Saturn Central Pressure and Density Bounds from Hydrostatic Models Checked Against Cassini Grand Finale Gravity Values

This paper computes a quantitative budget for the deep interior of Saturn from published spacecraft values, using a deliberately transparent calculation whose every step can be checked from the deposited script. The headline results are: mean_density_kg_m3 = 687.1; central_pressure_TPa = 0.937; central_pressure_range_TPa = 0.656 to 1.22; central_density_n1_kg_m3 = 2.26e+03; pressure_scale_ratio_to_jupiter = 0.186; surface_gravity_m_s2 = 11.19. Saturn's pressure scale is a small fraction of Jupiter's, and the mid central-pressure estimate falls accordingly, in the vicinity of one terapascal rather than several. The central density estimates, by contrast, are not proportionally smaller, because the density concentration factors multiply a mean density that is itself lower by less than the pressure scale is. This decoupling of pressure and density ratios is the central quantitative lesson: Saturn's centre is far softer in pressure yet only moderately denser material is required to produce it. The treatment states its inputs, its geometric and physical assumptions, and the sensitivity of each conclusion to those choices, so that the results function as a consistency test on the published values as much as a derivation from them. Where the computed budget agrees with independent determinations, the agreement corroborates both; where it strains, the strain identifies the input or assumption most likely to need revision.