Geologist: implications of a mountain top in space?

What is “space?” 50 miles above sea level? Supposing we had a mountain summit that reaches that height. What are the things that might happen? Erosion at the slopes will be rapid but you can’t have erosion at the top in space, right? Might the whole thing sink into the mantle by its sheer weight? How will it affect things like weather and the water cycle?

You can’t have erosion cause by wind in space, but erosion by other means can still happen. For instance, heating and cooling of the surface, which I the difference between the highest and lowest temperature will be significantly greater above the atmosphere, will result in expansion and contraction of the rock and soil. That may cause cracking and crumbling of the surface over time.

Sink into the ground because of weight? All depends which planet it’s on, what materials are nearer the top, which nearer the bottom, etc. While gravity may well prevent a mountain from getting tall enough to reach space, I’m gonna guess again that if it gets that tall the fact the peak is in space won’t change it’s odd of sinking.

Obviously, there would be either no life or only anaerobic life near the peak – I’m skeptical that it anaerobic life could survive the extremes of temperature.

Which reminds me (if it’s on Earth) – significant radiation from the sun at the top, it would make a permanent hole of some kind in the ozone layer. I have no idea what it would do to the jetstreams and climate but I suspect it would be very significant.

Perhaps an actual geologist can come along and calculate how big an area the base of such a mountain will have to be. I imagine it will need to be huge, maybe continent sized? It’s even possible there may not be enough material on a planet our size to support it.

I’m kind of picturing a planet shaped like an ice cream cone, and I have real doubts that’s a sustainable shape. There may be so much mass involved it would change the rotation of the planet by changing the center of gravity.

This site says that any asteroid larger than about 300 km in diameter would be compressed into a sphere. A smaller body could have an extreme shape…but of course wouldn’t have an atmosphere.

Searching for “Tallest Possible Mountain,” I bump into this old Straight Dope thread…but, alas, it doesn’t seem to give a definite answer. It was opined that Everest is probably close to the limit.

The wiki just says that the summit of Olympus Mons has an atmosphere density 12% to that down on the Martian plains. Compare that to the summit of Everest which is still 32% that of Earth’s at sea level. Add the fact that Martian amosphere is just 1% in mass per unit space that of Earth’s, it’s basically in space. But it’s still within the Martian atmosphere by definition. There’s lots of dust floating around the summit. Because of the light density and weaker gravity, the gasses and dust don’t scrunch down tightly as they do on Earth.