I'm not sure this actually provides the right perspective, in the sense of a useful intuition. Taking anything from the part of the Earth we live in (essentially, the troposphere plus the upper part of the crust) and visualizing it as a sphere will make it look small, because the troposphere + upper crust is a fairly thin shell, so doesn't take up a lot of volume when visualized as a solid sphere next to the earth.
I disagree. It is a useful perspective because it flies in the face of one's intuited perspective. How many of us would have estimated that the volume of water would be so small? We visualize the oceans as really deep gouges on the Earth's surface because to our puny asses a depth of 1 to 8 miles sounds amazingly deep. We'd never guess that even with miles deep depressions and miles high mountains, the Earth is smoother than a billiard ball:
Combining both of these counter-intuitive perspectives tells us that our oceans are akin to a very thin film of water on a wet billiard ball. A thin dirty film is all that billions of bacteria needs to thrive on a billiard ball, and a thin dirty film is all that billions of animals and plants need to thrive on Earth.
> How many of us would have estimated that the volume of water would be so small?
Well, I did, but that's because it's already been emphasized to me before (in some kind of geology class) how little volume the crust+troposphere shell takes up. It's not a water-specific thing, but a crust/troposphere thing, of which water is a subset. And actually I think the real underlying counterintuition is just a geometric one, that people don't realize little volume spherical shells occupy relative to solid spheres.
"How many of us would have estimated that the volume of water would be so small?"
I did. Before reading the article, I did the following very rough calculation in my head: earth is 40,000 km (equator length) by 20,0000 km (pole to pole). An average water depth of 1 km gives 800M cubic kilometers of water. From there, I guesstimated the diameter at about 1000km (a 1000km cube would be 1000M cubic kilometers). It might have ended up smaller if I hadn't approximated the surface of the earth to be a cylinder, but who cares about such a 'puny' rounding error, given that I totally guessed at that 1 km?
This gets at my reaction as well. It might be useful to have spheres of some of the precious metals (silver, gold, etc.) next to the water sphere to help set the frame of reference. I'm guessing they'll be much, much smaller than the water sphere.
At the least, this depiction jars against the common idea that water covers ~66% of the earth's _surface_. The mapping to this presentation is, presumably, the fact that surface of the earth is exceedingly thin with respect to its radius. Thus _delirium's point, that the absolute volume isn't as important as the manner of distribution in relation to other materials on the earth. The common adage that a human is 70% water doesn't, by itself, give a useful description of what it means to _be_ human.
> It might be useful to have spheres of some of the precious metals (silver, gold, etc.) next to the water sphere to help set the frame of reference.
I'm not sure how it compares to the total gold potentially available, but from what I can find, only about 8500 m^3 of gold has been mined in all of human history, which would make a completely invisible sphere on the scale of this image--- radius a bit over 50 m.
Starting with the earth's crust [1]: gold is one of the absolute rarest elements there -- at 72nd out of 78 [a] at between 1-4 parts per 10^9 (mass). The volume of the crust is on the order of 10^10 km^3 [2][b], with a density around 3 g/cm^3 [2], for a mass of gold on the order of 10^11 tonnes. Being extremely dense at 19 g/cm^3 [3], this would fill a compact sphere on the order of 1 km radius.
The mass of the earth [4] is about 200 times more than the crust -- almost 10^22 tonnes -- but the elemental composition of the core is unknown and very different from the crust. It's likely to be highly enriched in gold relative to the crust, because of gravitational separation (heavy metals sink down). Extrapolation from crustal abundance would give 10^13 tonnes, whereas one geologic estimate [5] gives 10^15 tonnes in the core alone -- a sphere 30 km in radius.
[a] excluding short-lived unstable elements and noble gases
[b] roughly, ~40% of the earth's surface (~5*10^8 km^2) is continental crust ~50 km thick
That is not a completely reliable measure of abundance when it comes to human purposes, after all it needs to be economical to extract these resources.
After all metals like lithium and most of the rest of the "alkali metals" and "rare earth metals" are relatively common, this issue is natural processes do not collect and concentrate them, as they are much more reactive and easily dispersed, so significant commercial deposits are rare compared to its crust concentration percentages.
Gold is a metal that naturally concentrates into deposits after aeons of time, as it is heavy and relatively non reactive, so there are many more commercially viable deposits than other metals with significantly higher abundance.
Indeed. The chemical properties of the elements will make some easier to extract than others. Metals that have been known since prehistoric times (copper, tin, lead, silver, zink and others) easily combine with sulphur in the crust, and can be found as easily extractable ores, while the rare earths are as abundant as these, but do not concentrate much in specific ores. The same goes for Uranium, that is surprisingly common in most minerals.
What matters is how easily the elements can be extracted and processed. Aluminium is 13% of the crust by weight, but was not possible to process before after around 1880, because electrolysis and large scale electricity production had to be in place first.
