Drakkith said:
. As Rive pointed out the sheet would act as a giant solar said, so we would constantly need to run our thrusters, wasting large amounts of fuel.
We could just move it inwards from L1 to compensate for the radiation pressure, as long as the radiation pressure is smaller than solar gravity, there will still be an equilibrium point.
If I can believe the wikipedia page on lightsails, we don't have any material, light enough to cancel the solar gravity with radiation pressure.
We might be able to tilt the sail for stationkeeping, altough this will be very hard for something with a 1000+ km size.
The better our weight/surface ratio, gets, the further away from the earth it has to be, and the larger it needs to be to get enough shadow.
Drakkith said:
A single layer of foil probably wouldn't work well, as it is very fragile and prone to tearing if anything goes wrong with one of the thrusters or if it gets hit by a stray pebble or something. You'd likely need a modular design that would drastically increase the cost and mass, which would then exponentially increase the size/number of launch vehicles.
Also, keep in mind that the sheer size of something like this is nearly unimaginable. At the L1 point, 1.5 million km away, our sheet would need to be 6500 km across to block half the Sun, 3250 km to block a quarter, etc. Just to block 10% of the Sun we would need 1300 km of sheet. That's about a third of the length of the continental United States.
Surface area is proportional to the square of the radius. If 6500 km across blocks half, 3250 would block only 12.5%.
Another thing is that L1 is about 1% of the earth-sun distance, and the shadow of an object at L1, will spread out about 10000km on all sides,, so a lot of the shadow won't fall on the earth.
To counteract the current global warming you might need to block about 1% of radiation, but you'll need a disk with about 2.5% of the earth's cross-section, with a diameter of about 2000 km.
If it has to be closer to the sun, because of the light pressure, it will have to be even bigger.