Let's say the Earth's oceans contained 10x less or 10x more water.

[Scytheria]

@Scytheria

10x deeper or 10x shallower is very different from 10x more or 10x less. In the latter, we’re talking about volume, not depth.

I just did this on Excel, assuming the Earth to be a uniform sphere of radius 6400 km and the oceans to be uniformly 3.5km deep over the whole surface. The result, surprisingly, was that 10x more water made the depth LOWER by a few metres…

Clearly this is wrong, but the error is in Excel’s rounding. Since it handles figures with up to 20 decimal places fairly well, we can be sure that the actual difference would be relatively insignificant. I’m suggesting plus or minus no more than 20 metres.

I quote myself, and now also declare myself an oaf of the worst kind.

Rechecking my results (and spotting the elementary error), I find that on a planet-sized scale a 10x volume of water results in as near as dammit 10x increase in depth. A 0.1x volume of water results in as near as dammit 0.1x the original depth.

[eburacum45]

Yes, but it does make my claim of accuracy to two decimal places nonsense.

[eburacum45]

Now I come to think of it, I’ve made a much bigger, stupid error; if you have 10 x the volume of Earth’s water, one of those volumes will still be needed to fill the existing oceans; so the water surface will only be 9 x Earth’s water volumes above sea level. That makes it around 22 km in total, plus a quarter of a kilometer for the mountains, about 22.24 km ignoring spherical corrections.