There are some smart[3] people on HN. I think it should be possible for someone to have an Earth globe, with a sidebar of statistically correct, usefully laid out information that the user asks for - how much alcohol is produced each year vs how much soya, or gold vs copper vs uranium; people living on less than $2USD per day vs people with average income of $20; amount of energy used by renewables and non renewables; amount of CO2 produced vs amount able to be 'sunk'; etc. Some data would need to be retrieved from other places (with sources given.) Caveats for biases and inaccuracies would need to be clear.
You'd monetise it by selling it to Wolfram Alpha.
I'm finding the spheres a bit tricky to get my head round.
How to Lie with Statistics covered this with the "money bags" example.[2]
I was told that the entire population of the Earth could fit on the Isle of Wight[1].
It might be useful to have spheres of some of the precious metals (silver, gold, etc.) next to the water sphere to help set the frame of reference. I'm guessing they'll be much, much smaller than the water sphere.
The actual amount of gold in the Earth is pretty poorly constrained, because most of it is expected to be at the core.
The first thing I thought when I saw is image was that I would love to see an animation of the sphere collapsing and refilling the oceans, etc. Assuming the animation simulated actual gravity and water fluid dynamics, I wonder how long it would take and what it would look like? (That is, the initial reflooding, reforming of rivers, clouds and ice caps, and so on.)
A realistic animation would not be pretty. Actual gravity will not allow the Earth's solid surface to stay where it is while you dump water on it.
Imagine what would happen if you dropped an 800-mile water balloon in the middle of Kansas. I'd be surprised if the North American plate didn't break up into several pieces under the weight of all that water. You'll probably get supersized volcanoes erupting all over the world due to the sudden stress on the crust. The volcanoes would then be extinguished by the megatsunami from the ball of water, causing massive steam explosions. One thing is certain: There won't be a Mississippi River anymore. Not sure about ice caps, that could take a few millennia.
Michael Bay and Roland Emmerich are going to love this.
Another interesting perspective: Earth's atmosphere is about five miles thick. Yes, it trails off exponentially and airplanes can fly and people can breathe (sort of) at 30,000 feet. However, were it uniformly as dense as it is at sea level (i.e. the atmosphere most of us are familiar with), it would fit in about five miles.
That's indeed an interesting perspective; I just double-checked in sane units:
Standard pressure 101 325 N/m^2 divided by standard gravity 9.80665 N/kg gives the mass of the air per area: 10 329 kg/m^2.
Divide that by an air density of 1.225 kg/m^3 to get a height of 8435 meters[1]. The Mount Everest is 8848 meters high. If the atmosphere were uniformly dense, the highest mountains would rise above it.
([1] Not in fact accurate to four digits because the constants I used aren't really constant across that height range.)
Thanks, codeflo. I calculated similar numbers and only gave a very crude approximation but I will take your word for it. Obviously, with the thermal distribution according to altitude it's a poorly defined problem.
Most intuitively, this means that when looking at some object on earth ~5 miles away, you are looking through roughly as much air as you are when looking at any given planet or star above you in the sky.
I'm very curious to know as well. However, in the illustration, a whole lot of that water would be in low earth orbit, so the thought experiment gets complicated ;)
At first I thought perhaps you could use tsunami wave speed data for a very rough estimate. But that's wrong, because tsunami speed (roughly between 500 and 900 km/hr depending on ocean depth) is a measure of the wave energy propagating through the ocean, not a measure of the water's speed over ground.
Instead, perhaps one could start by using a model for the flow of water from a catastrophic dam breach. Hopefully someone more mathematically inclined than I will give it a go...
Being high doesn't put you in orbit, it takes velocity relative to Earth to do that.
(Rockets going into orbit aren't just climbing, they're also building ground-speed. If there were an imaginary tower from ground to low-earth-orbit height, climbing it wouldn't put you in orbit - if you let go of something at the top of that tower, it would just fall.)
Unless the tower reaches to geosynchronous orbit (~36,000 km altitude). Then you've got a space elevator.
You do get some relative velocity due to the earth's rotation, it's just not enough to put you in orbit until you reach geosynchronous altitude (from your imaginary tower, not necessarily the imaginary sphere of water).
It's still not enough. At the equator, to do one revolution per day, you're doing ~1000mph. At 36,000km, because the circumference of the orbit is much longer than the circumference at ground level, to do one revolution per day, you need to be doing ~6900mph. So even if you get to geosynch, you still need to pick up ~5900mph sideways in linear velocity. As well as the energy it takes to get up there.
How likely is it that this sphere of water actually collided with our Earth billions of years ago? What is the possibility of even more such "water meteoroids" flying around nearby galaxies?
Water does not stay liquid in a vacuum. It is either solid or gaseous, depending on the ambient conditions. It is not well established where the primordial Earth gained its water. The matter in the protoplanetary disc from which the Earth coalesced probably didn't contain much water or other volatiles because of the proximity to the Sun. Instead, it is thought that water arrived afterwards, via numerous collisions - then commonplace - with icy comets that originated beyond the frost line.
