Much lighter, actually. Ceres isn't particularly dense as rocky bodies go (~2.2 g/cm^3, give or take), but it's still much denser than water (~1 g/cm^3).
Ceres could be taken apart with solar energy and rebuilt into a habitat much bigger than the Earth, never mind Mars. Ceres leads to the stars, Mars is just a dead end.
Is there reason to believe the stars are less of a dead end than Mars? It's easy to imagine us making a huge bet on interstellar travel, and just dying in interstellar space. Surely there's untold abundance in the stars, but if you can't actually reach it, then it may as well be a mirage.
Whenever I consider the possibility of interplanetary colonization, I come back to the conclusion that the only way to make it feasible is to reorient our economy towards sustainability in order to survive on Earth indefinitely. It's going to take a long, long time to develop the required technology, there's no real reason to believe artificial terraforming is even possible (since our sample size is 0), and even if it is it may take thousands or millions of years to complete.
I'm not being facetious with that last part, in the absence of information to the contrary, we should expect technology that works via geologic processes to run on a geologic timescale. I personally think artificial terraforming is probably possible, and that we could accelerate it to be much faster than the natural terraforming of Earth. But accelerating a 2 billion year process to be 10000x faster still takes 200k years. (ETA: I suppose a lot of that was the planet forming and the rate of bombardment falling to something tolerable, which eg Mars was already subject to, so maybe call it 1B/100k years.)
I did a lot of analysis for the problem of "build a solar sail factory on a carbonaceous chondrite asteroid that makes sunshades to deploy at the L1 point", particularly from a chemical engineering point of view.
One interesting thing was that a lot of the chemistry involved was similar to the chemistry of decarbonization and carbon capture, particularly when you get CO2 as a waste product it is too precious to vent so you are going to feed it back into your "petrochemical" line.
Objects like Ceres are the norm once you get out to the outer solar system, the difference is that Ceres is close enough to the sun for solar energy to be a good power source. Centaur objects, the moons of outer planets, and Kuiper belt objects like Pluto are similar but when you get far from the Sun you need to use a different power source such as D-D fusion.
If a species became independent of sunlight it could take advantage of very generic objects that exist throughout interstellar space (comets, rouge planets, etc.) and make the journey in hops of (say) 100 years from one object to another. At that rate it would be possible to visit another star system in 10,000 years with a comfortable lifestyle. People like that might as well keep comet hopping but if they came across a star system I'd imagine they start some project like a Ceres megastructure because it is generic you can find some object like that and be able to establish a huge industrial base and population larger than the Earth with the same head end you've used all this time and same comfortable lifestyle.
Earth would be priority two if that for those people. Grabby aliens might have disrupted Ceres but left the dinosaurs alone. But Ceres is here, so they were not. Ceres is such an attractive target that it should be a SETI goal to look for hardware left behind. Would be hilarious if they stole the Deuterium.
It's interesting speculation. I just can't accept the existence of a spacecraft that can last 100 years without a catastrophic failure, or Ceres being reforged into a factory, or a nation of people who live entirely independent of Earth until I see it.
Sometimes people talk about these things as if they are inevitable, but I would say there's an extremely good chance we go extinct without ever leaving this solar system (Voyager 1 notwithstanding). I think this is a valuable and grounding perspective in planning for the long term future of humanity, because we have to accept that that future takes place here on Earth and largely with the technology we already have. Space colonization is seductive, but like all silver bullets, impossible to operationalize within the constraints imposed on us by our situation.
But it's probably not a useful one when picking SETI targets or generating other research ideas, and that stands on it's own merit.
I'm trying to visualize the amount of water here, but it's hopeless unless an elementary student can calculate how many oil drums it would fill or football fields it would cover to a depth of one yard.
Assuming you mean "the depth of this water, if confined to a cross-sectional area the size of the United States", this is one of those nice Fermi estimation problems:
- I know the US contains hundreds of millions of people, and the world contains a single-digit number of billions. So the US has about 10% of the world's people.
- The US probably isn't particularly dense or sparse relative to other populated areas, so 1/10 the population should be 1/10 the Earth's land area.
- The Earth has twice as much ocean as land, and
- The ocean is a few miles deep - let's say 5 - so there's about 10 miles of ocean depth per land area.
- So compressing that to 1/10th the land area suggests the oceans should cover the US to a depth of about 100 miles.
The exact answer, it turns out, is about 89 miles - really close, without looking up a single piece of information!
I believe the US has about 350 million people out of about 7 billion people on Earth. That makes the US population equal to about 5% of the total, not 10%.
27 meter diameter in fact. A 27-meter sphere is about 150 times as voluminous as a 5-meter sphere.
It's still a mind bogglingly small amount considering that humans have spared no toil, sweat and blood on industrial scale gold mining ever since the dawn of written history - and since gold is so valuable and hard to destroy, most of it should still exist to this day in form or another.
Yet, if you smelted it all to a single object it would fit on a typical single family housing plot.
Spheres/circles are definitely surprising in how a seemingly small increase in radius changes the volume/area much more drastically. The cubing/squaring exponent is easily taken for granted.
Humans are notoriously terrible about estimating volumes when things are curved and volume functions are exponential.
A great example of this done in 8th grade science classes across the US is to put 100ml of water in a 100ml graduated cylinder, 150ml in a 1L beaker, and ask the class which has more. Humans are awful at estimating how much volume the increased radius adds, and usually will say the 100ml.
