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That's Cairn FYI

Now I want to know how high a mountain would have to be for that to happen. And how pointy.

1. Geostationary orbit, so about 35,786 kilometers
2. With a minimum Earth diameter of 12,714 kilometers, in order for the mountain to fit it would have to have an angle of repose of just under 80°.

With that peak about 2 times as high as it's wide, it has about 75°.

So the entire mountain has to look like that. And that curve on the peak's profile has to be compensated somewhere.

You have to use the Earth's radius, not diameter. Did you remember to divide by 2?

(Edit: and add the radius to the height since you're measuring from the base of the mountain, which is the center of the Earth when the mountain is that big... but that turns out to change the answer by much less than 1 degree of angle.)

What are you talking about? I used your angle.

That I just checked, and is correct.

Getting over it