Space mirrors/solar sail

The CNT = carbon nano tubes may be available soon and make the solar sail practical. I suggest a proto type with an area of several square miles in low Earth orbit up perhaps 300 miles in semi polar orbit. It has one mirror surface which can focus a beam of sunlight on a state or part of a state that is having cold weather. At the same time it can shade a different state that is hotter than usual. It needs some solar sail capability to get in the only position where it can do both of these simultaneously for more than a few minutes. The solar sail capability also allows it to increase it's altitude perhaps a mile per day. The proto type likely can not light up the dark side of the moon significantly, but will this be possible if the mirror parabolic curve can be made sufficiently accurate? Please comment, refute and/or embellish. Neil;