The problem only gets worse as we graduate from cylinders to spheres.
We can all visually see which sphere is bigger, but cannot come close to estimating how much bigger one is than another.
I don't think this word means what you think it does. Or I don't. Exponents are just the number the value is raised. Squaring a value just uses an exponent of 2 where cubing uses an exponent of 3. Polynomials are x^2 + x + 1 type of equations. But admittedly, it has been 30+ years since I've thought about them at that level, so maybe I'm the one with fuzzy groking
We can go a step further with the pedantry, and say that the commenter above is using an unreasonably narrow definition of the work "exponential" and that there are others which allow x^2 to be described as "exponential".
We could, but I would describe it as "mathematically accurate". Which is not incompatible with "unreasonably narrow", given that the definition of "exponential" has recently gotten polluted enough that it is now often synonymous with "fast growing". But what's the point of arguing over definitions if we're going to start with a baseline of saying that there is no basis upon which to argue definitions other than recent conventional usage?
> there are others which allow x^2 to be described as "exponential".
Those same definitions allow x*1000 to be described as "exponential". (x*1000000 would be "more exponential"!)
If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x*1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x*1000=x*10^3 and x*10^3 has an exponent in it.
(Again, I sadly accept that in today's world, "exponentially" is being used to mean "fast growing", or sometimes more specifically "faster than linear". If I'm trying to understand what someone means, then it doesn't matter whether I find that usage to be a good idea or not.)
No; to characterize "exponential" as "fast-growing" is a misunderstanding of what I'm saying. "Faster than linear" would be a good descriptor.
> > there are others which allow x^2 to be described as "exponential".
> Those same definitions allow x1000 to be described as "exponential". (x1000000 would be "more exponential"!)
> If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x1000=x10^3 and x10^3 has an exponent in it.
I don't agree with this. These are categorically different.
In f(x)=x*1000, as x increases, the function's output increases linearly. The slope of the derivative is 0.
In f(x)=x^3, as x increases, the function's output increases more than linearly. The slope of the derivative is positive and linear.
In f(x)=3^x, as x increases, the function's output increases much more than linearly. The slope of the derivative is positive and is itself a function of x.
These are all categorically different, and refer to something different than "fast-growing". "Exponential" in the mathematical sense, means the derivative is a function of x. "Exponential" in the colloquial sense means that the derivative has a positive slope. "Fast growing" just means that the derivative is large, even if it is a constant.
Um, ok. Your position baffles me, because you clearly understand what exponential means mathematically, yet you insist that the word means something else colloquially. Specifically "faster than linear". Usually, people who (mathematically) misuse the term do so because they don't understand what it actually means, but that's not what is happening here.
If it's going to mean something precise, such as
> The slope of the derivative is positive and linear.
then why not pick the precise thing that the word already means?
Is x*log(x) also exponential to you? If so, then why not use the word that already exists: superlinear? If not... oh wait, the above definition I quoted wouldn't even cover x^2, since the slope of its derivative is constant, not linear. So I'm just completely confused; I can't figure out which (mathematically) non-exponential functions you would like to label as exponential. x*1000, no. x^3, yes. x^2, I don't know. x*log(x), I don't know. x^2*log(x), I don't know.
> "Exponential" in the colloquial sense means that the derivative has a positive slope.
"Exponential" in the colloquial sense means that the speaker isn't using a mathematical sense, and so isn't considering first or second derivatives. I don't buy the argument that the colloquial sense accepts x^3 and rejects x^2, and in fact I bet I could find someone using it for a linear relation ("My workload has gone up exponentially since you laid off half the team!")
> "Exponential" in the mathematical sense, means the derivative is a function of x.
No it doesn't. x^2 is not mathematically exponential, yet its derivative is a function of x. Exponential means the derivative is exponential. But that's just a detail that doesn't really change the core of your message.
The main purpose of the mathematical definition is to exclude polynomials. The main purpose of the colloquial definition seems to be something like an impressive or important increase.
Already eight years ago, I complained that people were using "exponential" where it doesn't make any sense. (See these two data points? Clearly exponential growth happend there. They're so far apart!)
I believe the problem has increased exponentially since then. Now everyone is using exponentially in literally the same way as literally.
You might be interested to know that the first definition of "exponential" is "of or relating to an exponent". The second definition is, as you say, "involving a variable in an exponent". https://www.merriam-webster.com/dictionary/exponential
As this is an internet forum and not a rigorous mathematical setting, I assert that my use of "exponential" is correct in context and to claim otherwise is incorrect. :)
I'm not sure if you are kidding but just in case you are not this is very misleading and in fact misguided.
Refering to polynomials as exponential just results in confusion essentially removing any meaning from the word. Any function can be written as something involving exponents, so that statement becomes meaningless.
> This sphere includes all of the water in the oceans, ice caps, lakes, rivers, groundwater, atmospheric water, and even the water in you, your dog, and your tomato plant.
No, it doesn't. It includes all of the water in the oceans, ice caps, lakes, rivers, groundwater, atmospheric water, and even the water in you, your dog, and your tomato plant.
Geologically it probably isn’t. If all surface oceans disappeared, some of that water would likely come out to the surface and form new bodies of water, over millions of years.
