Re: Eight times brighter than the Moon?
Some Random Guy (tm) on slashdot did some calculations, and he figured it would take a perfect mirror (100% reflective) 2500 m^2 to equal the full moon over an 800 km^2 area. Assuming his calculations were correct, or close to it, if you want to be eight times as bright and account for the mirror being less than perfect, you're talking more like 25000 m^2.
Since the mirror would need to track to maintain the spot during the night, that's a LOT of mass to be moved (even assuming you using some sort of fabric with flimsy support structure behind it) given the size required. Maybe you can get the rotation of the satellite just right so it tracks as desired, but geosynchronous orbits are not stable, they need station keeping to maintain. Every time you fire the thrusters to tweak your orbit, you would destabilize the rotation - and if you can't find that 'just right' rotation you'll be using thrusters to move the mirror, meaning the satellite would have a pretty short life before it runs out of fuel.