The biggest peak in the world is Mount Everest.
Imagine someone starting to make an artificial hill (like pyramide) from soil (earth).
So, when starting with an 200x200 Km base area, with 45degree slope, its mathematical height is 100km (Low orbital space height). Is it possible to make such an artificial peak? (Without taking into account financial issues and so on.)
If not, why not? What would happen? Is there a height limit?
Answer
Your question is a classical college exercise. The limit is supposed to be the melting of the base of the artificial mountain under the pressure, which is linked with the energy of chemical bounds. You have an example of such a calculation here. You can also look it for an arbitrary planet size : the smaller the planet, the smaller the gravity is, and the bigger the biggest mountain can be. And when the mountain can be as big as the radius of the planet, you have roughly the dwarf planet / asteroid boundary.
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