But would this sphere of water have enough mass to hold itself together as a sphere in space? Put aside it freezing into a ball of ice as a thought exercise.
i knew there would be someone to just try to get out of the answer by failing to just go with the spirit of the question by being pedantic. even my own attempt at dispel pedantry just allowed for even more pedantry.
Going from a liquid to a gas takes energy, which rapidly lowers the temperature of what remains. Net result most of the water freezes without some external energy source. Sublimation then lowers the temperature of the ice until near absolute zero, again unless there’s some external energy source.
Depends on the temperature. At Earth-like temperatures, yes, it would. The transition between the two is around 175 K, give or take; below about 150 K ice is quite stable in a vacuum even over astronomical timescales; above 200 K it sublimates rapidly. (Surface liquid water is never stable in a vacuum or thin atmosphere regardless.)
The rate of evaporation ramps up exponentially, from ~irrelevant at the bottom of that range to fast at the top. (For a body of this size, any resulting vapor would be quickly lost at these temperatures, so the rate of evaporation is effectively the rate of water loss as well.)
This is why Jupiter can have icy moons (temperature ~100 K), but ice sublimates quickly on Mars (~200 K).
The freezing-into-a-ball-of-ice is relevant here. A body that small can't hold on to water vapor at anything a human would consider a reasonable temperature; the average velocity of light gases at human-sane temperatures is high enough to overcome their escape velocity. See [1] for a log-log plot of what gases a body can hold onto - even Mars, which is much larger and denser than a Ceres-sized ball of water, has lost most of its water (although other factors like the solar wind are contributors there).
A cold enough body, though, has a low enough vapor pressure that this isn't relevant even over cosmological timescales. That's why Europa can can have a stable icy surface. It's far enough from the Sun (and has a low enough albedo) that it's very very cold (about 100K), and at that temperature ice doesn't sublimate very much.
TLDR: a Ceres-sized ball of water could hold itself together, but only as long as it stayed water. But it wouldn't be able to. Either it'd be cold enough to freeze over at the surface, or hot enough to evaporate into vapor that would escape.
Given that water gets lighter when cooling down right above its fusion temperature, and that ice is a pretty good insulator. You'd have liquid water below an ice crust for a lot of time. It would eventually freeze entirely and be slowly eaten by the Sun's radiations. But that would take a pretty long time (well on a human scale).
Yeah, that's why I specified freeze over and not freeze through, although without doing the math I'm pretty sure it'd still freeze through on solar system timescales without radioactive (as in Earth's own mantle's case) or tidal (Enceladus, Europa, possibly Triton and Ganymede) heating.
The sphere of water would have a surface gravity of 0.016 g, 1.6% of Earth's gravity, 1/10th of the Moon's gravity. So yes, it would gravitate into a ball shape, aside from slowly boiling off if it's inside the orbit of Mars (our 32°F Goldilocks Zone) or freezing if it's farther out.
Yep, it's quite misleading since the region where they looked for water at all is an incredibly thin layer on the outside of the planet, but they show it all as if it applied to all of the volume.
It's not bad on purpose if that what you understood.
But the comments here are full of "it's so little!" variants, where if you took the rest of the Crust and smashed as a sphere, it wouldn't be much larger than the water one.
It did evidently mislead a large number of people.
The USGS detail pages are based on a 1993 publication, Igor Shiklomanov's chapter "World fresh water resources" in Peter H. Gleick (editor), Water in Crisis: A Guide to the World's Fresh Water Resources (Oxford University Press, New York).
Turn Randall Munroe loose on this idea and be prepared for unspeakable devastation as a tsunami of Lovecraftian proportions wreaks havoc on the planet...
He already did it with a 1km diameter ball (https://what-if.xkcd.com/12/) and the destruction was terrifying. Please keep him away from these other bigger water balls.
Literally just posted today: the video version of his What If? analysis of what would happen if you took that ball of water and dropped it on Mars: https://www.youtube.com/watch?v=FkUNHhVbQ1Q
I think this is kind of useless information unless presented with other spheres for humans, structures, animals, plants, forests etc. for comparison. And ants.
I had no idea where to start. ChatGPT had a rather impressive looking “proof of work” that put all living humans into a 976m-diameter sphere, compared to the ~1384km-diameter sphere. Ie ~1km human sphere and 1,384km water sphere.
Just a few quick calculations to make it more relatable...
They say the smallest sphere of freshwater lakes and rivers amounts to 93,113 cu km. There are 1 bil cu m per cu km. With a global population of 8.2 bil people, that comes to 11,355 cu m per person. That's a 22.5 meter wide/deep/tall cube (or about 7 or 8 stories tall building).
If we use the sphere that includes groundwater, 10,633,450 cu km. Then we end up with 1,296,762 cu m or a 109m wide cube per person.
> The largest sphere represents all of Earth's water. Its diameter is about 860 miles
Should be a radius of 430 miles, no?
The image is very non-intuitive, IMO, because it's making the water appear so small compared to the entire planet (which, duh, obviously the water is only part of earth), but also drawing the planet that small really hides how friggin big the earth is!
Yes. The fresh-water lakes and rivers sphere definitely does not look like it could fill the Great Lakes next to it. I am not saying it doesn't, I'm just saying it doesn't look like it could.
It does look very small in comparison to say Lake Michigan but most lakes are very thin. Lake Michigan is about 500km by 200km but only .085km(85m) average depth.
