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As I type these words in March 2021, there are numerous private companies developing engineering solutions for reliable, high-capacity and relatively cheap access to space. At this point in time, it appears plausible to imagine that the first demonstration refineries and matter processors would be on the Moon before the decade is out. With its puny gravitational field, this means cost per Kg into space from the Moon would be trivially small while still allowing relatively close control from Earth. With better automation, costs might be even smaller per Kg from the asteroid belt, since despite the distance the delta-v budget is even smaller. This in turn means the only constraints to building megastructures in space and seeding colonists on various planets and moons come from the lack of an obvious economic need for such things.

The current value of our assets in space is somewhere around USD 400bn, a tiny sliver (<0.1%) of Earth's value stock (currently valued between USD 400tn and USD 5000tn), and that's mostly an artifact of the high cost of launches. But, we have to remember that, once in place, most of these space-, belt- and moon-based assets can run on "free" solar power and would likely be highly automated, which means that once the initial infrastructure costs are sunk, maintaining a high rate of material output can lead to exponential growth in capacity. Imagine the kind of GDP growth seen in the industrialization of China, except with untiring robots that can produce more untiring robots, which in turn produce yet more infrastructure, etc. Space GDP growth upwards of 100% per year seems strangely plausible in the early decades of this process, which might mean that space GDP may eventually exceed terrestrial GDP, even with very few people actually in space yet.

Admittedly, the idea that constructing artificial habitats in space could end up being cheaper than purchasing and developing equal amounts of suburban land, exurban land, deserts, tundras or floating cities on Earth seems implausible currently. The cores of our biggest cities have huge valuations, but land is still currently cheap and plentiful elsewhere. In addition to temperate agricultural-friendly land, we have vast deserts, tundras, shallow seas. How could building an O'Neill cylinder in space be cheaper that building the most luxurious home downtown or in the suburbs? After all, we have the industrial capability on-world, air comes free, we have power grids, water, communications, relatively easier access to social and cultural centers, etc.

My best guess is that at some point, a combination of increased ecological consciousness (already seen in the reforestation of large tracts of Europe and North America) and good-old-fashioned NIMBY-ism will make further industrial and urban development on Earth impractical and increasingly expensive. Moreover, human access to space does not need to be (initially at least) a mass-market appeal proposition. You can have a cheap home in the back-wood taiga if you want, but it is not cool. So early human habitats could be built for entertainment or a way to signal high social status -- I can imagine the appeal of having say a wedding ceremony with the Earth looming large and blue over the celebrants, or a billionaire inviting her friends over to her O'Neill cylinder. So it seems moderately likely that the number of humans in space is set to increase over the next few decades.

My question is, given all I've discussed and any additional points you care to bring up, when if ever can we expect the off-world human population ever to match or exceed the human population on Earth?

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    – L.Dutch
    Mar 25 at 15:52
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pace GDP growth upwards of 100% per year seems strangely plausible

it can be even bigger than that, it all a matter of energy EROEI of that automated ecosystem, it can be a month or even less for 100% growth.

Admittedly, the idea that constructing artificial habitats in space could end up being cheaper than purchasing and developing equal amounts of suburban land, exurban land, deserts, tundras, or floating cities on Earth seems implausible currently.

Implausible? No, it will be exactly what happens - cheaper, cheaper than a tonne of dirt you can buy here on earth.

How could building an O'Neill cylinder in space be cheaper than building the most luxurious home downtown or in the suburbs?

Cities on the planet are the most expensive constructions we own, we build and put resources in them for hundreds of years and that process never stopped. We maybe chip a fraction of resources and power for that, but it is not such a small fraction, we could or would like to chip more for the goal, because it would be mean cheaper real estate, but we can't as we need those resources elsewhere as well, including to support other technological structures and infrastructure in between. But if it could be easy - we would absolutely do because population growth and a place to live in is one of the fundamental necessities for all sorts of reasons.

If we would imagine a necessity or a desire to build a freshly new city from scratch for let's say a million people, which is not even a big number for the good portion of countries - for any of those countries economy it would be a big burden, a job of titanic proportions.

After all, we have the industrial capability on-world

For any noticeable progress in space, technologies have to be moved in space, exported in space, we need to have them in space if we think about anything human-related on a scale of more than a thousand people.

So early human habitats could be built for entertainment or a way to signal high social status

Nah, not doing to happen, it like that argument that tourism will propel space exploration and all that. And if you look at numbers on how much money is spent on \$50k and more expensive tours - the market cap isn't high at all. At least, when I did such research I wasn't impressed.

yes, one can spend a billion on a yacht, and space hab may be considered to be a yacht-like expense/investment - but without a change of technological paradigm in space how big it will be? Will it even be a space hab.

