Ringworlds and Dyson spheres can be stable

In his 1856 Adams Prize essay, James Clark Maxwell demonstrated that Saturn's rings cannot be comprised of a uniform rigid body. This is a consequence of the two-body gravitational interaction between a ring and planet resulting in instability. Similarly, it is also known that a so-called Dyson sphere encompassing a single star would be unstable due to Newton's shell theorem. A surprising finding is reported here that both a ring and a sphere (shell) can be stable in the restricted three-body problem. First, if two primary masses are considered in orbit about their common centre of mass, a large, uniform, infinitesimal ring enclosing the smaller of the masses can in principle be stable under certain conditions. Similarly, a Dyson sphere can, be stable, if the sphere encloses the smaller of the two primary masses, again under certain conditions. These findings extend Maxwell's results on the dynamics of rings and have an interesting bearing on so-called Ringworlds and Dyson spheres from fiction. Moreover, the existence of passively stable orbits for such large-scale structures may have implications for so-called techno-signatures in search for extra-terrestrial intelligence studies.