On the mass of Saturn's rings

A gravitational model of the Saturnian system which included rings, satellites and the oblate planet was fit to the observed secular apsidal and nodal rates of the inner satellites. The solution |Mass of the rings = ( 6.2 ± 2.4) × 10⁻⁶ \,masses of Saturn| |Mass of Rhea = (4.8 ± 0.8) × 10⁻⁶ \,masses of Saturn| |J₂ = (1.664 ± 0.001) × 10⁻²| |J₄ = - (8.7 ± 0.1) × 10⁻⁴| was obtained using a functional relationship between the zonal harmonics J2 and J4 derived from the planetary interior modelling of Hubbard, Slattery & DeVito. The planetary model due to Podolak & Cameron was shown to be inconsistent with the observed secular apsidal and nodal rates of the natural satellites. A solution for the planetary figure by Garcia was found to suffer from defective data for Titan. The apsidal commensurability of particles in the rings with Titan was shown to produce no significant effect on the structure of the rings and, in particular, is not the cause of Guérin's division.