We do have some number of riches on the planet, and how much out of them are space-oriented? Five? I'm about right, eh? And who succeeds? One, maybe a second as well but it takes a long time for him.

They do have all the billions, all the billions they need but it does not look like enough, nor are the results that impressive. SpaceX is good, and I expect a lot from them, but yeah, it a long way to space habs that way.

So if we see space habs only if it will be interesting for many people. If the move promises them something better in terms of opportunities or future or present. Riches can make a pinhole, at best, the flood which breaks the wall is the people. Those riches who get rich forsee and cave in for the needs and desires of these many people.

That's your frame challenge if you like.

Can space be cheaper than Earth

Let's see which prerequisite we may have in space. Can goods be cheaper than on earth? Live cheaper and better?

Solar energy is on the rise on the hype, for quite a long time on earth. But let's see what it is in space, right?

The same solar panel as one my use on earth, let's place it in space:

  • it gets 30% more power, just because there is no atmosphere
  • it gets around 3-4 times(not an exact number) more sunlight just because there is no day/night cycle
  • no weather, not blackouts - constant supply of constant power

So energy price, in the case of solar panels, without a change of technology - can be improved about 5 times, compared to the same on the planet.

Solar for space, at least in our orbit, is one of the most convenient sources of energy, and that 5 times difference does not end yet, continue:

  • the panel does not have to be strong, robust as it is in a microgravity
  • there is no wind that tries to rip it off
  • not water, no snow - which tries to corrode it

So for the reasons and conditions which are in space, a panel loses weight considerably, and that are the materials on which we do not have to spend energy to produce them, making the thing even cheaper, improving EROEI.

And here is a nail in a coffin of expensive - food-grade foil that can be used to concentrate light. Do you know those stations?Crescent Dunes Solar Energy Project as seen from an airliner

This is Crescent Dunes Solar Energy Project, and its construction cost is $0.9B, for production, if everything is good, 110MW. In the picture, there are about 10'000 mirrors, and I guess it easy can be at least 10 grand apiece, and the mirror isn't that big less than 70 square meters, and that amount of aluminum foil in small rolls costs about less than 20 bucks (two rolls 44 meters each). And it will concentrate at least a few times more energy.

So how about that as price slashing - 10 grand best cases vs 20 bucks worst-case prices.

Energy prices can be orders of magnitude cheaper, there is just no way we can dream about such prices even if we get fusion working. Not talking about no need for land reclamation, works everywhere in orbit. There is no way we can achieve that in foreseeable future on earth.

But that isn't the most fun part of it, if you still there, let's get to the fun part

Goods, can they be cheaper?

Take look at your phone, tablet - those are small devices, they are technologically advanced devices, but the amount of materials used in them is small.

Do you think, that you would sell the materials, raw components - will you get even 1 percent of the sum you paid for the device?

The main cost of production, not the design, is the energy we use in conversion of initially small amounts of materials - shaping, purifying, etching, cutting, etc. And on the production of tools, we use in the processes.

Energy is the blood and air of technological society, civilization.

Wages in the production business are about, 20% of expenses in a place where I live, and the rest can be attributed to energy this or another way - wear and tear of equipment, direct energy expenses, raw materials - those are the main expenses.

Raw materials - making steel as an example - energy expenses are the main expense in that process.

Wear and tear mostly the same problem - spend energy to shape blanks and raw materials in some product, which makes the tool which wears and tears - to replace or make a brand new tool, and recycle the old.

Recycling - the same main problem is in energy for the separation of things in useful composition.

Nothing works in modern society without electricity and energy and it is an important part of GDP and its availability and its prices will be reflected in all the products which are made.

So they absolutely can be cheaper multiple times cheaper, especially if there is enough automation. And especially those which are high-tech units.

A lot can be said here but if you connect the two dots - you will be on a right track for anything else.

Speeds and feeds

The prerequisite for human expansion is exporting technologies in space, in its full capacity basically, it may be not that hard as many may perceive that problem, won't be easy as well. It can be significantly cheaper than many think, in terms of what we need to get in space to bootstrap that, and most of the work should be done here on earth, in a sense of designing systems and collecting technologies in a suitable package.

Exporting technology in space is a big topic, but it is a necessity if you like to think about human expansion and an absolute necessity if you think about overtaking the earth's production capacities.

It will take some time, but again things may be simpler, as bootstrapping technologies can be quite limited and not great in numbers, and the rest we can transmit over the link from the planet - so mostly a groundwork on the planet - how much it may take - there is no way to say this - a decade may be more than enough.

Growth

At quite extremes but the speed of growth of technologies, meaning production capacities, can be extremely high, like 100% every 3 days, based on EROEI.

