What is a *Dyson Sphere?
The Dyson sphere (or Dyson shell) was originally proposed in 1959 by the astronomer Freeman Dyson in "Search for Artificial Stellar Sources of Infrared Radiation" in Science as a way for an advanced civilisation to utilise all of the energy radiated by their sun. It is an artificial sphere the size of an planetary orbit. The sphere would consist of a shell of solar collectors or habitats around the star, so that all (or at least a significant amount) energy will hit a receiving surface where it can be used. This would create a huge living space and gather enormous amounts of energy.
A Dyson sphere in the solar system, with a radius of one AU would have a surface area of at least 2.72e17 km^2, around 600 million times the surface area of the Earth. The sun has a energy output of around 4e26 W, of which most would be available to do useful work.
The original proposal simply assumed there would be enough solar collectors around the star to absorb the starlight, not that they would form a continuous shell. Rather, the shell would consist of independently orbiting structures, around a million kilometres thick and containing more than 1e5 objects. But various science fiction authors seem to have misinterpreted the concept to mean a solid shell enclosing the star, usually having an inhabitable surface on the inside, and this idea was so compelling that it has been the main use of the term in science fiction. The earliest appearance of this version seems to be Robert Silverberg's novel Across a Billion Years.
LOL - a circle around Hillary - the stuff science fiction is made of.