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I'm interested in the limiting factors on the height of mountains. There is a very good explanation at https://www.quora.com/How-tall-can-a-mountain-become-on-Earth-Neil-deGrasse-Tyson-says-Mount-Everest-is-about-as-tall-as-a-mountain-on-Earth-can-grow-%E2%80%9D-but-Mauna-Kea-is-significantly-taller-about-15-than-Everest

The actual lithospheric limit to mountain height averages about half the height of Everest, which is why Fourteeners are so famous in Colorado. Mountains that exceed this limit have local geologic circumstances that make their height possible, e.g. stronger or denser rocks. In the case of Everest and the Himalayas, you have a geologic situation that is very rare in Earth history. The Indian plate is ramming into the Eurasian plate with such force that instead of just wrinkling the crust on either side into mountain ranges it has actually succeeded in lifting the Eurasian plate up on top. So the Himalayas have double the thickness of the average continental plate, thus double the mountain height that would be considered "normal".

That seems to make perfect sense, providing a logical explanation for why the Himalayas and Rockies are both the height they are.

But what about the Andes? Chimborazo 6268 m, Cotopaxi 5897 m, Aconcagua 6962 m, all considerably higher than the 14,000 feet (4270 m) suggested to be the normal limit. And this is not a case of two continental plates colliding. It's a continental plate and an oceanic plate, so the explanation that applies to the Himalayas cannot apply here.

How do the Andes manage to be as tall as they are?

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