We describe an improved method for determining the distances of planetary nebulae (PNs) based on a theoretical/empirical relationship between their radii and radio surface brightness. Like the Shklovsky (constant mass) distance method, our relationship requires only radio flux density and angular size measurements, which are widely available in the literature. Based on models matching the overall Galactic distribution of PNs, we determine how PNs observed in the direction of the Galactic center are actually distributed relative to the bulge in order to establish the usefulness of these PNs for distance studies. We then use the bulge PNs along with PNs with independent distances to establish, calibrate, and test the accuracy of the method. When compared to the best available data our distance method appears to yield distance errors consistent with a scatter of approx < 25% (1 σ). And, based on our models scaled to local PNs, we find a mean Galactic center distance of 8.3 ± 2.6 kpc for the bulge PNs. The relationship that PNs exhibit between radius and surface brightness is in excellent agreement with our simulated nebulae from Paper I (Buckley & Schneider 1995). We find that no simple power law can describe the changing mass and radius of a PN as it ages; however, our empirical relationship has a limiting behavior that is almost indistinguishable from the assumption made in Shklovsky's distance method that PNs have a constant ionized mass. We reexamine the dispute about the validity of the Shklovsky's distance method as applied to Galactic center PNs in light of these results, and we argue that the Shklovsky method does predict the distances of large, low surface brightness PNs well, but it increasingly overestimates the distance of smaller PNs.
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