Average depth of Lake Michigan is around 300 feet. Longest dimension is about 300 miles. If you drew a map of Lake Michigan on a sheet of letter-sized paper, the paper would be thicker than the average depth of water.
Helped for me to compare to the moon. The water sphere has less than half the radius of the moon (~1080 miles). Think that’s roughly 7-8% of the moon’s volume if it were a perfect sphere.
I thought the border with space is generally (and arbitrarily) said to be the Kármán Line, at 100 km / 62.1 mi. I'm not nitpicking, just curious about other definitions.
Also, I thought LEO typically begins around 180 km / 112 mi.
It's interesting to consider that there's about 26,000,000 km^3 of ice in the Antarctic ice sheet, which would give you a much larger ~150 m^3 cube of ice per person. That's not including the Greenland ice sheet or any sea ice.
Largest ocean in our solar system isn't even on Earth, apparently:
> ... Ganymede’s ocean is even bigger than Europa’s—and might be the largest in the entire solar system. “The Ganymede ocean is believed to contain more water than the Europan one,” he says. “Six times more water in Ganymede’s ocean than in Earth's ocean, and three times more than Europa.”
If we had the technology allowing us to move a full satellite through the solar system, we could probably do it in a way that would just make Mars a bit closer to the sun so that the weather gets nicer (sure, if it gets too close to earth it's going to mess up with both orbits, but we can as well correct it when it happens, right?)
It doesn't have to be near the sun to have heat or be warmed by the Sun. It is still currently in the goldilocks zone, same with Venus. The difference is how well each planet traps heat. No atmosphere no heat for mars, highest peak surface temperature is 70 fehrenheit or 20 celsius. Not much but enough green house gas and you could raise it by 20 degrees or more. Other thing to consider is that you don't need to move Mars, you could create artificial magnetospheres.
It would make Mars warmer. It would melt all the ice and CO2. It would give Mars an ocean. Of liquid rock. This is assuming that it doesn't destroy Mars completely. There might be enough fragments to make Solar System dangerous place and destroy life on Earth.
Europa is the size of our Moon. Colliding it with Mars would be similar to the collision that formed our Moon.
At some point I saw a design for a machine you could park at the Lagrange point between Mars and the Sun that would collect solar power and spit out a magnetic field strong enough to deflect enough of the solar winds that we wouldn't need to worry about that.
The largest ocean in the solar system actually is on Jupiter [1]. The gas planet has an absolute massive amount of liquid hydrogen on its "surface". But yeah, liquid hydrogen isn't water, so it might be the biggest ocean, but not the biggest ocean made out of water in our solar system :).
I'm aware, notice my comment specifically states "the Earth's *surface* " not just "the Earth". However, my kitchen counter is a flat surface, it's common knowledge the Earth isn't flat and the average ocean depth is 3,682 meters
That was my point. The Earth isn't flat, but its surface is very smooth.
You give the average ocean depth at 3.7km, but the Earth's diameter is about 12,742km, making those bumps pretty insignificant. If you cover your countertop in sandpaper and spill water on it, the difference in coverage going to be almost negligible.
Yea, just to be clear, I'm not disputing the image at all, my original comment is only an observation on the stark contrast when you juxtapose those two representations
The earth is smoother than a billiard ball when accounting for relative size. Highly likely the earth is actually flatter than your countertop when accounting for size.
I long assumed that the Earth is a "water planet" because water is mostly what you see from a distance. It wasn't until I did the math that I realized that is really about wet rocks in space vs dry rocks in space.
Earth isn't made of water, it's just a damp rock. Or a bowling ball that you squirted a dozen times with a spray bottle.
The volume of all water is 1,386,000,000 km^3, which is then 1.386e+21 liters, or right about the same number of kilograms.
The mass of Earth is about 5.972e+24 kg. So the percent fraction by mass is 0.0232%.
A "drop" is typically estimated at 1/20th of one mL, which is then 0.05 grams. We can estimate the mass of a small-ish bowling ball at 5kg, or 5000 grams. 0.05 / 5000 * 100 = 0.001%.
So it's an order of magnitude shy, but that's still closer than I expected! It's about 1 ml of beer on a bowling ball - a small splash. Or maybe a very large drop.
Lava is not really representative of the Earth as a whole, as it turns out. The mantle (which is the vast majority of Earth's volume) isn't a liquid, it's a squishy deformable solid. Magma that comes from the mantle is only liquid because of the removal of pressure or the addition of water; it wasn't liquid down there. And a lot of lava comes from crustal melting, not mantle material.
Earth as a whole has a density about 5.5x that of water.
The picture already answers this question. If the earth was a bowling ball the blue sphere would be much bigger than a single drop, maybe slightly bigger than a popping boba, the size of a small grape?
I don't buy it. Even allowing counting iron as separate from what rocks can be composed of (and using mass instead of volume) you still have 30.1%+15.1%=45.2% of the Earth as oxygen and silicon (which are most certainly part of what makes a rock) at which point you've already disproved the claim Earth is more a ball of iron than a ball of rock.
A ball of iron covered with a ball of rocks is a more fair statement though, and I'd agree with that. It's just that center ball isn't most of what makes up the Earth (by any measure).
