by C. S. Cooper, 13th July, 2019

Thinking about Water Worlds

I think my first experience with a water world was playing Lylat Wars (StarFox64 for US readers). It was a video game on the Nintendo64, and involved a team of elite fighter pilots travelling through the Lylat System, stopping at each planet to battle the evil forces of Andross, determined to take over the universe. It was a pretty fun shooter-on-rails, and I still occasionally play it on an emulator.

One of the paths on the campaign takes you to planet Aquas. For those whose Latin is a little rusty, that’s the water planet. Instead of being in a space fighter or a tank, you’re in a submarine with seemingly unlimited torpedoes. You go around shooting up genetically engineered water creatures that shoot laser beams at you. One nice part of that level was an Atlantis-style city you pass by. It looked really interesting, and my ten-year-old self wondered what kind of history there was to those ruins.

Another experience with water worlds was an episode of Star Trek: Voyager. In season five, episode nine, the helmsman, Tom Paris, explores a ball of water floating in space. Unlike most water worlds, this was just straight water; no solid ground beneath. At the centre was a device generating a gravitational field that kept the water in place. However, the inhabitants of this water world (who were not natives) had been harvesting the ocean for oxygen, effectively destroying the water world. It was an interesting perspective on environmentalism, which to be honest I don’t think was carried across too well in the episode.

There’s also the water world of The Legend of Zelda – The Wind Waker. People sing that game’s praises, but to be honest I could not think of a more boring or frustrating Zelda game. Okay, Skyward Sword was probably more annoying. But I’d prefer the interesting landscapes to nothing but cell-shaded water for the at least fifteen minutes it takes to get to the next tiny island on the map! Breath of the Wild was much better in this respect. I prefer hiking to sailing, anyway.

Then, of course, we have shows like One Piece. Think Pirates of the Caribbean meets Looney Tunes. It’s a story of a group of pirates hunting for treasure on a planet covered mostly by water, except for a strip of land that bisects the western and eastern hemispheres. The seas are inhabited by bizarre creatures, a Mardi Gras of giant hippo and bovine chimeras and bird-headed eels. Quite inventive and surreal, that show was.

And to be honest, when it comes to the human imagination, you can be as out there as you like.

I, on the other hand, am a bit more of a realist. And given what I’ve learned about geophysics over the years, I find myself more interested in the mechanics of a real-life water world.

Harsh Reality

We already have real-life examples of water worlds. Europa, Jupiter’s smallest moon, is one. Okay, it’s not a water world at its surface. It’s covered in pack ice, but based on surface scans, we’re pretty confident that there’s a subsurface ocean, thanks to tidal heating from Jupiter. Ganymede and Enceladus are also examples. Not just in our solar system; many exo-planets are candidates for water worlds (PTI, 2017). But the ones we can observe directly are all covered in ice.

If we want one like that in Kevin Costner’s movie or One Piece, we’ll need to set out a few required parameters. We want the water to be liquid at the surface. The reason Europa (et al.) is covered in ice is because its surface is exposed to space. The water radiates heat as infrared radiation, and promptly freezes. We need to have something to contain that heat at the surface. The best thing for that: an atmosphere. The atmosphere, with enough CO₂ to absorb the heat from the water’s surface, and O₂ for the seafaring inhabitants to breathe, will trap all that nice liquefying IR radiation and keep the water nice and fluidy. Yay!

But this has its own problems. Depending on the type of sun you have, it can stir up some pretty hefty weather. Let’s assume the sun above our water world is a G-type yellow dwarf, like our Sun. Let’s also add in the assumption that our water world is just as far from its sun as Earth is from ours.

Here’s what happens on our planet. Sunlight strikes the equator and heats up surface. Hot, moist air rises into the atmosphere and begins to cool. As it cools, the vapour precipitates over land and you get monsoons. The air starts to travel away from the equator, such that when it’s fully cooled at thirty degrees from the equator, it descends back to the surface in a process known as convection. However, on Earth, that air is bone-dry, which is why North Africa, the Middle East, parts of Asia, Mexico, and the southern United States are desert lands. The point is that land serves as a sponge of sorts, to draw water vapour out of the atmosphere. Without it, on our water world, you’d have heavy monsoon-level rains at the equator, thanks to the much higher area occupied by water, leading to a much higher rate of water evaporation. Even at that thirty-degree mark, the air isn’t likely to be terribly dry. You’ll still have lots of vapour in the atmosphere, and this can cause some more problems.

