Expansion Velocity and Shell Density Budget of the Cat's Eye Nebula NGC 6543

This paper computes a self-contained budget for NGC 6543 from published observational values, with every derived number produced by the deposited computation script. The Cat's Eye Nebula is among the most morphologically intricate planetary nebulae known, with nested elliptical shells, jets and arcs imprinted on a bright inner rim. Its bright core expands slowly compared with its outer structures, which makes it a useful test of whether a single expansion speed can describe a nebula that plainly formed in episodes. The bright rim radius and the expansion speed measured from split emission lines provide the two ingredients for a dynamical age, while the electron density from forbidden-line ratios sets the shell mass once a volume and a filling factor are ad The headline results are: R_pc = 0.2; v_exp_km_s = 16.4; dynamical_age_yr = 11924; electron_density_cm3 = 5e+03; thermal_pressure_Pa = 1.1e-09; ionised_mass_Msun = 0.242; kinetic_energy_J = 6.48e+37; emitting_volume_fraction = 0.05; sound_speed_km_s = 10.5; mach_number = 1.56. The rim has not expanded as a single coeval shell. The bright rim age is short compared with the ages implied for the outer halo structures reported in deep imaging, so the nebula records at least two mass-loss episodes separated in time. The shell pressure exceeds typical interstellar pressures by orders of magnitude, which explains why the rim remains sharp: it is still over-pressured and driving into slower material ahead of it. 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.