It will be different for different products, energy production is most basic, most important and fastest. With some lag next level production, next next level, and so on. But in the end, the first most basic layer in the technological pyramid will define the power of production output, and the whole pyramid establishing may take few years, depends on how you do that, how prepared you are. if you have all the plans ahead of time then it may take a year or something around that time, if not then a decade.

So for multiple reasons, a topic for a different q, technology won't be a source of the bottleneck.

Human growth is about 2 percent per year, but it is a number that can be regulated and the results of it take time if we talk about natural means to grow people.

2 percent of population growth is a relaxed number it can be higher and it can be lower no matter the other factors, but with 2 percent nobody is stressed, everyone has time for many things, one of which raising humans.

2 percent growth, per year, means in a century it is a 7 times increase of initial population. So if you start with a million then it just 7 million after 100 years.

But with technologies exported to space it possible to lift everyone who wishes to live in space, so the number may be bigger, to begin with, but it depends on the living places.

  • my apologies here, 2 percent, remembered the number incorrectly, history-wise there were 2.2 percent and a bit more, but today's averaged around 1.2 percent. All statements are still true, and it can be considered to be one of the fast versions of growth, but it may be more than just 1-2-3 kids in a family which is more like the modern way with all that. But all that does not affect conclusions or potential timeline.

Space habitats

it a topic on its own, but what is related to the question of speed of growth - is the attractiveness of those places.

Easier access to technological products, food, resources for personal and group projects - definitely may attract quite a number of people. Have 5 time more for the same work - quite good, maybe - work less, have more - like that better. So we may expect a potential of a billion or even a few billion people to consider the idea to move in space, but if their environment conditions will be good enough there.

if environmental conditions will be good - spreading the idea and catching up on it and moving to the idea to move won't be difficult in our days - youtube will help, or whatever user governed analog will there be in that time.

But designing, ironing the inside of space habitats will take time. We not exactly starting from scratch, and there may be healthy ideas out there about nuances and stuff, but ecological microbiological aspects it will take time - decades.

All in all, it may start with 10-100million people. Space and that growing expanding situation is the real future and where real opportunities and real rewards for your effort are, so based on regular migrations in the world, the number may be quite realistic. And better are the conditions, faster people move.

So growth probably will be mostly due to the move from the planet in space, so it may take less than a century before space population will be bigger than earth one, and thus make more and have bigger numbers in everything.

side note

This is one of the aspects I hate in The Expanse.

besides water, another aspect which irritated me the whole seasons is that - man, you already in space, nothing separates you from turning the sky with your hands why aren't you doing it - why???!!!! There are thousands of roads to heaven and no road to hell, but you manage to breach into hell - how, why, aaaaaa!!! LoL

Conclusion

The most critical part is exporting technologies in space, until it has done, nothing extreme will happen. Mars won't happen. Space habitats won't happen. And as long as this part is postponed, by so much you can delay the expansion. A century, few, as many as you pleased with.

The rest, dust most likely settles in 50 years after that.

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I'm probably gonna have to go for "not in the next few centuries", and it isn't beyond the realms of possibility that the answer will be "never".

Here's the thing: it is rubbish out there. Radiation soaked, freezing or roasting, gravity all wrong, toxic razor sharp ultrafine dust everywhere. Terraforming anything in any meaningful sense of the word is so mindbogglingly implausible it may as well be magic.

What you're left with then is the construction of habitats, which are a bit like cities you can't escape from and where failure to follow the rules could put you or everyone else's life in jeopardy. There will always be ceilings. The only oceans will be under kilometres of ice. Returning to Earth will still likely be expensive and unpleasant and risky.

My best guess is that at some point, a combination of increased ecological consciousness (already seen in the reforestation of large tracts of Europe and North America) and good-old-fashioned NIMBY-ism will make further industrial and urban development on Earth impractical and increasingly expensive.

Industrial stuff can be moved (what's the planetary equivalent to "offshored"? outwelled?) and probably will be once it becomes cost effective... the most polluting and destructive things would be moved out there because if nothing else there's lots of easily available power and once you've solved the transport problem, lots of convenient raw materials, too.

But people, though? that's a much tougher proposition.

Moreover, human access to space does not need to be (initially at least) a mass-market appeal proposition. You can have a cheap home in the back-wood taiga if you want, but it is not cool.

It would indeed be awesome to take a trip out to a big habitat at the Earth-Sun L1 point... the view back towards Earth and the moon would be amazing.

Thing is though, you might not want to live there. People have holiday homes and stuff now in places where it is nice to visit but incompatible with their lifestyle to remain there. Experiencing the reality of being on an expensive cruise ship where there are worse things that norovirus that can happen to you is not likely to encourage emigration.

