Central Pressure and Adiabatic Temperature Bounds for Uranus and Neptune

This paper examines the pressure and temperature at the centres of the two ice giants. Using only published input values and transparent formulae, the calculation addresses how large the central pressure must be, given only the measured mass, radius and mean density, and how the answer changes when the interior is allowed to concentrate toward the centre. The headline results are: central_pressure_uniform_GPa_uranus = 145.3; central_pressure_uniform_GPa_neptune = 227.4; central_pressure_concentrated_GPa_uranus = 514.0. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. The central finding is that Neptune sustains a materially higher central load than Uranus despite its smaller radius, because its mean density is nearly thirty percent larger and pressure scales with density squared. Agreement and disagreement with independent published estimates are reported at their actual size, and the conclusions are limited to what the budget arithmetic supports.