CO₂ is not the only greenhouse gas. Water vapour also absorbs infrared radiation, making it a greenhouse gas as well. In fact, it absorbs seventy per-cent of the infrared radiation entering the atmosphere (Maurellis, 2003). So if you’ve got a lot of moisture going into the atmosphere and not precipitating out, that’s going to increase your atmosphere’s heat capacity. You’re going to bloody hot and muggy at the equator, but what about the polar regions?  It’ll be bloody cold above sixty-degrees latitude, especially if your water world’s axial tilt leaves parts of the polar regions in darkness through much of the year. That’s freezing. But you won’t be safe in the area between thirty and sixty degrees. The temperature differential between the equator and poles will cause massive cyclones and choppy oceans between those latitudes. Very rarely will you have a favourable wind to throw up your square sail; if you had a lateen sail, the waters would be so rough you wouldn’t be able keep a stable footing on your boat long enough to tack into the erratic winds.

Hardly a world of adventure, is it?

And sightseeing would be out of the question because … well, what is there to see besides a vast expanse of water.

Going Down!

What about under the surface? Let’s hop in our submarine and go and find out.

We could say it’s an Earth-sized rocky planet covered in water. You’d likely have hydrothermal vents, like Earth, which can support a vast and varied array of life. You could even have mountaintops that serve as spots of land – like the Hawaiian Islands. But that’s kind of boring, don’t you think?

Let’s consider the other alternative. Warning: Math ahead!

Let’s say it’s just ocean through and through – a big ball of water floating in space. First off, how big is this ball? If we wanted the gravity at the water’s surface to be the same as that of the Earth, it’s gonna need to be much bigger than the Earth. This is because the density of water (997 kg/m³) is much lower than that of rock (between 5000 and 8000 kg/m³). Let’s do some math!

Let g_w be Acceleration due to gravity for our water world; r_w is the radius of our water world; D_w is density of our water world; Mw is the mass of our water world.

Density is related to mass by the formula: M = DV, where V is volume of the object, in this case a sphere. The volume of a sphere is: V = 4πr³/3. The acceleration due to gravity is given by the formula: g = – G M / r², where G is the universal gravitational constant. Since we know how to relate mass to volume, let’s merge the equations together.

g = -4GDπr³/3r² = -4GDπr/3

So, let’s say we want the acceleration due to gravity to be the same at the water world surface as it is at the Earth’s surface. We write out the equation:

g_E = -4GD_Er_E/3 = g_w = -4GD_wr_w/3

Run some simplification, and we get:

r_w/r_E = D_E/D_w

This relation basically says that the ratio of the water world’s radius to the Earth’s radius (how much bigger the water world is over the Earth) is equal to the ratio of the Earth’s density to that of the water world. If we use the values I cited above, this means that the water world would, at least, need to be five times bigger than the Earth! I actually calculated it to a whopping 35,196 km!

You might be wondering why this matters. It’s a big deal! Think about The Abyss by James Cameron. They couldn’t get more than a few kilometres down before their sub was crushed. The pressure goes up linearly with depth and is also proportionate to the surface acceleration due to gravity (MultimediaPhysics, 1997). The density of water is 997 kg/m³, and as we’ve already decided, the surface gravity is 9.81 m/s². This means that with every metre of depth, you’re increasing the pressure by almost ten tonnes! Your sub would need to be made of some ludicrously strong material to explore the entirety of this ball of water.

This consideration is also important for the structure of this ball. The higher the pressure, the higher the freezing point of water. At the centre of this ball of water, thirty-five kilometres down, the pressure would be about 344 gigapascals (about three-thousand five-hundred times the Earth’s pressure at surface). At this pressure, water turns to Ice-X, and starts behaving really weird. All the molecules line up in a cubic structure, and some of the molecules might even become ionised, meaning they’d carry electric charge. In fact, theoretically, if this ice had a little bit of ammonia mixed into it, it would be a superconductor (Chaplin, 2019). So if there was a nearby electromagnetic field – like that generated by, say, a sun – this field would induce an electric current in our water world’s core that would never stop running.

What would this do for our water world? You’d probably get stunning auroras, devastating thunderstorms in the atmosphere, and probably even lightning at the core! Hell! What if this water world had a moon not all that different from ours, including a metallic core? There would probably some massive electrical arcing across those worlds! Wouldn’t that be a spectacle? Just make sure it doesn’t fry your sub’s instruments … or you!

Water World Safari!

I doubt there would be much in the form of life on such a world. You could have indigenous life that adapts to utilise the electrical energy from the core. What it would look like would be anyone’s guess! But I doubt it would be showing itself at the surface. Given the atmospheric conditions I’ve just described, it wouldn’t be a very pleasant environment for life forms. But there’s an issue that hasn’t been covered.

