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How many people would be able to live in the Solar system before resource problems similar/comparable to what we have now on Earth would arise (rough estimation)? Is that equation/extapolation just correlating available space, energy and mass of relevant elements with projected human population demand?

That is, what are maximum physical limits for growth? (we may become independent from fossil fuels but the constraints like space, energy and mass remain)

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  • $\begingroup$ As far as we know, Earth is the only place in the solar-system with fossil fuels - so the answer would seem to be straight away.. Is that what you mean? Can you be more specific about what you're referring to as it's rather broad if you mean "everything except fossil-fuels". $\endgroup$ Jun 10 at 19:56
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    $\begingroup$ What resource problems do we have now on Earth? As far as I know, each and every resource of interest--food, oil, gas, iron, copper and so on--is becoming cheaper and cheaper. (Smoothing out temporary fluctuations.) It would be of some importance to the answers if you explained what resource constraints you have in mind. While of course in the fullness of time we may reach physical limits of growth, as far as we can tell we are nowhere near those limits. $\endgroup$
    – AlexP
    Jun 10 at 20:03
  • $\begingroup$ I am looking for physical limits of growth $\endgroup$
    – J. Doe
    Jun 10 at 20:09
  • $\begingroup$ The technology level is unclear. A geothermal-powered, stylish steampunk utopia will have a different carrying capacity than an anti-matter-powered Star Trek-style utopia with trivially simple teleportation and transmutation. $\endgroup$
    – user535733
    Jun 10 at 20:26
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    $\begingroup$ Bottlenecks are energy and phosphorus if I recall correctly, but which comes first depends how generous you will be with energy per human and do you mine sun for elements or not. But as it is physical limits, then probably phosphorus per 60W per human, buut then it needs to dig and ... $\endgroup$
    – MolbOrg
    Jun 10 at 20:26
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I'm actually researching this right now for my book. I'm happy to share my work...

It all comes down to energy as the unit of measure.

You CAN harvest asteroids for lead, iron, silicon, and other bulk heavy material. In the inner solar system, the rule of thumb is that a typical asteroid is 600 thousand kilometers (0.004 AU) from the next closest asteroid. The belt is approximately 0.5 AU from Earth.

These are rough estimates, because at certain times of the year many asteroids are much closer. Like Cruithne comes within the Earth-Moon L3. Or Bennu gets a few fractions of an AU from the Moon.

  • The cost of transporting one ton of bulk raw material at a slow pace of 18 $ {month} \over {AU}$ is 9.5 gigaJoules per ton.
  • The cost of transporting one ton of freight up the gravity well from Mars is 12.5 gigaJoules per ton.
  • The cost of transporting a ton of freight up the gravity well from Earth is 62.7 gigaJoules per ton.

So, this sets a "tax" on the price of the cheapest items : water, air, fuel, food, construction equipment and materials. Using modern energy prices of \$0.14 per kWh and the average energy cost of 10 gigaJoules (2,600 kWh) per ton, 1000 liters of water (1 ton of water) has a "fee" of \$370 tacked on, not including harvesting costs.

This above assumes perfectly efficient engines. In truth, if you have antimatter energy, you can probably use the number above. If you have fusion energy, multiply the above by about 1,000 (\$370,000 per ton per AU). If fission, another thousand ($370 million per ton per AU). Chemical engines : not possible.

This stacks. Raw materials generally need to move somewhere for processing, then move get moved to the consumer. Sometimes with more than one intermediary step.

If we have a space elevator (not possible with currently known construction materials) the cost drops to 0 joules per ton. A space elevator sends a counterweight down the gravity well. This counterweight's loss in potential energy "pays" the energy cost for the similar-weighted item coming up. There would be some sort of friction and imbalance, but you get the picture. At the higher altitude of the "top" of the space elevator, the load can be at or close to escape velocity.

The following planets in the solar system can not have a space elevator

  • Mercury : too hot
  • Venus : does not rotate fast enough (243 days per "day")
  • Mars : the precession of the moon Phobos interferes with all possible paths.

Therefore, your poorest person in space needs to be able to generate enough value to be worth the cost of upkeep (either \$370, \$370 thousand, or \$370 million per year in 2018 USD, for example, to be able to earn enough to buy a ton of water, which I'm using as the threshold for "poverty")

There are other taxes. If you want to ship things more quickly, the cost goes up. Rockets aren't 100% efficient.

The outer solar system is a little bit harder. It doesn't show in most models of the solar system, but the inner planets are all within 1.5 AU of one another. The first outer planet is close to 30 AU. There is an order-of-magnitude rise in the cost of everything.

Things are also further apart. The typical comet that could be harvested for carbon, hydrogen, oxygen and nitrogen is 1 AU from it's nearest neighbor.

Radiation is an obstacle. The Earth has a wonderful radiation belt that absorbs most of the bad things out there. It would be an essential pre-condition for either good shielding to be developed, or medicine be advanced enough to deal with radiation damage as casually as allergies.

But, other than that, there's no real limiting factor (in my opinion) to people settling wherever they want.