Everything up to and including the mantle is either iron or has a lot of iron. But to your point the mantle also has a lot of silica. So I guess it depends on your definition of "mostly".
Mass is the defining characteristic of a quantity of matter. Given that much of the iron is under far higher compression than the outer layers of silicate rock, this also advantages iron.
By mass, iron (32.1%) is still a minority constituent of the Earth.
The ballpark math is easy to do in your head too. The diameter of Earth is 8,000 miles, and the deepest point in the ocean, the Mariana Trench, is only 7 miles deep. It's immediately apparent that the oceans are tiny by comparison to the rest of the mass that is Earth.
It's fun to scale down the Earth's depth to a 8 metre long measuring tape on the floor and then having kids guess things lik, how deep is the ocean, how deep is the deepest hole we've ever dug, how high is the atmosphere.
Adding in how far of a drive is it to X place or how far of a walk is it, is also fun.
Not completely accurate, it depends on your definition of smoothness. The Earth scaled down to the size of a billiard ball would have a texture more like sandpaper, certainly not what most people would consider smooth.
>So, based on the data, just how smooth is a CB? And how does this smoothness compare to the surface of the Earth? The highest point on earth is Mount Everest, which is about 29,000 feet above sea level; and the lowest point (in the earth’s crust) is Mariana’s Trench, which is about 36,000 feet below sea level. The larger number (36,000 feet) corresponds to about 1700 parts per million (0.17%) as compared to the average radius of the Earth (about 4000 miles). The largest peak or trench for all of the balls I tested was about 3
microns (for the Elephant Practice Ball). This corresponds to about 100 parts per million (0.01%) as compared to the radius of a pool ball (1 1/8 inch). Therefore, it would appear that a pool ball (even the worst
one tested) is much smoother than the Earth would be if it were shrunk down to the size of a pool ball. However, the Earth is actually much smoother than the numbers imply over most of its surface. A 1x1
millimeter area on a pool ball (the physical size of the images) corresponds to about a 140x140 mile area on the Earth. Such a small area certainly doesn’t include things like Mount Everest and Mariana’s Trench in the
same locale. And in many places, especially places like Louisiana, where I grew up, the Earth’s surface is very flat and smooth over this area size. Therefore, much of the Earth’s surface would be much smoother than a pool ball if it were shrunk down to the same size.
> Earth isn't made of water, it's just a damp rock. Or a bowling ball that you squirted a dozen times with a spray bottle.
Yeah, the image with the oceans being dry is wow-inducing... On further thought, of course it'd be very close a sphere, because gravity forces it to be. A sphere where e.g. a slice of it is water (imagine a clementine with one of its segments being water) would be very wobbly if even possible at all..
Yup, the mere fact that we can have oceans and continents on a planet means we can only have so much water, lest we become a water world or something more like mars.
I do wonder if the OP includes water locked away in rocks though, to my understanding the majority of the water is in the mantle and not even the oceans, but my source is my butt for that one
Oceanus's ocean tosses with slow, tall waves, beneath a pale blue sky. The colonists live in tall cities of steel and concrete with buildings sealed against the planet's harsh environment, on platforms floating on the planet-wide ocean. They spend their time pursuing art, leisure, and spiritual fulfilment, while automatic machines take care of their material needs.
Not sure this is accurate as we've discovered that water can reside deeper in the Earth than previously imagined and in addition to that the density of water at the surface is different than at the bottom of the ocean. I suppose they are also accounting for the salt being removed too. But my argument is probably in the margin of error so what do I know?
The density of water at the bottom of the ocean is actually quite similar to the density on the surface; it differs by only a few percent. Gases compress proportionally to pressure, but liquids act more similar to solids and compress very little even under enormous pressures.
The oceans are only about 3.5% salt by weight, so that doesn't make a huge difference, either.
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[ 3.0 ms ] story [ 281 ms ] threadhttps://en.wikipedia.org/wiki/Ceres_(dwarf_planet)
(Much heavier, I suspect, as well.)
Whenever I consider the possibility of interplanetary colonization, I come back to the conclusion that the only way to make it feasible is to reorient our economy towards sustainability in order to survive on Earth indefinitely. It's going to take a long, long time to develop the required technology, there's no real reason to believe artificial terraforming is even possible (since our sample size is 0), and even if it is it may take thousands or millions of years to complete.
I'm not being facetious with that last part, in the absence of information to the contrary, we should expect technology that works via geologic processes to run on a geologic timescale. I personally think artificial terraforming is probably possible, and that we could accelerate it to be much faster than the natural terraforming of Earth. But accelerating a 2 billion year process to be 10000x faster still takes 200k years. (ETA: I suppose a lot of that was the planet forming and the rate of bombardment falling to something tolerable, which eg Mars was already subject to, so maybe call it 1B/100k years.)
One interesting thing was that a lot of the chemistry involved was similar to the chemistry of decarbonization and carbon capture, particularly when you get CO2 as a waste product it is too precious to vent so you are going to feed it back into your "petrochemical" line.
Objects like Ceres are the norm once you get out to the outer solar system, the difference is that Ceres is close enough to the sun for solar energy to be a good power source. Centaur objects, the moons of outer planets, and Kuiper belt objects like Pluto are similar but when you get far from the Sun you need to use a different power source such as D-D fusion.
