If you could pull it off (our civilization would have to be VERY MUCH further advanced and have access to LOTS of raw materials - I hope the Understatement Police aren't monitoring my computer, or I'm in big trouble), you would have quite a problem on your hands. Not only would you be getting radiation pressure from the sun on every portion of the sphere, you would be getting radiation pressure from every other part of the sphere that is not perfectly absorbing.
A ringworld would be marginally more do-able, but would still be far beyond the capacity of our civilization for any conceivable time into the future. An advantage (bootstrapping) is that the more effective radiation collectors you have, the more efficiently you could produce more collectors, providing that you're able to access more matter and scale up production as the increased energy comes on-line. Larry Niven's novels are a great place to pursue ideas like this. They are dated, but they are based on real (contemporary to publishing dates) engineering and theory. I know some career scientists, including a man who is in his 80's and STILL can't tell me any details about projects he worked on (classified), and you would be surprised how many of them are fascinated with "hard" science fiction .
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