What's the best way to construct a space-based sun shield large enough to put an entire city in shadow?

I've done some searching and found some interesting links (1. How many spaceships would it take to block the Sun from the daylight side of the Earth? and 2. https://www.quora.com/Does-the-International-Space-Station-throw-a-shadow-on-the-Earth), but I'm still unsure exactly how to work this out, or if the idea is feasible.

In this story setting, a certain type of entity that has an aversion to sunlight wants to demonstrate their domination of the Earth by constructing a sun shield in orbit large enough to put an entire city into shadow. In terms of size, let's say Vancouver.

Link 1 above would suggest using something huge at Lagrange Point SEL-1, but my setting is kind of near-future, so I think something a lot smaller in geostationery orbit would be more feasible. Link 2 above suggests that, say, a solar sail of 3,200km would be the minimum size required to cast a shadow on the Earth, but how big would that shadow be? And how big would the solar sail need to be to cast a 100% UV-proof shadow of about 50km - either squared, or a 50km wide circle? (I've gone with 50km so there is room for error and drift without the city's residents being torched at the smallest slip-up, but if that's not required then I'm happy for it to be smaller.)

And then, once I've worked out the size of the solar sail (with attached space station for maintenance workers), how best to keep it in position so the shadow stays above the city? Assume resupplies of oxygen and fuel are possible, but something like the (now disproven?) M-drive that can just use energy harvested via the solar sail would be nice and neat too.

First time asking, so I hope I've kept it clear enough.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Nov 14, 2022 at 7:02
• Keep in mind the difference between "geosynchronous" and "geostationary". A satellite can't be parked perfectly over something that isn't on the equator. It instead will trace out an analemma overhead: en.wikipedia.org/wiki/Analemma#Of_geosynchronous_satellites Nov 14, 2022 at 7:08
• And even if parked above a point of Earth, it doesn't matter, because the Sun moves across the sky. Nov 14, 2022 at 7:28
• everything wobbles in the universe. Nov 14, 2022 at 10:07
• To permanently block the sun over a city you would have to block every part of the sky that the sun can appear in for that city. That's pretty much a complete cover. Is that what you are looking for? It's not clear. Nov 14, 2022 at 15:56