If a species became independent of sunlight it could take advantage of very generic objects that exist throughout interstellar space (comets, rouge planets, etc.) and make the journey in hops of (say) 100 years from one object to another. At that rate it would be possible to visit another star system in 10,000 years with a comfortable lifestyle. People like that might as well keep comet hopping but if they came across a star system I'd imagine they start some project like a Ceres megastructure because it is generic you can find some object like that and be able to establish a huge industrial base and population larger than the Earth with the same head end you've used all this time and same comfortable lifestyle.
Earth would be priority two if that for those people. Grabby aliens might have disrupted Ceres but left the dinosaurs alone. But Ceres is here, so they were not. Ceres is such an attractive target that it should be a SETI goal to look for hardware left behind. Would be hilarious if they stole the Deuterium.
Sometimes people talk about these things as if they are inevitable, but I would say there's an extremely good chance we go extinct without ever leaving this solar system (Voyager 1 notwithstanding). I think this is a valuable and grounding perspective in planning for the long term future of humanity, because we have to accept that that future takes place here on Earth and largely with the technology we already have. Space colonization is seductive, but like all silver bullets, impossible to operationalize within the constraints imposed on us by our situation.
But it's probably not a useful one when picking SETI targets or generating other research ideas, and that stands on it's own merit.
- I know the US contains hundreds of millions of people, and the world contains a single-digit number of billions. So the US has about 10% of the world's people.
- The US probably isn't particularly dense or sparse relative to other populated areas, so 1/10 the population should be 1/10 the Earth's land area.
- The Earth has twice as much ocean as land, and
- The ocean is a few miles deep - let's say 5 - so there's about 10 miles of ocean depth per land area.
- So compressing that to 1/10th the land area suggests the oceans should cover the US to a depth of about 100 miles.
The exact answer, it turns out, is about 89 miles - really close, without looking up a single piece of information!
https://www.wolframalpha.com/input?i=%28332%2C500%2C000+cubi...
Apparently all the mined gold in the world would fit inside a 5 m diameter sphere.
Spheres are suspicious in hiding weight.
> If every single ounce of this gold were placed next to each other, the resulting cube of pure gold would only measure around 22 metres on each side
So that can't possibly be right, you must be off by a factor of 10 or so at least—Wolfram Alpha says a 30m diameter sphere.
It's still a mind bogglingly small amount considering that humans have spared no toil, sweat and blood on industrial scale gold mining ever since the dawn of written history - and since gold is so valuable and hard to destroy, most of it should still exist to this day in form or another.
Yet, if you smelted it all to a single object it would fit on a typical single family housing plot.
A great example of this done in 8th grade science classes across the US is to put 100ml of water in a 100ml graduated cylinder, 150ml in a 1L beaker, and ask the class which has more. Humans are awful at estimating how much volume the increased radius adds, and usually will say the 100ml.
The problem only gets worse as we graduate from cylinders to spheres.
We can all visually see which sphere is bigger, but cannot come close to estimating how much bigger one is than another.
(Fair point that people are lousy at estimating even polynomial functions, though...)
I don't think this word means what you think it does. Or I don't. Exponents are just the number the value is raised. Squaring a value just uses an exponent of 2 where cubing uses an exponent of 3. Polynomials are x^2 + x + 1 type of equations. But admittedly, it has been 30+ years since I've thought about them at that level, so maybe I'm the one with fuzzy groking
Exponentials eventually grow much faster than polynomials, no matter what the exponent is.
I mean, look, in v = x^3, the "3" is an exponent. But it's not an exponential function because the variable isn't in the exponent.
Since we're being pedantic, that last clause should be: "as long as the exponent is greater than 1."
https://www.merriam-webster.com/dictionary/exponential
https://www.merriam-webster.com/dictionary/exponent
which is how I was taught. I only went to CalIII back in the early 90s, so who knows what's being taught now???
> there are others which allow x^2 to be described as "exponential".
Those same definitions allow x*1000 to be described as "exponential". (x*1000000 would be "more exponential"!)
If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x*1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x*1000=x*10^3 and x*10^3 has an exponent in it.
(Again, I sadly accept that in today's world, "exponentially" is being used to mean "fast growing", or sometimes more specifically "faster than linear". If I'm trying to understand what someone means, then it doesn't matter whether I find that usage to be a good idea or not.)
> > there are others which allow x^2 to be described as "exponential".
> Those same definitions allow x1000 to be described as "exponential". (x1000000 would be "more exponential"!)
> If you're describing something as exponential, then either you're just saying "fast growing", or you're trying to describe the type of growth. If you're describing the type of growth, then neither x1000 nor x^2 is exponential. The fact that x^2 has an exponent in it is no more relevant than saying that x1000=x10^3 and x10^3 has an exponent in it.
I don't agree with this. These are categorically different.
In f(x)=x*1000, as x increases, the function's output increases linearly. The slope of the derivative is 0.
In f(x)=x^3, as x increases, the function's output increases more than linearly. The slope of the derivative is positive and linear.
In f(x)=3^x, as x increases, the function's output increases much more than linearly. The slope of the derivative is positive and is itself a function of x.
These are all categorically different, and refer to something different than "fast-growing". "Exponential" in the mathematical sense, means the derivative is a function of x. "Exponential" in the colloquial sense means that the derivative has a positive slope. "Fast growing" just means that the derivative is large, even if it is a constant.
