Jupiter Central Pressure and Density Bounds from Hydrostatic Polytrope Models Checked Against Juno Gravity Values

This paper computes a quantitative budget for the deep interior of Jupiter 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 = 1326; central_pressure_TPa = 5.03; central_pressure_range_TPa = 3.52 to 6.54; central_density_n1_kg_m3 = 4.36e+03; central_density_n15_kg_m3 = 7.94e+03; surface_gravity_m_s2 = 25.92. The mean density that follows from the measured mass and volume is modest, close to that of water-rich rock, because most of Jupiter's volume is compressed hydrogen at densities far below the central value. The hydrostatic scale is large, and half of it, the mid estimate adopted here, lands inside the published model band, which is a non-trivial check: a coefficient error of a factor of three would have placed the estimate outside the band. The two polytropic indices give central densities differing by less than a factor of two, so the central density is considerably better constrained by this argument than its reputation suggests. 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.