People will, of course. People want to go live in Musk's Mars habitats, which will be effectively be prisons given how unhomely and thoroughly policed they'll need to be. The prospect of debt-slavery to a bunch of libertarian techbros in a place where you need to earn your next breath is no discouragement to some! They'll be few and far between compared to the bulk of Earth's population.

Remember that human population growth rates slow as people become safer and healthier and (comparatively) wealthier. Running out of living space on Earth may only be something to worry about in the relative short term, and space in Space is going to be every bit as cramped and expensive as a city apartment (if not more so!) whilst that particular population peak is experienced, but as Space gets cheaper you might expect there to be less pressure on living room on Earth, and so the drive to leave will be reduced, too.

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    $\begingroup$ 'Returning to Earth will still likely be expensive and unpleasant and risky.' For third and fourth generation 'spacers', it might be nigh on impossible. We now know that it is not just about what genes you have, but about which of these genes are expressed. After a few generations in space, it is possible that the genes that are expressed are incompatible with living on Earth, for exactly the reasons you mention - to our expressed genes, space is rubbish. To their expressed genes, Earth might become rubbish. genome.gov/genetics-glossary/Gene-Expression $\endgroup$ Mar 24 at 14:54
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    $\begingroup$ @JustinThymetheSecond the effects of micro gravities on an organism born on earth living in space (atrophy of muscles & bones) may do it all on its own without any need for any genes to tell us how they feel (umm, express themselves), any born there will experience even more severe problems on earth. $\endgroup$
    – Pelinore
    Mar 24 at 15:00
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    $\begingroup$ Nanobot handwavium aside, I assume rotating habitats can provide a passable simulated gravity that is easily within our current engineering capabilities. The only thing holding us back is simply the issue of launch costs from Earth, absent a space manufacturing capability. $\endgroup$ Mar 24 at 18:01
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    $\begingroup$ "where failure to follow the rules could put you or everyone else's life in jeopardy" - I can just imagine the results when the libertarians get in power. Actually, someone should write a story about that. A libertarian moon colony where nobody is allowed to stop other people from doing things. $\endgroup$
    – user253751
    Mar 25 at 13:10
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    $\begingroup$ To draw a parallel between the last time humanity found a new place to move lots of people to, it's worth noting that ~85% of the world population still lives in the "Old World", Asia, Africa, and Europe. We've had centuries to populate the Americas, and we're still nowhere near the point where the New World population will exceed the Old. $\endgroup$ Mar 25 at 13:41
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Historically, colonization and emigration hasn't been driven by profit, but by lifestyle -- specifically, people colonized or emigrated because they hoped for a "better" life than they had in the "old country."

America has recent enough history of this to have good records -- the first colony north of Florida was founded by those fleeing religious persecution, or seeking to live better than they could as bond servants or farm hands in the Old World. For the next four centuries, people came to America because they wanted a better life, if not necessarily (realistically) expecting it for themselves, then for their children and grandchildren.

Once people have the ability to choose to live off Earth, there will be some who do so for this same reason -- and they'll be the ones who find ways to support and raise families, despite different gravity, no air outside the "house", and so forth. Only after that's been going on for a good while will there be more people off Earth than on it (the population of the United States still doesn't exceed that of Europe, or if it does it's very recent and not by much).

If Elon Musk succeeds with his plan to colonize Mars in this century, we can expect that to start -- but it'll take a very long time for off-Earth population to catch up with the ability of eight billion people (and counting) to reproduce.

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  • $\begingroup$ But America never exceeded the population of Europe, and never will, and its GDP has not exceeded the GDP of Europe overall. The only reason America is where it is in comparison to Europe was the second 'world war'. Without that conflagration, Europe would never have not dominated. $\endgroup$ Mar 24 at 14:38
  • $\begingroup$ @JustinThymetheSecond Isn't that approximately what I just said? $\endgroup$
    – Zeiss Ikon
    Mar 24 at 14:40
  • $\begingroup$ "Only after that's been going on for a good while will there be more people off Earth than on it" Yes, approximately. Only I put a 'but' in it, you did not. $\endgroup$ Mar 24 at 14:45
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    $\begingroup$ The difference between Earth colonization and space colonization is that the Earth colonists could reasonably expect to have a better life. Barring a very severe degradation of Earth's biosphere (e.g. extreme global warming, a universal theocracy, or similar), living in space will always be worse than Earth. $\endgroup$
    – jamesqf
    Mar 24 at 19:17
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    $\begingroup$ @jamesqf "living in space will always be worse than Earth" That seems like an unfounded opinion. Living on Earth is already worse than living on Earth used to be (in a number of important ways); if we don't stop using fossil fuels PDQ, living on Earth is likely to become pretty awful in your lifetime (I'll be dead by then). And don't forget, "off Earth" can and will include planetary colonists, who while still living in domes or other sealed structures, won't be living in a space the size of a third class steamship cabin. $\endgroup$
    – Zeiss Ikon
    Mar 25 at 11:05
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/How long will it take for the off-World population to exceed Earth's population?/

Answers so far have concerned themselves with the off world population. But what about the on world population?

relic

https://www.deviantart.com/jflaxman/art/Relic-538709214

What great concept art. Well done Flaxman. I am reminded of Ozymandias. "Billions and billions served".

