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In Geostorm, the intro specifies that storms and cataclysms started in 2019, then the 17 nations build a system of climate-controlling satellites called "Dutch Boy" and 3 years later the story begins.

What I am most interested in is how long did it take to build the Dutch Boy? Is there any information regarding which year this movie takes place? Or in which year was the system construction finished?

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Unfortunately, there's no conclusive answer.

There is no novel adaptation, no public script that I could find that was more than just the dialogue repeated, no other spin-off material that might be an indicator. It's almost as if the movie wasn't a success...

So, all we have to go in is the film itself. The most pertinent scene is probably the one where Lawson is interviewed about the project, relevant segment copied:

Senator: Mr. Lawson, we find ourselves heading toward a crossroads. As you know, as per UN Resolution 28-14, the United States will be handing over control of Dutch Boy to an international oversight committee in three years. This in spite of the fact that we actually built the thing.

Lawson: Uh, excuse me, Senator, I-I don't wanna slow things down. It's just the you said, "we" built it?

Senator: Yes, indeed I did.

Lawson: Because I know what I did. I'm the guy that led the team, that built the station. I was up there with a international crew of 600 people... not just Americans. And I know all of their faces, but... I don't remember yours. We had a-a plumber up there. He looked a little like you.

Senator: Very clever, Mr. Lawson. Yes, Dutch Boy was an international effort. And yes, it may one day, very well belong to the world.

Now, I'm going to gloss over the plumber bit and focus on the quantitative element, 600 people. Let's compare that to some actual space expeditions, shall we?

There have currently been 61 ISS expeditions, with 3-8 members per expedition. It's common practice since Expedition 13 for a part of the members of one expedition to transfer to the next expedition.

Let's assume that this is a huge, urgent international undertaking is ten times larger in scope than the ISS, which managed 61 expeditions in 18 years (or 0.3 years per expedition).

How long would it take to involve 600 people?

Lower bound:
8 people per expedition, no carry over, 10x the speed of the ISS expeditions.
600 / 8 / 10 * 0.3 = 2.25 years

'Upper' bound:
4 people average per expedition, 50% carry over, still 10x faster expeditions.
600 / 4 * 2 / 10 * 0.3 = 9 years

So, my rough estimate comes to 2-9 years. Which I would interpret as 5-ish years.

However, I made several assumptions here, assumptions you might not (/probably won't) agree with.

So maybe look at what I did, how you would estimate the factors I used, and calculate your own estimate?

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