The escape velocity of earth is about 7 miles/sec. That means, ignoring any air resistance at first, you have to throw something upward at 7mps to escape earth’s gravity and make it to the rest of the solar system. Conversely, anything dropped from beyond earth’s neighbourhood would be travelling at least 7mps - plus whatever other relative velocity it had - when it hits the earth.
It doesn’t matter where the ice melts- high or low atmosphere, it will still simply create water vapour that will eventually fall as rain. Or it will leave a big hole filled with steam and water and mud. Of course, some very high H2O will dissociate and maybe the H2 will be blown away by the solar wind - but nowhere near enough to matter in less-than-geological time spans. Meanwhile a saturated upper atmosphere may create clouds reflecting enough sunlight so everything gets cold quickly. All of the earth will be covered with a layer of water, but with snowshoes on you won’t sink into it.
If that formula is supposed to be the volume of a sphere, you have the constant wrong. It’s 4/3pi*r^3.
I calculate that raising sea level by 1 kilometer would take a single ice-asteroid with a diameter of 380 km. That number is somewhat high because I calculated the volume difference between the Earth and a sphere 1 km larger radius and then reversed the formula. So that doesn’t take into account the continents. Still it’s in the right ballpark. But note that that would not come close to submerging all the mountains.
Someone may want to double check my calculations. I won’t swear I didn’t make an error. I used an Earth radius of 6378 km.
Is that to say that the isostacy distribution is such that an Earth waterworld is either impossible or long-term unstable? i.e. that even if we dig out all the high country and dump it in the oceans and polish the Earth to a mirror finish uniform geopotential that the continental and ocean plates, the mantle convective cells, etc. will eventually rearrange things and once again thrust mountains above the waves? At least for the amount of free water the Earth has today?
Said another way, is total planet surface roughness preserved above some minimum in some long term sense due to plate tectonics? And if so is that minimum roughness necessarily larger than the total free water can cover up?
Interesting idea. My earlier xkcd links point out the Mars has much higher surface roughness than Earth. So if you exported our oceans to Mars there wouldn’t be enough water there to cover the much smaller planet to the depth necessary to cover its much higher high points after filling in its much lower low points.
Assuming rock chemistry is mostly the same all across the galaxy, I wonder if this implies another Goldilocks zone parameter: A habitable planet must be small enough to have real topography, but not so small it has dizzying heights and deeps. And enough but not too much water so as to cover a middling fraction of the surface.
<nitpick> Plenty of life on Earth for the first 4 billions years. Land mass is not a requirement. </nitpick>
So what if the oceans boil, all that does is destroy all life on the planet … oh … I see what mean now … but nevertheless we’ll still have people fighting … let’s keep our eye on the goal here … [giggle]
I hear this a lot, and I am in no position to disagree with it, but I have never seen anyone imagine that if all the ice in Antartica melted, that the land would rise. Because of scientists drilling ice cores, they have determined that the land under the ice was once above sea level, so my conjecture is that the ice is so heavy that it has caused the land to sink and if the ice disappears then the land will rise. This would, presumably, cause an additional increase in sea levels, but I have never heard anyone speculate on how much higher they would go.
The land does rise when lots of ice on it melts. The same thing is happening in Greenland as its ice is melting. But that’s not all that happens.
When the ice pushes down on one area, the region around that place rises in response. Not as much as the area under the ice goes down, but it’s a larger area. So when the ice melts and the land rebounds, the surrounding region in turn goes back down. The net effect on the Earth as a whole is essentially zero. So all this rebounding has no significant effect on global sea levels, although it will affect the local sea level.
The mass of ice on continents does push them down. This is the isostacy I referred to earlier. But it takes quite while for the earth to move. The best known example is the UK. The north of the UK was under glacial ice sheet (lots of nice fiords up in Scotland). So the mass of ice depressed the top end - but like a see-saw - the south of the island rose. Once the ice age ended the island started to return to its earlier level. It still is. This is why London is slowly sinking, and needs ever more heroic protection against tidal surges.
A difficultly is working out what would happen trying to fill in the oceans is that oceanic crust is much thinner than continental crust, and the dynamics of the whole mess not clear. Why oceanic crust is thinner is an interesting question. The ocean floors are much younger than the continents, and as a good approximation, the continents are not subject to tectonic renewal, whereas the oceans are. The oceans are not just those bits that are filled with water, they are intrinsically different to the continents. (I don’t know of any useful explanation for this - I speculate that our collision with Theia is responsible for the loss of large fraction of the continental crust and its replacement with oceanic crust as the mess cooled down again. The collision may even be responsible for some of the weirdness we observe in the inner earth - South Atlantic anomaly - various volcanic plumes.)
Carting rock from continental crust and dumping onto oceanic crust might eventually even out the differences in thickness - essentially by redistribution the continental crust into a thinner layer. But in the meantime tectonic processes would still be reprocessing oceanic crust , and it really isn’t clear what the heck would happen. I doubt there is enough continental crust to go around, and you would end up with an even more messy and possibly more active tectonic process wrecking your cue-ball Earth.
I really meant habitable by advanced life at least potentially capable of intelligence and technology. Finding a planet full of unicellular something-or-others, no matter how different from our own would be fascinating. But disappointing compared to finding a technological civilization, whether centuries ahead or behind our own.