Saturn A Ring Viscous Spreading Timescale and Particle Density Budget from Self-Gravity Wake Viscosity Estimates

This paper computes a quantitative budget for the ring system 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: viscosity_m2_s = 0.0114; spreading_timescale_years = 5.94e+08; particle_number_density_per_m3 = 0.0106; surface_density_kg_m2 = 400; orbital_period_hours = 14.1. The spreading timescale comes out far shorter than the age of the Solar System, of an order that implies the A ring's present width would be substantially reworked in a small fraction of planetary history if transport ran unopposed at the computed viscosity. That result does not by itself date the rings, because sharp edges are maintained by resonances with moons that return angular momentum to the ring, but it quantifies the power those resonances must supply and explains why the ring's edges coincide with resonant locations rather than sitting at arbitrary radii. 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.