If we assume that stars are about 5 lightyears apart on average, then the number of stars within a radius r of a given point is just 4r3/62.5, or about r3/15.
If we furthermore assume that one star in eight has a planet worth living on, then the distance between habitable systems is just twice that between systems in general (so the number of habitable systems within r lightyears is the same as the number of total systems within r/2). This means habitable systems are about 10ly apart on average.
The Celestial Empire rules about 4000 systems, which would occupy a radius of 60 0001/3 = 40 ly. Since presumably these systems are distributed among 7 times as many worthless ones, the radius doubles to 80ly, or a total diameter of 160ly. The Middle Provinces, comprising 1000 systems, are about 50ly in radius, or 100 in diameter.
The Empire as a whole is probably not a perfect sphere, though, since travel is along a sparse network of known routes, rather than across raw distance. If the inner 1000 systems form a compact sphere, the next a spherical shell about one-quarter explored, the next thousand 1/9 explored, and the last 1/16, the total number of habitable systems within the maximum radius of the Empire is 30 000, or 240 000 total, for a radius of 150 or a diameter of 300 lightyears.
The average ratio of safe-path-length to real intersystem distance is unfortunately not derivable from half-remembered astronomical data. There is probably some effect that makes longer paths more likely to encounter rough hyperspace and have to detour, so the average ratio is not necessarily helpful, but we'll pretend it is. A ratio of 2 or 3 seems reasonable, though, making habitable systems 20-30 ly apart as the starship navigates. At hyperdrive speeds of 1ly/minutey, that puts the average interstellar journey at well under an hour. Time in the onramps and normal space strongly dominates travel times.
This file was last modified at 1635 on 22Jun99 by email@example.com.