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eirenicon comments on The Popularization Bias - Less Wrong
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There are multiple types of Dyson sphere. Dyson's original vision, a swarm of satellites, would be in orbit, but the popular version more commonly seen in fiction - a solid shell - would not, any more than the Earth orbits its own core (although any one point on the shell could plausibly be said to orbit the centre, provided the sphere is spinning).
A solid Dyson sphere is a dumb idea, the dynamics are unstable. See Niven's essay on the dynamics of ringworld for the problems, and realize a sphere would be even worse. I don't remember whether he discussed that in "Bigger than Worlds" or in an essay specifically on building Ringworld, he did discuss the dynamics problems in the novels as well.
So you have to expend a bit of energy moving it back to the midpoint every so often. What are attitude jets for?