[nitrogen]

Clearly a solid Dyson sphere is not orbiting its host star, and could eventually drift into the star. However, might it be possible to harvest enough energy from the star to power a propulsion system that keeps the sphere in place?

[technolem]

Won't gravity stop this from happening? Seriously, the shell of the sphere will be balanced on the outskirts of a gravity well right? So if it moves this will move the center of the gravity well and both the star and sphere should fall back towards the center.

[nitrogen]

According to Newtonian gravity, an object inside a sphere experiences zero net gravity from the sphere, and vice versa.

http://en.wikipedia.org/wiki/Dyson_sphere#Dyson_shell