In any case - there is some fancy expensive stuff happening off world. Boutique getaways. Pilot mining operations. Planetary surveyors. But then Earth becomes much, much less nice. These few and diverse space folk find themselves the hope for their species and maybe their phylum.

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    $\begingroup$ Nice artwork. However, nothing here even tries to answer the question. $\endgroup$ Mar 24 at 20:13
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    $\begingroup$ There is a lot of preamble in this question. The trick is to look for the ?mark in the text. Here it is pasted: "when if ever can we expect the off-world human population ever to match or exceed the human population on Earth?". There are 2 different numbers to consider. space population and earth population. My answer: "when the population on earth crashes.". It is like "when if ever will Willk be as rich as Bill Gates". Answer: "when Gates gives away all his money". $\endgroup$
    – Willk
    Mar 24 at 20:16
  • $\begingroup$ I hope he will gives it all to me, lol)) $\endgroup$
    – MolbOrg
    Mar 24 at 21:21
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    $\begingroup$ Frame challenge accepted, overly focused on the (splendidly provocative) artwork, but valid. $\endgroup$ Mar 24 at 23:05
  • $\begingroup$ Okay, figured out what is wrong with the answer, nifty trick with question mark, realy, plenty of people should learn it here on wb, but crash of earth popoulation is trivial solution, that one thing, and it can't be predicted as with very high probability it is in category of sudden events, which even less prediction friendly than black swans. But does not mean preppers do something wrong, last year showed it clearly, I guess $\endgroup$
    – MolbOrg
    Mar 25 at 5:38
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I have written an entire series of books on this topic, so I have a lot of thoughts:

Generational Cycles

Some may not know that the Apollo program was extremely unpopular. No less a luminary than Martin Luther King's successor, Ralph Abernathy, spoke in extremely strong terms against the moon landings.

Steve Bannon popularized Howe & Strauss four turnings idea to explain why we do such things. It's a coloring-in of the "rags to riches to rags" idea, but more simply (and to the point of this question) : we have a single generational (20 to 40 years) tolerance for trying out big leap forwards. Then, historically, we wait 60 to 120 (let's say 70 to 90 to keep in the mean) years before doing anything else bold.

After Apollo, we took a 70+ (still not over) year break from manned flights out of Earth orbit. Space Shuttle was an idea to keep us in space for pennies compared to the Apollo program.

Required Leaps to the Inner System

For my series, I used a number of 90 years between big leaps forward. Here's all the things we need to do:

  • Reduce the cost to get out of Earth's gravity well :
    • \$200,000 per kilogram (1960s)
    • \$20,000 per kilogram (1970s)
    • \$10,000 per kilogram (now)
    • \$200 per kilogram (space elevator - proposed TRL-1)
    • Pennies per kilogram (orbital ring - proposed TRL-0)
  • Reduce the time, increase the payload percentage, and decrease the cost to get around in the inner system
    • Not Possible (pre-1970s)
    • 3 months / 92% fuel - 8% payload / \$261,000 per kilogram (now)
    • 1 month / 72% fuel - 28% payload / \$74,000 per kilogram (torch drives - proposed, TRL-0 25% reactant burn - 0.000036% mass-energy efficiency)
    • 1 month / 24% fuel - 76% payload / \$6,000 per kilogram (torch drives - proposed, TRL-0 100% reactant burn - 0.000144% M-E)
    • \$85 per kilogram (peak fusion 0.0075% mass-energy efficiency)
    • \$0.85 per kilogram (antimatter @ 0.75% mass-energy efficiency)

Putting It All Together

  • I feel like we're going to miss this window (2010 to 2030), or at best put a permanent robotic settlement on the Moon and Mars.
  • During the down window (2030 to 2120) I hope we might leap-frog fusion into anti-matter technology
  • During the next opportunity (2135 $\pm$15) I'd like to imagine the first no-joke permanent settlements start springing up in the inner and outer solar system.
  • And during the next down (2150 to 2240) we build up those inner system settlements so that they might think of themselves as economically independent. Hopefully, maybe at this time, we could try to launch something for the nearest few stars.
  • At the next exploration phase (2255 $\pm$15) we start seriously settling dwarf planets in the cometary halo past Neptune. Anti-matter becomes mainstream. Maybe a Not In My Backyard movement makes this anonmyous mass-energy the big import, and injects some wealth.
  • At the next exploration phase (2345 $\pm$15) we seriously reach for a permanent settlement on Sedna, which will have just passed it's closest approach.

