Wikipedia has lists of the highest mountains on Earth, Mars, Venus, and the Moon, but no aggregate list for the entire universe—or at least, those parts of it which we can observe accurately enough to measure mountains, which probably limits things to the planets and moons in this solar system. Does anyone know the top ten mountains by height? According to Wikipedia, Mars’s Olympus Mons is the highest thus far observed at 25 km. Where are the remaining nine? Any on Earth? Which planets and moons have the greatest number of tallest mountains?
Neutron stars can have mountains as high as a few millimeters. That doesn’t sound like much, until you try to climb one. The potential energy difference from top to bottom dwarfs Olympus, Everest, and anything else on any non-neutron star structure.
With that sort of gravity, I suppose you’d have to climb ‘flat out’ to reach the summit. A ho ho ho…
So there must be a limit as to how high a mountain can be. as a small planet will have a small mountain as well. What size planet is capable of suporting the tallest mountain?
Part of that is because, on smaller objects, you don’t really think of them as “mountains.” If we find an orbiting body that’s 80 km long, with most of the mass in a 10 km wide spherical mass at one end, you wouldn’t call it a 10 km wide planet with a 70 km tall mountain. But that’s (arguably) what it is. I’d think that smaller masses are actually capable of supporting much larger mountains, simply because there’s less gravitational force to push them into spheres. There’s also less gravitational attraction to random junk that might crash into them and level those mountains.
I doubt that any of the mountains so far noted are anywhere the theoretical limits for mountain height. But all of our solar system is roughly the same age, and anything large enough to be a planet has had stuff hitting it for hundreds of millions of years. So any big mountains have to have been recently formed, else they’d have been pounded and eroded into dust. Olympus Mons is volcanic, and the Himalayas are due to plate tectonics. Offhand, the best candidate for producing a really big mountain is to have a stray asteroid run into a very small moon and create a huge lump. Of course, you’d have to get very lucky with the velocities to have that happen, and not have one or both just destroyed on impact.