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There are many proposed geoengineering solutions that could reduce temperatures on earth. Unfortunately, a lot of them have a mix of side effects and lock-in effects where the changes in temperature come years after deployment which creates risk of unintended consequences.

If we would have a constellation of space mirrors that can be rotated as we desire to let in less or more sunlight, how much would it cost to bring up enough to reduce temperatures on earth by an average of 1° C? Let's say that Elon's promise of being able to launch a Starship that brings up 100,000 kg for $1,000,000 works out, what would it cost to produce and deploy those mirrors?

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    $\begingroup$ The Earth's energy imbalance is estimated to be about 0.71 watts per square meter. Multiply by the Earth's surface area, divide by the solar constant, and multiply by 2 to account for some of the mirrors being in the Earth's shadow and to get some amount of cooling. The result is a set of mirrors whose total size is equal to that of Germany. $\endgroup$ – David Hammen Sep 14 '20 at 20:38
  • $\begingroup$ @David Hammen I remember calculating a while ago that even if the mirrors were made of the thinnest aluminized mylar available, it would still need 1000x F9 payload capacity. It would be interesting to have a canonical Q&A on this site... $\endgroup$ – 0xDBFB7 Sep 15 '20 at 2:37
  • $\begingroup$ If ever the screens will launched - how to keep them at the point to shield Earth? Lagrange L1 point is unstable, so the shields will need propulsion (expendable) or solar pressure attitude control (not sure it's technicslly possible). Also for solar pressure the shields should be very thin, so not rigid but like "free floating blankets". Complex gravitational environment (perturbations by Moon and planets) don't help here, too. $\endgroup$ – Heopps Sep 15 '20 at 6:06
  • $\begingroup$ There is detailed analysis of this question here: Space Shades: Humanity's Last Hope. TLDR: it's not economically feasible to launch the mirrors, but it may be economically feasible to fabricate them in space, from lunar or asteroid material. $\endgroup$ – Wouter Sep 15 '20 at 9:26
  • $\begingroup$ This isn't an answer to the question, but personally I think that if we were to use such geoengineering approaches to deal with climate change, we would use CO2 sequestration. Space mirrors and similar approaches don't help with other effects of climate change, like ocean acidification. $\endgroup$ – Pitto Sep 16 '20 at 12:28
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Here is a spherical-cow physicist's estimate. Beware: spherical-cow physicist's estimates are extremely dangerous when dealing with climate: for instance the obvious model of how the greenhouse works that physicists (including me) have is simply wrong: it's not approximately right, it's wrong, and it totally mispredicts the effect. So be very wary about numbers below: they could be out by orders of magnitude.

OK, so first of all let's model the Earth as a black body and compute the change in flux for a given temperature change (this is probably the most egregious bit of spherical-cowism here).

So flux is given by

$$F = \sigma T^4$$

And so

$$ \begin{align} F + \Delta F &= \sigma (T + \Delta T)^4\\ &= \sigma T^4\left(1 + \frac{\Delta T}{T}\right)^4\\ &= \left(1 + \frac{\Delta T}{T}\right)^4F\\ &\approx \left(1 + \frac{4\Delta T}{T}\right)F \end{align} $$

Where in the last line I've assumed $\Delta T \ll T$.

And this gives us

$$\frac{\Delta F}{F} \approx \frac{4\Delta T}{T}$$

But $\Delta F/F = \Delta A/A$ where A is the area of the Earth that is intercepting the Sun's light (this is another spherical-cowism to some extent), and hence

$$ \begin{align} \Delta A &= A\frac{\Delta F}{F}\\ &\approx 4A\frac{\Delta T}{T}\\ &\approx 4\pi R^2 \frac{\Delta T}{T} \end{align} $$

Where $R$ is the radius of the Earth.

So, plug in the numbers: $T\approx 287\,\mathrm{K}$, $\Delta T = -1\,\mathrm{K}$, $R \approx 6.37\times 10^6\,\mathrm{m}$, and we get

$$\Delta A \approx -1.78\times 10^{12}\,\mathrm{m^2}$$

If this is to be in orbit, then even with the rotating mirror trick we need to double it, so we need to fly an area of about $3.55\times 10^{12}\,\mathrm{m^2}$.

OK, what will the mass of this be? Let's make it from aluminium and let's make it $0.1\,\mathrm{mm}$ thick (so, not foil, but this accounts for all the structure to make it rotate as well). The mass of this is

$$3.55\times 10^{12}\,\mathrm{m^2}\times 10^{-4}\,\mathrm{m}\times 2700\,\mathrm{kg/m^3} \approx 4.8 \times 10^{11}\,\mathrm{kg}$$

Let's assume they can lift $2\times 10^5\,\mathrm{kg}$ to LEO (200 tonnes), which is more than they can by a fair factor. So this is

$$\frac{4.8 \times 10^{11}}{2 \times 10^5} \approx 2.4\times 10^6$$

launches.

Let's say I'm out by a factor of 100 – I have the mirrors too heavy by a factor of 10 and too large by a factor of 10. So that brings it down to a mere 24,000 launches. If they can launch one of these things every day then 24,000 launches takes 65 years. And I'll refer you to an older answer of mine for some calculations about the climate cost of launches: 24,000 might not be too bad, but millions would be awful, and 24,000 is very, very low estimate I think.

So, not even slightly plausible. Almost certainly not even slightly plausible to mine the stuff on the Moon and lift it from there.


A note on geoengineering

Nothing in this answer or in my replies to comments below should be taken as meaning I think that this or any other form of geoengineering is a good solution to climate change. Any form of geoengineering is clearly a last-ditch thing which is fraught with terrifying risks and uncertainties. However if we do want to (or have to) to do geoengineering then lifting half a billion tonnes of material into LEO seems to me a particularly mad approach due to the enormous energy (and therefore carbon!) cost of getting material into orbit.

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    $\begingroup$ @Christian: it's an absurdly bad approach. If you want to do geoengineering do the sulphater-aerosols-in-the-upper-atmosphere thing which is much, much cheaper and much, much more practical. $\endgroup$ – tfb Sep 15 '20 at 16:01
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    $\begingroup$ @Christian: yes on the ocean problems, but compare those to the carbon cost of a million launches. No on the day-to-day thing: that's a complete non-issue for mitigating climate change. Worse than that the big-mirror-in-space is clearly weaponisable, while aerosols in the upper atmosphere aren't (people worried that they were, but it turns out that mixing-times in the atmosphere are short enough that they aren't). This is not the place to argue about the costs & benefits, but I'm pretty sure the big mirror in space idea is just what it sounds like: mad science. $\endgroup$ – tfb Sep 15 '20 at 17:06
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    $\begingroup$ It's a good thing thing we completely understand the effects of geoengineering and are sure it won't make things much, much worse. $\endgroup$ – Chris B. Behrens Sep 15 '20 at 19:45
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    $\begingroup$ There Ain't No Such Thing As A Free Launch. $\endgroup$ – Camille Goudeseune Sep 15 '20 at 20:41
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    $\begingroup$ @ChrisB.Behrens: I'm not sure if your comment is aimed at me, but I'm not trying to support geoengineering: it's clearly a last-ditch thing which is fraught with terrifying risks and uncertainties. All I'm saying is that, if we do want to (or have to) to do geoengineering that lifting half a billion tonnes of material into LEO is a particularly mad approach due to the enormous energy (and therefore carbon!) cost of getting material into orbit. In fact I will put a note on this in the answer. $\endgroup$ – tfb Sep 16 '20 at 10:01

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