Answer: Spaceships orbiting near Saturn, in dozens of little domes.
Don't look at me. I thought the "Silent Running" concept was inane, too. Fun movie, though, with decent effects for the time (most of it was filmed inside an aircraft carrier) and we can all see where R2D2 came from.
"Hey, where should we preserve these forests? It's not like we have a spare few acres for domes on the entire frigging surface of the Earth!"
"Whoa, how about in orbit beyond Saturn?"
"Well, yeah! As long as we're going to toss them all into space, why just stop with low Earth orbit, or the Moon? That'd be too damn easy!"
"Say, what exactly are we doing with all this sewage, now?"
"Don't ask."