If it's going to mean something precise, such as
> The slope of the derivative is positive and linear.
then why not pick the precise thing that the word already means?
Is x*log(x) also exponential to you? If so, then why not use the word that already exists: superlinear? If not... oh wait, the above definition I quoted wouldn't even cover x^2, since the slope of its derivative is constant, not linear. So I'm just completely confused; I can't figure out which (mathematically) non-exponential functions you would like to label as exponential. x*1000, no. x^3, yes. x^2, I don't know. x*log(x), I don't know. x^2*log(x), I don't know.
> "Exponential" in the colloquial sense means that the derivative has a positive slope.
"Exponential" in the colloquial sense means that the speaker isn't using a mathematical sense, and so isn't considering first or second derivatives. I don't buy the argument that the colloquial sense accepts x^3 and rejects x^2, and in fact I bet I could find someone using it for a linear relation ("My workload has gone up exponentially since you laid off half the team!")
> "Exponential" in the mathematical sense, means the derivative is a function of x.
No it doesn't. x^2 is not mathematically exponential, yet its derivative is a function of x. Exponential means the derivative is exponential. But that's just a detail that doesn't really change the core of your message.
The main purpose of the mathematical definition is to exclude polynomials. The main purpose of the colloquial definition seems to be something like an impressive or important increase.
Polynomial is x^c=y
Logarithmic is c^y=x
I believe the problem has increased exponentially since then. Now everyone is using exponentially in literally the same way as literally.
You might be interested to know that the first definition of "exponential" is "of or relating to an exponent". The second definition is, as you say, "involving a variable in an exponent". https://www.merriam-webster.com/dictionary/exponential
As this is an internet forum and not a rigorous mathematical setting, I assert that my use of "exponential" is correct in context and to claim otherwise is incorrect. :)
Refering to polynomials as exponential just results in confusion essentially removing any meaning from the word. Any function can be written as something involving exponents, so that statement becomes meaningless.
Also it's by the Water Science School, so it doesn't seem your definition of completeness was the intention.
Obviously that water would be somewhat less accessible and quantifiable, but...
Anyone familiar with the current geoscience on this?
> and even the water in you, your dog, and your tomato plant.
Does it include water in the mantle? (https://www.bnl.gov/newsroom/news.php?a=111648)
or other non-liquid water for that matter like hydrates (ebsom salts, etc)
https://lightsinthedark.com/wp-content/uploads/2013/06/ceres...
If you wanted to ask whether that amount can hold together and become spherical, then just by comparing to Ceres doesn't that make it plenty?
It's not crazy to interpret "hold itself together" as more complex and including vapor escape.
The rate of evaporation ramps up exponentially, from ~irrelevant at the bottom of that range to fast at the top. (For a body of this size, any resulting vapor would be quickly lost at these temperatures, so the rate of evaporation is effectively the rate of water loss as well.)
This is why Jupiter can have icy moons (temperature ~100 K), but ice sublimates quickly on Mars (~200 K).
A cold enough body, though, has a low enough vapor pressure that this isn't relevant even over cosmological timescales. That's why Europa can can have a stable icy surface. It's far enough from the Sun (and has a low enough albedo) that it's very very cold (about 100K), and at that temperature ice doesn't sublimate very much.
TLDR: a Ceres-sized ball of water could hold itself together, but only as long as it stayed water. But it wouldn't be able to. Either it'd be cold enough to freeze over at the surface, or hot enough to evaporate into vapor that would escape.
[1] https://en.wikipedia.org/wiki/Atmosphere#/media/File:Solar_s...
But the comments here are full of "it's so little!" variants, where if you took the rest of the Crust and smashed as a sphere, it wouldn't be much larger than the water one.
It did evidently mislead a large number of people.
The mantle-water research is fairly new, with this report from 2017:
"There’s as much water in Earth’s mantle as in all the oceans"
<https://www.newscientist.com/article/2133963-theres-as-much-...>
The USGS detail pages are based on a 1993 publication, Igor Shiklomanov's chapter "World fresh water resources" in Peter H. Gleick (editor), Water in Crisis: A Guide to the World's Fresh Water Resources (Oxford University Press, New York).
<https://www.usgs.gov/special-topics/water-science-school/sci...> and <https://www.usgs.gov/special-topics/water-science-school/sci...>
I had no idea where to start. ChatGPT had a rather impressive looking “proof of work” that put all living humans into a 976m-diameter sphere, compared to the ~1384km-diameter sphere. Ie ~1km human sphere and 1,384km water sphere.
https://www.wolframalpha.com/input?i=estimated+total+volume+...
Which has a link that gives us the radius.
https://www.wolframalpha.com/input?i=4.73%C3%9710%5E8+cubic+...
They say the smallest sphere of freshwater lakes and rivers amounts to 93,113 cu km. There are 1 bil cu m per cu km. With a global population of 8.2 bil people, that comes to 11,355 cu m per person. That's a 22.5 meter wide/deep/tall cube (or about 7 or 8 stories tall building).
If we use the sphere that includes groundwater, 10,633,450 cu km. Then we end up with 1,296,762 cu m or a 109m wide cube per person.
Should be a radius of 430 miles, no?
The image is very non-intuitive, IMO, because it's making the water appear so small compared to the entire planet (which, duh, obviously the water is only part of earth), but also drawing the planet that small really hides how friggin big the earth is!
