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The accurate determination of Saturn's gravitational coefficients by Cassinicould provide tighter constrains on Saturn's internal structure. Also,occultation measurements provide important information on the planetary shapewhich is often not considered in structure models. In this paper we explore howwind velocities and internal rotation affect the planetary shape and theconstraints on Saturn's interior. We show that within the geodetic approach(Lindal et al., 1985, ApJ, 90, 1136) the derived physical shape is insensitiveto the assumed deep rotation. Saturn's re-derived equatorial and polar radii at100 mbar are found to be 54,445 $\pm$10 km and 60,365$\pm$10 km, respectively.To determine Saturn's interior we use {\it 1 D} three-layer hydrostaticstructure models, and present two approaches to include the constraints on theshape. These approaches, however, result in only small differences in Saturn'sderived composition. The uncertainty in Saturn's rotation period is moresignificant: with Voyager's 10h39mns period, the derived mass of heavy elementsin the envelope is 0-7 M$_{\oplus}$. With a rotation period of 10h32mns, thisvalue becomes $<4$ $M_{\oplus}$, below the minimum mass inferred fromspectroscopic measurements. Saturn's core mass is found to depend strongly onthe pressure at which helium phase separation occurs, and is estimated to be5-20 M$_{\oplus}$. Lower core masses are possible if the separation occursdeeper than 4 Mbars. We suggest that the analysis of Cassini's radiooccultation measurements is crucial to test shape models and could lead toconstraints on Saturn's rotation profile and departures from hydrostaticequilibrium.

Interior Models of Saturn: Including the Uncertainties in Shape and Rotation