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 lunch a Starship that brings up 100,000kg for 1,000,000$ works out, what would it cost to produce and deploy those mirrors? 

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Fermi estimate

Cross Sec area of earth= 1.3e15

Proportion needed to cover for 1C temp, 1.3%

Area needed=1.7e13

Assume aluminium foil is used.

Assume that it needs to have 500nm thickness to block light.

Assume most of the mass is ultrathin foil.

So 8.5e6 cubic meters of foil

At 2700 kg/m^3 thats 2.3e10 kg

Making 2.3e11$ at that price tag.

Ie 230 Billion $.

Plus another 41 billion $ for aluminium at 1.8$/kg current prices.

There would also almost certainly be some on-going costs. The Lagrange points aren't fully stable, so eventually we'd need to ship up propellant for station keeping. [EDIT]: We could likely use solar radiation for station keeping... Probably on much longer timescales mirrors would need to be replaced. These costs would probably be less than 1% of the upfront investment, but if the system gradually falls apart, you then find yourself in a bad situation.

For context, the US congress passed the CARES act quite quickly (relative to normal timelines for passing legislature) earlier this year and that dropped $2.2 trillion into the economy.

Seems like this question relies on a huge number of technical questions and assumptions such that a back of the envelope estimate would be meaningless and a rigorous examination would be highly difficult, nigh impossible. Natural albedo fluctuates wildly on a global scale from year to year and there are so many confounding factors and feedback systems in global climate that it seems insane to even estimate how much artificial mirror surface is needed, let alone how much it would cost not just to launch all that material, but to coordinate orbital patterns and control systems for it.

I think it's useful to distinguish knowledge of truth from gears-level understanding, these two different things can occur in any combination. Your point is that attaining specific understanding of a plan that's good enough to make the estimate in question is a hopeless endeavor, and you list particular issues with getting such a plan fleshed out.

But it's also possible to know truths about the world without understanding why they are true or how they came to be known (originally). The main example of this is seeking expert consensus in an area you don't understand: by finding out what the consensus is, you get a reasonable credence in what the truth of the matter is, without necessarily understanding why it's this way, or how specifically anyone came to know it's this way.

This post asks for a Fermi estimate, which is another way in which a very vague model can yield truths about the world. Even if a detailed model is unattainable, such truths might be in reach.

(It's often a lost purpose to seek truths about the world instead of seeking understanding, so it's natural to scorn some forms of pursuit of truths. I have a lot of sympathy for this position. That doesn't make such forms of pursuit of truths unworkable, just not relevant to improving understanding of what's going on.)