Sorry for the late answer, I intended to write this 2 weeks ago but couldn't find the time.
OK, so let's look at the amount of potential energy locked up in our configuration of water spheres: I calculated the radius to be km. By symmetry, the potential energy would be the same if all the water were located at the center of these spheres, i.e. 133.322 km above ground. Add negative potential energy of Earth's oceans in its equilibrium state (1.844 km, half the average ocean depth), and we get a total of
That's a lot of energy. Let's assume the water is at 0°C initially (most ocean water is in the cold deep layers). To bring all this water to the boiling point, we'd need . That leaves us to boil the water. Given the latent heat needed, we can boil of the water.
Since Earth's oceans is 262 times as massive as the atmosphere and we boiled almost half of it, we now have an atmospheric pressure of 105 bars, exceeding that of Venus. Of course, the boiling point of water increases with pressure, but the latent heat of vaporization decreases and these two effects pretty much cancel each other out. It does mean however that we'll have a surface temperature of 315°C, approaching that of Venus. In other words, all life on Earth's surface, including the hardiest extremophile bacteria, is toast (or rather steam buns). Absolute overkill actually, since DNA itself disintegrates completely at around 200°C. The only safe place would be deep underground where the heat can't penetrate until it is radiated off into space.
What about seeking refuge in the ISS? Let's see what the atmospheric conditions are at its orbital height of 400 km. We'll use the barometric formula without temperature lapse because this isn't an equilibrium state anyway. This is equivalent to the air density of our current atmosphere at 60 km height.
Here's a video of the Mir space station at 80 km height.
Woah, tks a bunch man. But exactly what happens starting from t=0? I suppose that at 1st the water must be falling down, right? How will the Earth's surface be altered by the tremendous force of water? How will the potential energy from height turn 40% of water into vapor? I mean, how will it happen over time? If it takes time, then maybe some people will have a chance to understand what's going on & run into the nearest underground mine, no?
Regarding the ISS, I suppose that even at the hypothetical altitude of 460km, it will still burn. But ...
These follow-up questions pertain to a dynamic context, and I'm afraid I'm not equipped to answer them. Moreover, I would also claim that not even Randall Munroe himself would be able to answer these questions, or anyone who hasn't got a supercomputer and a team of physicists at disposal.
I bought the What If book myself and loved every chapter of it. But if you look closely, you will notice that basically every analysis in that book was made from a static context or a dynamic one that has ridiculously simple solutions (i.e. linear or exponential). Even exotic topics like neutron star matter and supernova neutrinos can be analysed with ease under a static context; just a matter of typing large numbers into a calculator. But as soon as dynamics is involved, even mundane things like Earthly weather or air flow over ailerons are going to require a supercomputer.
It doesn't help to analogize the problem with more familiar scenarios, either. Quantity has a quality of its own, as Stalin famously said. Things like the cube-square law make big things behave very differently than small things even if they're made out of the same material or undergoing the same basic p...
I was inspired by the APOD pictures and discussion here and here. The conditions for the 'experiment' are:
So, what will happen to us, the Earth and things on it?
My prediction is very grim for humanity, thus I turn to the ISS as our last hope. Supposed that at t=0, the astronauts can choose the station's direction of flying. Can they avoid all the 17 falling balls? Is there any chance they can land back on Earth without any help from Houston when things settle down, in case the water does settle down and not all turn into vapor? (That's a possibility I can't calculate and will need your help).
I'm looking for answers in xkcd style, which IMO is a textbook way to respond to absurd "What if?" questions. It's detailed, with nice pictures to help our imagination, displaying formulas when necessary but also very rookie-friendly, tackle the problem from many different angles & POVs, and takes into account some easy-to-overlook stuffs. Too bad he doesn't answer anymore.
Anyway, thank you just for reading! :)