This is when, in my opinion, a few centuries of maturing and emigration from Earth will put the rest of the solar system at an equal level of political clout to humankind's homeworld. But, I'd be surprised if the population of the rest of the solar system combined equalled Earth's at this point (it's just so much easier to grow a population here).

However, perhaps only another century later (2450), I think the multiplier effects of so many additional places outside of Earth, and time spent maturing, might bring populations equal.

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  • $\begingroup$ Predicting anything beyond when we get a hold in space is meaningles, as impact on technologies and abilities to develol them is unimaginable. We need jusg one root for it ro become a blast, it won't be that singularity thing, but it will trash our perception about limits. Not accounting that, hardly any prediction can be any close. $\endgroup$
    – MolbOrg
    Mar 25 at 0:51
  • $\begingroup$ That’s true. I was tempted to put a caveat in the post that nobody thought it would take 83 years (and counting) for fusion to make it to the mainstream. Barring “Chicago Pile” moments, however, there’s a lot of precedent for ~1 century between concept and production model : the internal combustion engine (concept 1798, cars 1910), the computer (difference engine 1820s, ENIAC 1945), steam boats (concept 1705, first commercial route 1780) $\endgroup$ Mar 25 at 1:19
  • $\begingroup$ I feel like what I’ve described has a few Chicago Pile moments (like antimatter bearing fruit early) but depends on most of our advances seeming to happen at the average speed of other advances $\endgroup$ Mar 25 at 1:24
  • $\begingroup$ Interesting. However, I would challenge that theory with internet & cell-phones with a roughly 30 year concept to ubiquity path. Moreover, one can argue that high-performance computers act as empowering cognitive prosthetics, speeding our design-fail-retry OODA loops. It's not clear to me that we're talking cycles rather than "the first half of the chessboard" when it comes to the industrialization (and possibly associated population) of space. $\endgroup$ Mar 25 at 2:11
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    $\begingroup$ Cell phones lingered as not-quite-ready for mass market radio telephones since about 1900. $\endgroup$ Mar 25 at 3:04
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Let's start with what we know

enter image description here

Click on that image for a larger version. Image courtesy Open Oregon Educational Resources. I intentionally searched for an image with a starting point as far back as reasonably possible. Obviously, the beginning number is increasingly a wild guess the further back you go. But we only need it to get far enough back that we have a sensible starting point.

The Premise

Let's assume that humanity's basic nature doesn't change. If we believe that's not true (e.g., if we believe humans will become more environmentally conscious, or more population-growth conscious, or anything else that affects the growth curve just presented), then this question is 100% opinion-based because there's no way to guess how humanity will behave in the future.1

Let's further assume that space technology has increased quickly enough that we can ignore the time between launches. In other words, since there is nearly no population growth on the graph between 1,000 and 1,200, we can assume we have 200 years to get some number of people out there.

Finally, let's review some reality.

  • Even a planet is capped in how much population it will support. Don't get me wrong, I think Earth can hold a whole lot more people than it does right now — but there will be a cap. The cap may be politically imposed (through policy or war) or environmentally imposed (even science doesn't let you grow more crops), but there's a limit. I won't even speculate as to what a planetary limit is, but it exists. This is why, below, you'll find me saying that a single planetary colony can at best equal Earth's population. Multiple colonies are required to exceed it.

  • Next, in a moment I'm going to tell you I'm ignoring space habitats. There's no point to building a space habitat with the same population potential of a planet and no practical reason I can think of to build so many habitats that they'd add up to the population potential of a planet. The idea that building space habitats could become so cheap that we'd expand off-planet at a rate faster than we can birth children on-planet violates every rule of economics I can think of. Habitats, obviously, have greater resource limitations than planets and would require shipments of raw materials no matter how good the recycling is. Besides, the idea of building a habitat that could house, say, 10 billion people and then start them off with just 400,000 (using the chart, above)... I can't think of a bigger waste of time, energy, and resources. Someone would need to give me an incredibly good reason why that would win out over a station that can hold, say, 1,000 people for scientific research or a communications outpost. Anyway, long story short, since habitats (in my book) have a dramatically lower population potential than planets, I don't consider them even worth considering.

How long will it take for Mother Earth to become a minority?

You're not getting a fixed date. Anybody who gives you one should be down-voted, because it all revolves around (a) how many locations can be seeded and (b) what the maximum population potential of each location is.

I'm going to entirely ignore space habitats. The belief that a habitat (or many habitats) can be built to support billions on the order of multiples-of-Earth is, frankly, impossible to believe. That would put us beyond a Kardashev Type II civilization, and IMO that makes your question unanswerable because that level of technological advancement seriously impacts the nature of the above growth pattern (and may happen so far into the future that it makes the predictability of the reference population number impossible).

