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We present 'empirical' models (pressure vs. density) of Saturn's interiorconstrained by the gravitational coefficients J_2, J_4, and J_6 for differentassumed rotation rates of the planet. The empirical pressure-density profile isinterpreted in terms of a hydrogen and helium physical equation of state todeduce the hydrogen to helium ratio in Saturn and to constrain the depthdependence of helium and heavy element abundances. The planet's internalstructure (pressure vs. density) and composition are found to be insensitive tothe assumed rotation rate for periods between 10h:32m:35s and 10h:41m:35s. Wefind that helium is depleted in the upper envelope, while in the high pressureregion (P >~ 1 Mbar) either the helium abundance or the concentration ofheavier elements is significantly enhanced. Taking the ratio of hydrogen tohelium in Saturn to be solar, we find that the maximum mass of heavy elementsin Saturn's interior ranges from ~ 6 to 20 M_Earth. The empirical models ofSaturn's interior yield a moment of inertia factor varying from 0.22271 to0.22599 for rotation periods between 10h:32m:35s and 10h:41m:35s, respectively.A long-term precession rate of about 0.754" yr^{-1} is found to be consistentwith the derived moment of inertia values and assumed rotation rates over theentire range of investigated rotation rates. This suggests that the long-termprecession period of Saturn is somewhat shorter than the generally assumedvalue of 1.77 x 10^6 years inferred from modeling and observations.

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Empirical Models of Pressure and Density in Saturn's Interior:  Implications for the Helium Concentration, its Depth Dependence, and Saturn's  Precession Rate