Yes, sort of. I believe the current theory is that much of Earth's water came from thousands or millions of meteorites that carried ice and/or hydrogen and oxygen compounds that later stabilized to water. This would have happened during the solar system's infancy, when there were far more asteroids flying around our solar system. In fact, it is thought that the planets started this way. Lots of free flying rock colliding together, gaining mass, gravity, etc. over billions of years.
Another related perspective on earth oceans. Take a thimble of water and pour it into the ocean. Allow sufficient time for it to evenly mix. Now scoop a new thimble of water out of that ocean. Your new thimble will have several molecules from the original thimble of water.
Orders of magnitude and all that. To me though this shows how connected all of our resources are and how dangerous pollution can be.
That's more of a "hey look molecules are small" illustration than anything else. It just so happens that the number of molecules in a thimble of water is roughly equal to the number of thimblefulls in the ocean, but it could easily be ten thousand times either way.
Based on the statement that "[t]he sphere includes all the water in the oceans, seas, ice caps, lakes and rivers as well as groundwater, atmospheric water, and even the water in you, your dog, and your tomato plant", I would guess not (although it doesn't specifically say that that's a comprehensive list). That conclusion is further supported by the observations that 1) we don't actually know exactly how much water there is distributed through the mantle, but 2) more water gets subducted than is released by volcanoes, so it's a large volume and getting bigger and 3) the total amount is probably comparable in size to the amount of surface water, which would make that sphere significantly bigger if it were included.
Considering that the surface water came from outgassing volcanoes, it would be reasonable to think that there might even be 2 or 3 times as much water still trapped down there.
The question of the origin of water on Earth is yet un-resolved, with a contender to the out gassing theory being deposition by asteroids [1]. Even by that theory I believe it was volatiles (hydrogen, oxygen) that were "outgassed" and then allowed to form into H20 in the atmosphere.
That being said, the possibility of large masses of water subducting under the crust and sitting in the lower mantle has been deemed plausible [2](but not probable).
Interestingly, there is an estimate of the size of a sphere containing the water of the world's seas in Twenty Thousand Leagues under the sea:
"THE PART OF THE planet earth that the seas occupy has been assessed at
3,832,558 square myriameters, hence more than 38,000,000,000 hectares.
This liquid mass totals 2,250,000,000 cubic miles and could form
a sphere with a diameter of sixty leagues, whose weight would
be three quintillion metric tons."
According to Google and Frink, 60 leagues is less than 1/4 of the 860 miles estimated here; I'm not sure how much of that is due to the smaller scope of the estimate in Verne's book.
Those numbers don't make any sense. 2,250,000,000 cubic miles is ~100 times the volume of a sphere with a diameter of sixty leagues. It's also over 6 times the volume cited in the article, while having only twice the weight. That can't happen unless water's density varied dramatically.
So Verne both overestimated and underestimated, and didn't bother to check if his numbers were consistent with one another.
I can't speak for this estimate in particular, but Verne usually did his (quite extensive) calculations in metric units. Many older translations of his work swapped in imperial or US customary units without adjusting the values for the 'benefit' of English-speaking readers.
Aha, that might actually explain the inconsistency between the volume and weight. Imagine that the volume was originally stated as 3.6 billion cubic kilometers, which would actually weigh around "three quintillion tons" (actually close to four, but let's forgive that). A translator might have turned that into 2.25 billion cubic miles, thinking that one mile = 1.6 kilometers. But of course, non-mathematical types usually don't notice that one cubic mile = 4.1 cubic kilometers.
I've looked up the original text and it uses the same units except for the weight which is expressed in "tonneaux" instead of metric tons: "[...] dont le poids serait de trois quintillions de tonneaux." So they basically swapped the units without bothering to calculate the correct value.
Now how much a tonneau weights is left as an exercise to the reader...
This seems geared to make the amount of water on the planet look small, but it backfired for me.
I still remember the first time I flew over Lake Michigan, and my mind was blown at the impossible scale of all that water.
In this image, most people compare the water to the Earth. Nice, homey, medium sized Earth. In comparison, the water looks tiny.
I was drawn to that far tinier lake to its right, which once blew my mind. Comparing the lake to the big wet globe feels like skipping a few steps in Powers of Ten (or Gurren Lagann).
All I know for sure is that my poor human brain sucks at scale. "Bigger than I understand" arrives far too soon.
Nice work. It would be fun to see a comparison of the sphere containing Earth's water against a sphere of Earth's [relatively-]habitable area (say, the cumulative mass between the average depth of the sea-floor to the average height above sea level (of all exposed land massess)). For your intents, it could be a meaningful comparison in conjunction with you recent works. Thanks for sharing!
That's really not a lot of water, huh... And even less of it is directly consumable or even usable. This actually makes me think that mining asteroids for frozen water might not be such a bad idea (although it would still need to be purified)...
Here is an image showing just that, in a cubic format. The sphere of ocean water would have a radius of 684 kilometers, while the remaining water, most of which is glaciers and groundwater, would form a sphere of 227 km radius.