That leaves planets. I'm an optimist2 in that I believe we're going to find habitable, colonizable planets....

Which means I'm also going to completely ignore the expected activist-driven, environment-first, humans-suck politics that would fight tooth-and-nail to stop colonization because that effort would also impact the predictability of the above chart.

TL/DR; My Answer

Given that each colonized planet has the population potential of Earth, how long would it take for the off-Earth human population to outnumber Earth's population? The traditional equation for population growth is:

$$P = P_0e^{rt}$$

  • $P_0$ is the starting population.
  • $r$ is the percentage rate of population growth.
  • $t$ is time.
  • $e$ is the Euler number (2.71828...)

We can ignore just one colony. For that case, $t=\infty$ because, basically, the one colony can't catch up to Mother Earth unless the birth rate of the former is magnificent or something like a catastrophic world war decimates the later. Neither is at all predictable, therefore we must rely on the chart, which means $t=\infty$.

For two colonies...

$$P_0e^{rt_0} = P_1e^{rt_1}$$

and solve for $t_0-t_1$. For two colonies (here's where a better mathematician than I could help make the formulas look nice).

$$P_0e^{rt_0} = P_1e^{rt_1} + P_2e^{rt_2}$$

and solve for $t_0-t_2$ or... for any number of colonies.

$$P_0e^{rt_0} = \sum_n^0 P_ne^{rt_n}$$

and solve for $t_0-t_n$.

Note that I've assumed $r$ is the same for all colonies and Earth. It might not be!

Disclaimer: It's been a very long time since I had to deal with summations. I may have constructed that incorrectly. If you see an error, please either correct the answer or let me know in comments. Thanks!

Conclusion

So, based on Occam's Razor, we have an equation that would let you solve for the time required to exceed Mother Earth's population given...

  • We ignore anything and everything that could change Earth's population growth over the last 1,000+ years,

  • We ignore anything and everything that might modify population growth on colonies,

  • We ignore any consequence of space-born population,

  • We ignore the removal of Earth's population for the purpose of seeding space.

  • We ignore things I'm sure I haven't thought of.

You've asked a simple question with a very complicated answer that requires us to ignore a whole lot of "what if?" So much so that I was seriously tempted to vote to close, but I thought the exercise might be valuable.


1If 2020 didn't convince you of that last assertion, then we have a problem. Using U.S. politics as a baseline and oversimplifying so much that angels weep, a liberal-optimist will believe humanity will eventually adopt zero population growth. A liberal-pessimist will believe violence is required to assure zero population growth. A conservative-optimist will believe in free-market-style population growth. A conservative-pessimist will believe in wiping out the liberals, and then free-market-style population growth. Where in that massive spectrum the future falls is an enormous guess that also makes angels weep.

2In a non-political way.... See the previous footnote.

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  • $\begingroup$ I did not downvote your answer, but I am surprised by the space habitats write-off, as I suspect that will be the primary human off-world habitation space in the long run. Fundamentally, it's just a matter of producing enough construction material to make large spinning cylinders. Besides manufacturing metal beams and sheets in space being an unproven technology, neither seems to be more than a moderate technological challenge, and definitely there there's no new science needed to build such things. $\endgroup$ Mar 24 at 18:42
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    $\begingroup$ Your answer ignores the fact that population growth is 1) slowing down globally; 2) projected to stop by the end of this century. Moreover, all developed countries struggle even with maintaining birthrates close to replacement rates (the USA is the only exception, but the trend of declining birthrates is present, too) and will have to rely on immigration in the near future to keep their populations more or less stable. Once Africa is more developed, it will see exactly the same below-replacement birthrates and the global population will start to decline. [cont.] $\endgroup$
    – Otkin
    Mar 24 at 19:16
  • $\begingroup$ [...] The most important factors in declining fertility are education (especially for women), access to birth control, accessible and effective medical services, and non-agricultural society. Space colonies and habitats will satisfy all of these requirements for a very long time due to their inhospitable nature. One can try to restrict birth control in order to boost birthrates, but most attempts to do so are highly ineffective and result in a high number of avoidable deaths and female infertility. Moreover, any space habitat will have to have high-tech medical facilities, so abortions [cont.] $\endgroup$
    – Otkin
    Mar 24 at 19:23
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    $\begingroup$ @SerbanTanasa No number of space habitats can outnumber the population of Earth in any practical economic model I can think of. Space habitats are closed systems. You must constantly bring new resources to them just to maintain them (there's no such thing as perfect recycling, especially when the recyclers break down). Why bother with so many space habitats when populating a planet is simpler and cheaper? $\endgroup$ Mar 24 at 19:41
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    $\begingroup$ @MolbOrg One of us doesn't understand the answer. A single colony can only catch up to Earth's population unless Earth's population is decimated. Any number of colonies above one can and will exceed Earth's population. The more colonies you have, the faster you'll catch up. No offense, but what were you expecting? A date? $\endgroup$ Mar 24 at 19:46
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A lot of this is about the 'R' number.

