It appears that a number of people are misunderstanding my description of the space habitat (on the order of the "invasion fleet being swallowed by a small dog" scale).
So here's a picture, approximately to scale:
(Edited to correct drawing the moon orbit too small.)
The large circle is the earth's orbit. The circle in the middle is the Sun. The little circle on the left, that's the Moon's orbit around Earth. (Earth itself is a teensy dot in the middle of that circle, about as big as the line marking the orbit of the Earth around the Sun. I drew the Earth in, but you probably can't see it in the small image). The relatively large circle on the right, that's the space habitat sitting at a Lagrange point (or rather, sitting with a Lagrange point at its centre). It is so phenomenally big it might not actually be stable here (I have not done the calculations to check).
(By comparison, the original Ringworld would be represented by the really big circle. Much larger.)
Now the habitat goes around the Sun in the same orbit as the Earth, offset by 60 degrees. It rotates about its own central axis once every 24 hours, giving it a day-night cycle. The ring would be tilted a little, so it doesn't shade itself most of the time - in fact the ring will precess as it goes. The artificial gravity induced by the rotation would be about 1g (it would, I think, vary somewhat between night and day, because at midnight you're orbiting a fair bit nearer to the Sun than you "should" for the center of mass of the habitat, and midday you're a bit further from the Sun).