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  • $\begingroup$ If we talk about physical limits, then we absolytley should not see $€£¥₩ etc. Energy and matter, and nothing else. The way you go you even won't get even close to limits. $\endgroup$
    – MolbOrg
    Jun 10 at 20:43
  • $\begingroup$ The currency is used to help provide a feel for the rarity of the resource (in this case energy). I don't know about you, but I have no intuition for how much a gigaJoule is. $\endgroup$ Jun 10 at 20:46
  • $\begingroup$ Use kWh, everyone more or less can fluently translate it to their currencies, but it such a ridiculus number that it just pointless. Not sure how much 300$ is, I guess it depends.// If as limit of bearing capacity for solar system, a limit, a physical one, you get less than 1e18 humans, a thousand pentalion heads, then some assumptions are way too generous or wrong. It is not a limit yet, limit is a bigger number, but it close enough. $\endgroup$
    – MolbOrg
    Jun 10 at 20:53
  • $\begingroup$ I did include the 10 gigaJoule in the text. Divide by 3.6 MJ per kWh. I'll add that to the text. $\endgroup$ Jun 10 at 20:56
  • $\begingroup$ I mean, if u have similar question, you overcomplicate the way to do the estimation. Way too earthly $\endgroup$
    – MolbOrg
    Jun 10 at 20:56
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The ultimate limits are supply of energy and waste heat dissipation.

The cheaper the energy per KWh the larger the population can be supported. It allow more manufacturing more resource extraction etc. Dense populations are in general more efficient economically then sparse. All these things though produce waste heat. How quickly waste heat can be dissipated will limit maximum density more then energy availability. People don't tolerate being broiled well.

The highest limit we can achieve foreseeable would be type II on the Kardashev scale. Given we don't screw up in the mean time.

Some estimates (take with salt)

Difficult to estimate, but if you take the densest populations currently exiting on earth in first world nations(60e3/Km2), assume lots of fission power, have that density of population in 1% of earths land surface area 150e6km2. That's ~900 billion / 9e11. That would have many problems to overcome to make sure we don't trample earths biosphere to non functional.

Once fusion and O'Neil cylinders are practical that would make it possible increase populations without threatening earths biosphere. That will allow next major population expansion. In my opinion we will have far larger populations in O'Neil cylinders(and other habitats) then on any of the other planets/moons in the solar system. Population? take solar output put energy per person per year (3e26J/1e6Kwh/ year/person) something like 1e20 population. Probably got numbers wrong and to scale that large requires many major societal and technological changes.

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You haven't specified a max tech level. So lets go for broke.

The ultimate limitation is the energy output of the sun. Lets capture it all using a Dyson sphere.

You haven't banned travel to neighboring star systems, so we can mine deposits out of the solar system if we're running short. We may need to capture ice and iron from outside the solar system to grow our population as we deplete our solar systems resources. Some rare metals will also likely need fetching.

(We could mine energy rich substances, eg uranium, from neighboring star systems, but that will be a short term solution and run out eventually, returning our limit to solar power eventually)

Lets assume energy consumption per person remains constant from 2020 onwards - any future efficiency improvements are perfectly countered by either:

  • new functionality adding new devices to drain power
  • or the cost of maintaining life support in progressively more uninhabitable environments.
    • Food, water, oxygen, etc all need to be more carefully managed and recycled better.
  • or the cost of transport of required materials to progressively more distant environments.
    • We may need to mine very undesirable places to offset material shortages. Possibly neighboring star systems.

Going off my countries energy usage data of 6.1 exajoules per year over 25.3 million people; gives a per capita per year average energy consumption of 241 gigajoules (66.9mwh/year). Dividing it out you get 7.6kw of average power per person.

The sun puts of 4 * 10^26 watts of power. Lets assume 25% efficient power capture and distribution. Dividing that out gives 1.3 * 10^22 people. That's many trillions of trillions.

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  • $\begingroup$ A billions(13) of trillion (trillion eq 1e12). Good answer overall, may u look in matter limitations, of which human body is made of (carbon) and phosphorus which lifing creatures use abiut 10x of its natural abundance. Assuming typical element abundances does Jupiter has enough for that number of people to construct their biological bodies? With that the answer would be perfect IMHO $\endgroup$
    – MolbOrg
    Jun 11 at 7:21
  • $\begingroup$ @MolbOrg We can import carbon and phosphorus from neighboring systems. $\endgroup$
    – Ash
    Jun 11 at 7:26
  • $\begingroup$ Okay, seems matter isn't a bottleneck with this energy consumption, it may become if we assume just matrix style 60W per human(I mean it close "just" 2 orders of magnitude) useful links are: nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html ods.od.nih.gov/factsheets/Phosphorus-HealthProfessional chemeurope.com/en/encyclopedia/… en.m.wikipedia.org/wiki/Abundance_of_the_chemical_elements $\endgroup$
    – MolbOrg
    Jun 11 at 7:52
  • $\begingroup$ Sure we can, but then it won't be a limit for The star system. There are more than one way to overcome the difficulties, why stop on resources of the system of the galaxy etc. OP asks how to calculate, so we may assume he may use it as to derive number for milky way galaxy by multiplying by stars with some weight coefficients and then assuming export may lead to an error, but it does not in the case, everything is sufficient so, no problems there, but just as principle you find limitations of a system first, what they are and then move to how to solve them as a different problem. $\endgroup$
    – MolbOrg
    Jun 11 at 7:59
  • $\begingroup$ Did put sun fact sheet instead one I wanted Jupiter nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html mainly for mass and CH4 concentration which indirectly points to P concentration as well. Jupiter can be processed, as any other planet in solar system $\endgroup$
    – MolbOrg
    Jun 11 at 8:03

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