Also, I thought LEO typically begins around 180 km / 112 mi.
> ... Ganymede’s ocean is even bigger than Europa’s—and might be the largest in the entire solar system. “The Ganymede ocean is believed to contain more water than the Europan one,” he says. “Six times more water in Ganymede’s ocean than in Earth's ocean, and three times more than Europa.”
https://www.scientificamerican.com/article/overlooked-ocean-...
Ganymede vs. Earth is indeed very surprising!
Europa Clipper launches in October [1]. I've seen talk of crashing it into Ganymede to give JUICE novel data [2].
[1] https://en.wikipedia.org/wiki/Europa_Clipper
[2] https://www.space.com/europa-clipper-might-crash-into-ganyme...
Europa is the size of our Moon. Colliding it with Mars would be similar to the collision that formed our Moon.
Not sure if Europa's water would be flung into space, make atmosphere, or make a boiling ocean.
[1]: https://science.nasa.gov/jupiter/jupiter-facts/ (Under "Structure")
You give the average ocean depth at 3.7km, but the Earth's diameter is about 12,742km, making those bumps pretty insignificant. If you cover your countertop in sandpaper and spill water on it, the difference in coverage going to be almost negligible.
Earth isn't made of water, it's just a damp rock. Or a bowling ball that you squirted a dozen times with a spray bottle.
lol it's funny when you put it that way
The volume of all water is 1,386,000,000 km^3, which is then 1.386e+21 liters, or right about the same number of kilograms.
The mass of Earth is about 5.972e+24 kg. So the percent fraction by mass is 0.0232%.
A "drop" is typically estimated at 1/20th of one mL, which is then 0.05 grams. We can estimate the mass of a small-ish bowling ball at 5kg, or 5000 grams. 0.05 / 5000 * 100 = 0.001%.
So it's an order of magnitude shy, but that's still closer than I expected! It's about 1 ml of beer on a bowling ball - a small splash. Or maybe a very large drop.
Earth as a whole has a density about 5.5x that of water.
It's a ball of iron covered with rocks (i.e. metal oxides) cover with water (i.e. hydrogen oxide).
A ball of iron covered with a ball of rocks is a more fair statement though, and I'd agree with that. It's just that center ball isn't most of what makes up the Earth (by any measure).
Everything up to and including the mantle is either iron or has a lot of iron. But to your point the mantle also has a lot of silica. So I guess it depends on your definition of "mostly".
By mass, iron (32.1%) is still a minority constituent of the Earth.
<https://en.wikipedia.org/wiki/Abundance_of_the_chemical_elem...>
https://en.wikipedia.org/wiki/Origin_of_water_on_Earth#Aster...
I have a mental image of a gigantic cosmic being grabbing the Earth, wiping off the wet stuff with a rag, and bowling it at Proxima Centauri.
Adding in how far of a drive is it to X place or how far of a walk is it, is also fun.
https://billiards.colostate.edu/bd_articles/2013/june13.pdf
>So, based on the data, just how smooth is a CB? And how does this smoothness compare to the surface of the Earth? The highest point on earth is Mount Everest, which is about 29,000 feet above sea level; and the lowest point (in the earth’s crust) is Mariana’s Trench, which is about 36,000 feet below sea level. The larger number (36,000 feet) corresponds to about 1700 parts per million (0.17%) as compared to the average radius of the Earth (about 4000 miles). The largest peak or trench for all of the balls I tested was about 3 microns (for the Elephant Practice Ball). This corresponds to about 100 parts per million (0.01%) as compared to the radius of a pool ball (1 1/8 inch). Therefore, it would appear that a pool ball (even the worst one tested) is much smoother than the Earth would be if it were shrunk down to the size of a pool ball. However, the Earth is actually much smoother than the numbers imply over most of its surface. A 1x1 millimeter area on a pool ball (the physical size of the images) corresponds to about a 140x140 mile area on the Earth. Such a small area certainly doesn’t include things like Mount Everest and Mariana’s Trench in the same locale. And in many places, especially places like Louisiana, where I grew up, the Earth’s surface is very flat and smooth over this area size. Therefore, much of the Earth’s surface would be much smoother than a pool ball if it were shrunk down to the same size.
Yeah, the image with the oceans being dry is wow-inducing... On further thought, of course it'd be very close a sphere, because gravity forces it to be. A sphere where e.g. a slice of it is water (imagine a clementine with one of its segments being water) would be very wobbly if even possible at all..
I do wonder if the OP includes water locked away in rocks though, to my understanding the majority of the water is in the mantle and not even the oceans, but my source is my butt for that one
The problem with that was, 1. there are better sources of water (the oort cloud) and 2. they aren't stuck in an gravity well.
Understandably, since, in this case, surface area is more intuitively captured by our brains than volume.
Also because we are very small. The amount of water, from our perspective, makes it look like a water planet.
https://www.technology.org/how-and-why/what-would-happen-if-....
So I feel like the USGS is exagerated.
The oceans are only about 3.5% salt by weight, so that doesn't make a huge difference, either.
I find this pretty interesting, https://phys.org/news/2023-11-reveal-earth-surface-penetrate...
Imagine the headline:
VShttps://www.youtube.com/watch?v=FkUNHhVbQ1Q
So the medium blue sphere includes groundwater and swamp water while the tiny dot does not.