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 \gtrsim 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 \sim 6 to 20 M _ { \oplus } . 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 \times 10 ^ { 6 } years inferred from modeling and observations .