rock). We know it is a solid because it easily transmits shear waves, which can’t move through liquids (i.e., the outer core).
The asthenosphere can flow over long periods of time (1-10 thousand years). As an example, the Canadian and Scandinavian shields are still rising as a result of the retreat of the continental glaciers ~18-20 thousand years ago.
The Himalayan plateau has an average altitude of about 15,000 feet and has a lithospheric root, or keel, that extends into the asthenosphere. If you add mass by, say, having the Indian plate continue to push northward into Asia, you find that the plateau just continues to widen at its edges, rather than thickening in the middle. This implies that the maximum thickness the asthenosphere can support has been achieved.
But the highest mountain? Everest and K2 are just tiny chunks of rock sitting atop the broad shoulders of the plateau. What controls the highest mast you could put on a ship at sea? You would run into a lot of physical limitations before the weight of the mast started to sink the ship. For tall mountains those limitations include river/glacial erosion at the flanks, rock falls, and earthquakes (since those are always going to play a big role in regions where mountains are actively growing).
Ironically, since erosion is often caused by water/ice, which tends to collect in valleys, rock is more easily removed between mountain peaks than from their tops – the removal of this mass from the range decreases its total mass, causing the asthenosphere to push the range up, and making the peaks higher! In the long run of course, deeper/steeper canyons lead to increased mass wasting which ultimately destabilizes the peaks.
Is this the formula you were talking about billfish678?
-XT
That link is not working for me.
Ttried that link — “Internet Explorer cannot display the webpage.”
Well, Everest obviously isn’t quite as tall as you can get, because Everest gets a little taller all the time.
Good stuff here, folks. Thanks.
Note the coding of your link, XT:
Is <URL=“billfish678”>this</URL> the formula you were talking about billfish678?
:smack: Sorry about that. I’ve been on planes, trains and automobiles and didn’t see that I screwed up the link. I don’t have the link from before, but here is the same formula (warning, .pdf file).
-XT