Distances to planetary nebulae BD +30 degrees 3639 and NGC 6572

Third-epoch Very Large Array proper-motion measurements on the planetary nebulae ED +30 degrees 3639 and NGC 6572 have been made. Combining these measurements with simple models for the nebulae and using improved analysis, it has been determined that the distance to ED +30 degrees 3639 is 1.5 +/- 0.4 kpc and NGC 6572 is 1.2 +/- 0.4 kpc. These measurements are consistent with the distances determined from the previous epoch. However, the errors are significantly smaller and are now dominated not by the measurements but by the modeling and the uncertainty in the flux variation. The distances are significantly higher than those determined by statistical methods, with important consequences for calculation of the nebular masses and luminosities. In addition to their distances, the observations have elucidated the dynamical properties of the objects. First, the expansion of a shell is consistent with the self-similar expansion that is usually assumed for these objects, with the magnitude of the proper motion of a portion of a shell being linearly related to its distance from the center of symmetry. Second, the proper-motion measurements have directly yielded the ages for the nebulae, which are determined to be 900 +/- 200 yr for ED +30 degrees 3639 and 1000 +/- 200 yr for NGC 6572.