A Shape Model for Rhea and Implications for Its Gravity Coefficients and Internal Structure

Introduction: Models of the interior structure of planets and their satellites rely heavily on the determination of their gravitational potential. In addition, the shapes of the bodies reveal important information about subsurface processes, such as relaxation to a gravitational equilibrium and, when combined with mean density, a quantification of departure from a homogeneous structure [1]. We have determined the shape of the Saturnian icy satellite Rhea in the form of a spherical harmonic expansion to degree 10 from limb profile data obtained from Cassini imaging [1]. We also investigated whether the gravitational effects of this surface topography are sufficient to have biased existing estimates of the degree-2 gravity field. Radio tracking of range and range-rate measurements to Cassini gave estimates of the mass and quad-rupole gravitational moments of Rhea [2,3]. Estimates of the zonal gravitation harmonic J 2 and sectoral harmonic C 22 have led to varying conclusions, from an undifferentiated interior (assuming the hydrostatic constraint 3J 2 =10C 22) [4], to models favoring an " almost undifferentiated " satellite [2], to the latest analysis [3] exploring a broader range of geophysical assumptions as well as the implications of the presence of degree-3 and 4 gravity coefficients, and concluding that Rhea is non-hydrostatic. Only if Rhea is hydrostatic can measurements of its quadrupole gravitational moments be used simply to determine its internal structure. Whether Rhea is hy-drostatic or not can be tested by measuring J 2 and C 22 and seeing whether their ratio has the hydrostatic ratio of 10:3. Unfortunately, estimation of J 2 and C 22 may be complicated by the presence of unestimated higher-order gravitational coefficients [3]. One source of such higher-order terms is uncompensated surface topography , which is our interest here. Method: We determined the shape of Rhea using topography from 22 limb profiles [1]. The topography was expanded into spherical harmonic coefficients up to l=m=10 via a least-squares fit method with the appropriate normalization of the Legendre functions. We verified the ability of the code to recover the correct coefficients using synthetic data placed at the locations of the real profiles. Results: Table 1 lists the low-order spherical harmonic topography coefficients. Figure 1 shows the coordinates of the limb profiles on a map of Rhea [1]. Figure 2 shows the topography derived from spherical harmonic expansion superimposed on a map of Rhea.