Is there a limit to how high a mountain can be due to gravity?

[ravachol]

i've read sth like there cannot be a mountain higher than 15000 meters because of the gravity. this was like a do you know statements in magazines.
is there anyone knows sth about that

 

[robphy]

Try to calculate the pressure at the base of a mountain. Assume a column of material as high as your mountain.

 

[luckycharms]

The tallest mountain we know of is Hawaii's Mauna Kea at ~9700 meters. Of course, about 5000 of those meters are under the Pacific Ocean. Mars' largest mountain comes in at 27000 meters, which does roughly scale with the difference in gravity. Of course, we're not considering the effects of erosion (or really any geologic principles).

The approximation suggested seems correct. Using the density of a particular rock, calculate the pressure at the bottom of a column and compare that to the known compressive yield strength of that particular rock.

 

[Bob3141592]

The approximation suggested seems correct. Using the density of a particular rock, calculate the pressure at the bottom of a column and compare that to the known compressive yield strength of that particular rock.

But when we think about a column of rock, when the material at the bottom breaks, it has somewhere to go. It ejects material sideways. In a mountain, the column is surrounded by other rocks, thus helping to hold it up since any broken material has nowhere to go. I suppose if the mountain were large enough the sideways force could break the rock at the outer regions of the base of the mountain, where the columns would be of much reduced height. Or is this not a consideration, or maybe it wouldn't change the estimate by much? I'd just think that a mountain with a gentle slope on it's sides could rise much higher than a mountain with a steep slope, for the reason described above. Given a sufficiently gentle slope, I'd expect the height to be nearly unlimited, unless the compression turned everything to liquid.