What does Oxygen actually do for life on Earth? It’s often taken for granted that Oxygen is required for life, but why is it a requirement? It’s because Oxygen is an electron donor, and thus a carrier of energy in the chemical reactions of life. Well, on our water world, there is a source of energy in the core (all that electricity), but could Oxygen or similar analogue carry that energy in a similar capacity? Well, I don’t think so. Oxygen isn’t the only element used as an electron donor. Organisms at hydrothermal vents on Earth don’t have access to sunlight and can’t engage in photosynthesis, for which Oxygen is useful. Instead, they use Hydrogen, which allows them to access energy in the form of chemicals released from those hydrothermal vents – sulphurous compounds formed deep in the Earth’s interior.

But they’re not drawing energy from electrical arcs. They’re not time-travelling De Loriens! What chemical element could allow energy to be extracted from lightning?

I suppose that electrical arcs from our water world’s core could spark the formation of important biomolecules in the higher layers of the ocean, triggering reactions between ammonia, methane, and other goodies that have been dissolved in our water world from meteorite impacts. These could not only be used as food for life forms, but may in fact be the building blocks for the first life forms in our ocean – you can check out the Miller-Urey Experiment (Stated Clearly, 2015) for more information on that; it’s too damn complicated at the moment. Suffice to say, the superconducting core could generate arcs, which break apart water into Oxygen and Hydrogen while triggering chemical reactions to produce biomolecules deep in the water world’s interior. These chemicals then rise up to the higher layers to feed bacteria, which would then feed more complex life forms closer to the surface.

Journey to the Core

So, possibly, if you took your sub down into our water world, away from the violent storms and lightning strikes, you might first encounter carnivorous fish and bizarre creatures swimming about. Some – maybe all – of them might be fluorescent, and may even resemble Earth’s aquatic life … at least initially.

Before long, you’ll start seeing some nightmarish creatures in the deeps, not unlike the abyssopelagic demons of Earth’s trenches. Assuming you survive an onslaught by these hungry creatures and the sub isn’t crushed under the pressure, you’d eventually reach a zone dark as deep space where a water sample would reveal a veritable zoo of different microorganisms, no two alike.

Deeper still, you’d see light flashes searing through the water as far as you can see, until you reach the outer reaches of the core. Electricity would arc from mountainous electrodes made of ice, bubbles of Oxygen and Hydrogen gas billowing upwards. The water currents would be unstable and violent, and your viewport would be full of brightly lit bubbles, as if you were moving through a foamy bubble bath, or the froth of a cappuccino … a flammable cappuccino! Bubbles of molecular oxygen and hydrogen gas make for a wonderful explosion!

And the sound! Oh … my … GOD! The sound! Those arcs would likely create thunderclaps in the water just like in the air. But because the pressure is so high, those claps would travel much faster and further. Your sub would have a tough time handling the sudden pressure changes, and your ears would be no match.

But it would be a fun sight in the nanoseconds before your brain squirted out your ears and nostrils. Good luck getting that image out of your head!

Not all doom and gloom

Okay, so I’ve kind of ruined everyone’s vision of a water world. But at the same time, wouldn’t a movie about such a world be cool? Imagine a journey into a dark abyss, braving violent storms, besting hungry leviathans, avoiding nightmarish demons, crossing crushing darkness … to uncover the true Thor’s Hammer, a glassy sphere seething with energy.

Sounds pretty cool to me.

 

ed: apologies to C. S. Cooper for this long delayed post. 

 

Bibliography

Chaplin, M. (2019, May 12). Water Phase Diagram. Retrieved July 13, 2019, from Water Structure and Science: http://www1.lsbu.ac.uk/water/water_phase_diagram.html

MultimediaPhysics. (1997, June 6). Pressure-Depth Relation. Retrieved July 13, 2019, from http://lectureonline.cl.msu.edu/~mmp/kap9/cd246.htm

Maurellis, A. (2003, May 01). The climatic effects of water vapour. Retrieved July 13, 2019, from PhysicsWorld: https://physicsworld.com/a/the-climatic-effects-of-water-vapour

PTI. (2017, September 5). First evidence of water found on TRAPPIST-1 planets. Retrieved July 13, 2019, from The Indian Express: https://indianexpress.com/article/technology/science/first-evidence-of-water-found-on-trappist-1-planets-4827977/

Stated Clearly. (2015, October 27). What Was The Miller-Urey Experiment? Retrieved July 13, 2019, from YouTube: https://www.youtube.com/watch?v=NNijmxsKGbc