  We present 'empirical' models (pressure vs. density) of Saturn's interior
constrained by the gravitational coefficients J_2, J_4, and J_6 for different
assumed rotation rates of the planet. The empirical pressure-density profile is
interpreted in terms of a hydrogen and helium physical equation of state to
deduce the hydrogen to helium ratio in Saturn and to constrain the depth
dependence of helium and heavy element abundances. The planet's internal
structure (pressure vs. density) and composition are found to be insensitive to
the assumed rotation rate for periods between 10h:32m:35s and 10h:41m:35s. We
find that helium is depleted in the upper envelope, while in the high pressure
region (P >~ 1 Mbar) either the helium abundance or the concentration of
heavier elements is significantly enhanced. Taking the ratio of hydrogen to
helium in Saturn to be solar, we find that the maximum mass of heavy elements
in Saturn's interior ranges from ~ 6 to 20 M_Earth. The empirical models of
Saturn's interior yield a moment of inertia factor varying from 0.22271 to
0.22599 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 consistent
with the derived moment of inertia values and assumed rotation rates over the
entire range of investigated rotation rates. This suggests that the long-term
precession period of Saturn is somewhat shorter than the generally assumed
value of 1.77 x 10^6 years inferred from modeling and observations.

Astrophysics