While this is still obviously not a realistic solution to the damage we're doing to our climate because it still involves launching 35,000 tonnes of material in to space and moving 100 times that much to the right location, the solar sail thing has been accounted for in the paper. Basically you stick it slightly closer to the sun than the actual L1 point, where the force from solar radiation balances out the slightly higher pull of the sun's gravity
Let's assume SpaceX's Starship starts working flawlessly tomorrow. It is apparently intended to get 100 tonnes to the moon, but it needs a second launch to get fuel in to orbit to reach higher energy targets. So we're looking at two launches per hundred tonnes. Assuming flawless operation and literally no weight for equipment to actually assemble the stuff once it's at the location, that's 700 maxxed out Starship launches just to get the shield in place.
After that, you've still not even started on getting the 35 million tonnes of counterweight in to position. And yeah, it helps if you only have to get 35 million tonnes of rock out of the moon's gravity well instead Earth's, but you still have to move 35 million tonnes of stuff. Getting 35 million tonnes to lunar escape velocity requires equal energy to 1.6 million tonnes to Earth's escape velocity (which would be 32,000 Starship launches), and that's before you account for having to get your rockets, fuel, and infrastructure to the moon in the first place.
After that, you still need to stop blanketing Earth in greenhouse gases or you need to keep making the shield and the counterweight bigger to compensate.
This just isn't happening on any realistically helpful timeline. This is maybe helpful to just start repairing some of the damage in a scenario where we fail completely.
Moon’s got no atmosphere so you can build a railgun to launch containers.
They still have to be caught, which will
require a shit ton of fuel, but at least you cut it in half.
Maybe you can get the containers to collide. You shoot them to the lagrange point in opposite directions. All the energy could be input via railgun on the moon, then removed via well-timed collisions. Big cumple zones
of foam or something would be necessary, unless you use stabilized magnetic repulsion. Heck they could slow each other down with laser beams if they had a big enough collector.
Then your engineering hurdle isn’t “How to produce fuel for 32,000 starship launches”, but rather “how to catch a flying container full of material” and you balance the momentum by sending other containers around the other way to meet it and get caught going the other direction.
And how to build a railgun on the moon for launching cargo containers. Not my idea, incidentally.
Who knows, it might even be good for our species to have some huge stretch goal to be pursuing in space.
Maybe the aliens will let us borrow some flying saucers and we can have it done in a month.