His work covered solar studies, globular clusters, and stellar dynamics. His analyses of the radial velocities and proper motions of large numbers of stars clarified the structure of our Galaxy and identified groups of stars that formed at different stages in its evolution. This led to the modern view that a galaxy such as ours is born from a collapsing cloud of gas that gradually flattens out into a disk, with the oldest stars being in a surrounding halo and the youngest stars in the disk. Woolley was the eleventh Astronomer Royal (1956–71).