The accurate determination of Saturn ’ s gravitational coefficients by Cassini could provide tighter constrains on Saturn ’ s internal structure .
Also , occultation measurements provide important information on the planetary shape which is often not considered in structure models .
In this paper we explore how wind velocities and internal rotation affect the planetary shape and the constraints on Saturn ’ s interior .
We show that within the geodetic approach ( Lindal et al. , 1985 , ApJ , 90 , 1136 ) the derived physical shape is insensitive to the assumed deep rotation .
Saturn ’ s re-derived equatorial and polar radii at 100 mbar are found to be 54,445 \pm 10 km and 60,365 \pm 10 km , respectively .
To determine Saturn ’ s interior we use 1 D three-layer hydrostatic structure models , and present two approaches to include the constraints on the shape .
These approaches , however , result in only small differences in Saturn ’ s derived composition .
The uncertainty in Saturn ’ s rotation period is more significant : with Voyager ’ s 10h39mns period , the derived mass of heavy elements in the envelope is 0-7 M _ { \oplus } .
With a rotation period of 10h32mns , this value becomes < 4 M _ { \oplus } , below the minimum mass inferred from spectroscopic measurements .
Saturn ’ s core mass is found to depend strongly on the pressure at which helium phase separation occurs , and is estimated to be 5-20 M _ { \oplus } .
Lower core masses are possible if the separation occurs deeper than 4 Mbars .
We suggest that the analysis of Cassini ’ s radio occultation measurements is crucial to test shape models and could lead to constraints on Saturn ’ s rotation profile and departures from hydrostatic equilibrium .