  Measuring the distances to Galactic planetary nebulae (PNe) has been an
intractable problem for many decades. We have now established a robust optical
statistical distance indicator, the H$\alpha$ surface brightness- radius or S-r
relation, which addresses this problem. We developed this relation from a
critically evaluated sample of primary calibrating PNe. The robust nature of
the method results from our revised calibrating distances with significantly
reduced systematic uncertainties, and the recent availability of high-quality
data, including updated nebular diameters and integrated H$\alpha$ fluxes. The
S-r technique is simple in its application, requiring only an angular size, an
integrated H\alpha\ flux, and the reddening to the PN. From these quantities,
an intrinsic radius is calculated, which when combined with the angular size,
yields the distance directly. Furthermore, we have found that optically thick
PNe tend to populate the upper bound of the trend, while optically-thin PNe
fall along the lower boundary in the S-r plane. This enables sub-trends to be
developed which offer even better precision in the determination of distances,
as good as 18 per cent in the case of optically-thin, high-excitation PNe. This
is significantly better than any previous statistical indicator. We use this
technique to create a catalogue of statistical distances for over 1100 Galactic
PNe, the largest such compilation in the literature to date. Finally, in an
appendix, we investigate both a set of transitional PNe and a range of PN
mimics in the S-r plane, to demonstrate its use as a diagnostic tool.
Interestingly, stellar ejecta around massive stars plot on a tight locus in S-r
space with the potential to act as a separate distance indicator for these
objects.
