Saturn Intrinsic Heat Flux Budget: Internal Power, Absorbed Sunlight and the Cooling-Time Problem Quantified

This paper computes a quantitative budget for the atmosphere and its energy transport 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_flux_W_m2 = 2.01; intrinsic_power_W = 8.57e+16; absorbed_solar_power_W = 1.04e+17; intrinsic_to_absorbed_ratio = 0.826; energy_at_present_rate_over_age_J = 1.22e+34. Saturn's intrinsic power is a large fraction of its absorbed solar power despite the planet receiving far less sunlight per unit area than Jupiter, because the intrinsic flux declines between the two planets by less than the solar flux does. The lifetime benchmark reaches an energy comparable to a substantial fraction of the planet's gravitational binding scale when set beside interior models, which is the arithmetic root of the cooling-time problem: a passively cooling Saturn would have had to start implausibly hot or cool implausibly slowly to still be radiating at the measured rate. 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.