Central-Star Luminosity and Temperature Position of the Saturn Nebula NGC 7009

This paper computes a self-contained budget for NGC 7009 from published observational values, with every derived number produced by the deposited computation script. The Saturn Nebula is a bright elliptical nebula with ansae extending along its major axis and a hot central star whose luminosity and effective temperature place it on the horizontal part of the post-asymptotic-giant-branch track. The stellar radius follows from the luminosity and temperature through the Stefan-Boltzmann law, and the surface gravity follows once a core mass is adopted from the track itself. Comparing the nebular dynamical age with the track crossing time tests whether the star and the shell tell the same story about when the envelope was ejected. The headline results are: luminosity_Lsun = 2.8e+03; effective_temperature_K = 8.2e+04; stellar_radius_Rsun = 0.262; surface_gravity_m_s2 = 2.39e+03; log_g_cgs = 5.38; core_mass_Msun = 0.6; nebular_age_yr = 6053. The stellar radius is a small fraction of a solar radius, as expected for a star that has finished contracting toward the white-dwarf sequence. The surface gravity is high but still below white-dwarf values, placing the star in the late contraction phase. The nebular age and the track age agree to within the usual factor-of-two tolerance of such comparisons, which supports the adopted distance and core mass jointly rather than either one separately. The calculation is presented with its inputs, relations and sensitivities stated openly, so that any revised distance, density or stellar parameter can be substituted and the verdict recomputed directly.