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Does beaming power to earth change the energy in the system? At least with solar all energy was already being absorbed by the earth's atmosphere, just being converted to another form and ultimately back to heat. By beaming energy that would not otherwise have passed through the atmosphere we are effectively warming the planet. Though I've no idea if the number is material or not.

> Only half of our 500M square kilometre planet faces The Sun at any one time, and only half the surface (barren land and, more likely, oceans) could be used for solar panels. That gives us 125km2 of usable area.

You're off by a factor of 1,000.

By a factor of a million in my typo of “125M km2”, right? The available solar power calculation is still correct, I believe.

Indeed. As for the available solar power insolence is about 1000 W / square meter at solar noon with panels aimed at the sun, depending on tracking you either have zero, one or two axis that are going to be 'off' and then there is panel efficiency to account for, so in practice a 100 square meter area of panels will provide out of the 50 KW available only about 17 KW peak, and usually less than that.

> The atmosphere attenuates our 1300W/m2 of solar energy down to 300W/m2 so for a 125M km2 planet you only get 40PW of available power, or 5PW after 80% loss in solar panels and distribution.

I think you've got a mistake and a bad assumption here, too. I think the atmosphere attenuates by not to 300W/m^2, but you might also mean that the earth being spherical rather than flat geometrically reduces the solar irradiation to an annual average of 340W/m^2? But then you'd be double-counting the effect of night, and ignoring weather. The currently installed PV systems produce about 10% of their nameplate capacity, so I tend to just use that in my approximations of all the different effects together, so a 20% efficient cell[0] would produce 1kW/m^2 * 10% (capacity factor) * 20% (efficiency) gets 20 W/m^2 in practice.

1% of land with those percentages gets us 29.79 TW[1] which is indeed only about 1 order of magnitude away from current use (and we definitely want to use more energy than we do as most people don't have the luxury of energy abundance found in developed nations), but that already accounts for it being "neither sunny nor midday all the time either".

But also, 1% of Earth's land area is already built up[2], so I think this may be too tight a constraint (after all, PV can be used as a surface covering for buildings and even vehicles).

With sufficient political will (yes yes, I know that's wishful thinking), it's not unreasonable to build a thick enough set of conductors to make even a global power grid have negligible resistance — you'd need a 1m^2 cross section for an equatorial ring of aluminium[3] to have 1Ω resistance, and while this would be a big project today, it's not so large as to be absurd for a decade-long project.

[0] The record for efficiency is 47.6%, though this will only matter if we ever ran out of land: https://en.wikipedia.org/wiki/Solar-cell_efficiency

[1] https://www.wolframalpha.com/input?i=land+area+on+earth+*+1%...

[2] https://ourworldindata.org/land-use

[3] Don't put 20 TW through a single ring. If I did the maths right, the magnetic field at the surface will be in the order of 1 tesla depending on how you choose to distribute current and voltage.

Also, I have no idea how much energy such a thing would absorb from a CME, but I think the big CMEs can be in the range of 5e25 J, and if that's efficiently absorbed it would vaporise even a ring that big.

>Moreover, if the goal is for power generation to have zero impact on our biome

I don't know if it is. The impacts could be positive, or at least counteract other negative impacts.

For instance, shading some ocean might counteract the heating of it.

But would kill light dependent life and increase some bacterial and fungi populations that might not be healthy for animals.

Oceans are where co2 is turned into oxygen. We really dont want to be deliberately hampering that cycle. Put the panels on land, preferably atop sand or bare rock.

Primary production is mostly concentrated in the costal regions. The following map's colour bands are on a log scale: https://upload.wikimedia.org/wikipedia/commons/4/44/Seawifs_...

There's other reasons not to put PV in the middle of the oceans, like the storms, and that if you're willing to make suitable transmission lines of that kind of distance, you can also perfectly well connect the Nevada and Namib deserts and put panels in each so the time zones are powering each other after sunset/before sunrise).

On that scale simply using power on earth will have a devastating impact on the environment and microwaving more power in makes it even worse.

Yes and this goes into some awkward Thanos did nothing wrong territory. I’m sure there’s serious research out there on what the fundamental population limit of Earth should be if we are to bound it based on minimal ecological impact.

"Malthus" is taught in high school. The idea comes up all over intellectual history and has yet to pan out. One of these days.

What's taught in high school is generally simplified to the point of falsehood.

What Malthus wrote about was basically the lived experiences of those around him for basically all of what he knew of to be recorded history: improved farming meant more people, not happier people.

Now, I'm not qualified to even judge if Jared Diamond's even fair let alone correct, but he wrote in Collapse (2005) that the Rwandan Genocide was brought about in part due to excessive population pressures, that it "illustrates a case where Malthus's worst-case scenario does seem to have been right."

On the other hand, it also seems plausible to me that widespread access to contraceptives may break the assumptions behind Malthus.

May? All developed countries have subreplacement fertility [1] (and falling) the world population is predicted to peak before the end of the century.

https://en.m.wikipedia.org/wiki/Sub-replacement_fertility

For now, yes; there is also a distinct possibility that the sub-populations who have more kids do so because of some genetic tendency (singular or plural) which would, if it actually exists and isn't mere hypothetical, rapidly reverse this.

There probably is such research, but "minimum ecological impact" is highly subjective and technology dependent.

We had some impact as hunter-gatherers at 10M population, probably made some species extinct from hunting. If I assumed c. 1940 tech was the limit and wanted to minimise human ecological impact, this population would be the maximum sustainable given CO2 emissions.

Conversely, if we put submarine cities in deep water, powered by PV on the surface that are ready to withdraw when storms come[0] and feed ourselves on the most efficient foods we already know how to grow in sealed environments, we could probably support trillions of people… but at that level we might possibly need to find some asteroids rich in, IDK, phosphorus or something.

I have seen larger maximum population numbers, but they're for scenarios where you fairly strongly disregard the ecology — if you're willing to do weird stuff like putting up an L1 sun shade to block wavelengths of sunlight that serve only to heat us up because they get fully absorbed by the atmosphere, but somewhere in the 10-100 trillion range our direct heat emissions become dominant.

[0] ignore the expense, this is a thought experiment

> I’m sure there’s serious research out there on what the fundamental population limit of Earth should be if we are to bound it based on minimal ecological impact.

There is but there is a 7/8ths probability that you're not going to like the answer.

https://en.wikipedia.org/wiki/Sustainable_population