Let's assume that all we had to concern ourselves with were basic questions of economy on the basis of limitless(!) space.

Let's also assume that there were limitless resources (everything necessary for life) available within easy reach from anywhere within limitless(!) space.

A conservative estimate (given unlimited space/resources) is about 50 years to double a human population.

So, if we saw a net migration of 100,000 to space, and we provided ideal circumstances (but no forced breeding programme) it would take about 500 years to exceed the global population (assuming that the global population is stabilised due to limits of space and resources).

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    $\begingroup$ "this is about the 'R' number" I'm sorely tempted to downvote you for egregious use of a topical term that I'm heartily sick of hearing about, I come here to escape that sort of thing, but I'll restrain myself ;p $\endgroup$
    – Pelinore
    Mar 24 at 14:37
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    $\begingroup$ This analysis does not consider the 'E' factor - Emigration from Earth. $\endgroup$ Mar 24 at 14:41
  • $\begingroup$ @JustinThymetheSecond There is almost no circumstance (barring unlimited, copious free energy, which has its own problems) where E is going to be bigger than R. (In terms of effect, rather than raw numbers, obviously.) $\endgroup$
    – jdunlop
    Mar 24 at 15:28
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    $\begingroup$ @Otkin, this is not the place but I couldn’t agree with you less. Your assumption is based upon a single culture sample which is still entrenched in ideas of scarcity. $\endgroup$
    – Konchog
    Mar 24 at 19:59
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    $\begingroup$ @Otkin (Monetary) resources are one of the primary reasons many aren't, right now. $\endgroup$
    – nick012000
    Mar 25 at 1:30
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Unknown, because it requires technical advances we don't currently have

We're going to have to assume Mars here, as the place which is currently most survivable long-term in our solar system. Gravity is close enough to Earth's that we're unlikely to have problems there. The Moon (at 1/6th G) is unproven safety-wise on that side of things, as well as being generally harder to work in vacuum.

Once you get outside the Van Allen belt, your radiation exposure goes way up. As described here, the radiation exposure on Mars is 10x the maximum permitted for DOE radiation workers. In transit, you're getting 30x the maximum. This greatly increases the risk of leukaemia and a number of other issues related to radiation exposure.

Until we have viable and well-tested shielding abilities, we really don't know whether it's possible for humans to survive there long-term without major health issues. Of course we can (and do) send volunteers into high-rad, high-risk environments like the ISS for limited periods. A colony requires children though, and it would not be ethical to bring up children in an environment which is inevitably damaging to them.

A common concern is that radiation exposure causes birth defects. This at least is largely disproved by research following people exposed to the nuclear attacks on Hiroshima and Nagasaki. Birth defects in children of hibakusha were not statistically different from the regular population. However the same studies show a range of issues depending on the age of the survivors at the time of the bombing. It should be obvious that anyone growing up in an environment of continuous exposure would experience all of these.

Some consideration of this has already happened - for example, there are suggestions that people might live in underground bunkers. This brings its own problems though, with all the health impacts (from mental health to eyesight) observed in prisons without regular outdoor time. Even for people who can tolerate long periods in confined spaces, there are simple physiological impacts on health which are unavoidable. Some of those (vitamin D deficiency from lack of sunlight) can be solved with dietary supplements, but some of them (atrophy of eye focussing muscles) can't be fixed so easily.

Unless we have reliable methods to shield people from cosmic rays, and to ensure their long-term health inside whatever shielding structure, the answer to this has to be "not until then". This would all need to be thoroughly evaluated before anyone could consider having children there.

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  • $\begingroup$ What's wrong with few meters of regolith, or how many u may need. Why not neccessity to have few 10's of millon tons of materials to make a space hab for a million people for an example. If one can build does it mean he automatically capable to solve the problem u mention? Aren't priorities here scrambled? $\endgroup$
    – MolbOrg
    Mar 25 at 11:52
  • $\begingroup$ Have we proved that permanently living in a cave has no adverse effects? We know that "outdoor time" in prisons is important for mental health. It's a fair point though, and I'll update my answer to say that the "solutions" need to not have unacceptable consequences themselves. $\endgroup$
    – Graham
    Mar 25 at 12:32
  • $\begingroup$ I do not talk about caves in a any way shape and form, I talk about space habitats. $\endgroup$
    – MolbOrg
    Mar 25 at 15:11

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