Saturn Helium Separation Energy Budget: Gravitational Energy Release Compared with the Measured Intrinsic Luminosity

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: intrinsic_luminosity_W = 8.57e+16; separated_helium_mass_kg = 4.26e+25; gravitational_energy_release_J = 4.16e+33; equivalent_power_W = 6.6e+16; power_ratio_to_intrinsic = 0.77; intrinsic_flux_W_m2 = 2.01. The equivalent power from helium settling is of the same order as the entire measured intrinsic luminosity, which is the quantitative form of the statement that helium separation can power Saturn's excess emission. It does not need to supply all of the luminosity, since ordinary secular cooling contributes as well; it needs to supply the excess over passive cooling, a smaller target, and the budget clears that target with room to spare under the stated assumptions. The separated mass required is a modest fraction of the envelope, consistent with the observed atmospheric depletion when the deep interior is allowed to hold the balance. 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.