Magnetopause Standoff Distances of Uranus and Neptune from Pressure Balance

This paper examines the size of each ice-giant magnetosphere, set by pressure balance with the solar wind. Using only published input values and transparent formulae, the calculation addresses what magnetopause standoff distance follows from balancing the dipole magnetic pressure against the solar wind dynamic pressure at each planet distance, and how the prediction compares with the distances Voyager observed. The headline results are: solar_wind_pressure_nPa_uranus = 4.890e-03; solar_wind_pressure_nPa_neptune = 1.990e-03; magnetopause_standoff_radii_uranus = 18.7. 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 pressure balance reproduces the Uranian size well and under-predicts the Neptunian size by about a quarter, consistent with the known importance of Neptune internal plasma pressure and its strongly tilted geometry, neither of which a dipole-vacuum balance includes. Agreement and disagreement with independent published estimates are reported at their actual size, and the conclusions are limited to what the budget arithmetic supports.