Gravity field and interior structure of Rhea

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Abstract

Doppler data generated with the Cassini spacecraft’s radio carrier waves at X- and Ka-bands can be used to determine the quadrupole moments of Rhea’s gravitational field. The resulting tri-axial field should be consistent with the assumption that Rhea is in tidal and rotational equilibrium. If so, we can construct interior models that are consistent with Rhea’s mean density of 1236 kg/m3, determined previously from Pioneer and Voyager data, and its axial moment of inertia, to be determined from Cassini’s gravity data. Two-zone models consisting of a rocky core overlaid by a deep layer of ice are explored in some detail. While three-zone models consisting of an iron core, or a eutectic mixture of iron and iron sulfide, plus a rocky mantle and an outer layer of ice are possible, Rhea’s relatively small density suggests that the satellite is not iron rich. Finally, we show that a flyby at the planned altitude of 500 km provides sufficient accuracy for the gravity experiment.

Section snippets

Rhea’s equilibrium figure

Rhea is the second largest satellite in the Saturn system. It has a mean radius R=764±4 km (Davies and Katayama, 1983) and a mass μ=GM=154±4 km3/s2 (Campbell and Anderson, 1989). With the gravitational constant given by G=(6.67259±0.00085)×10−20 km3/(s2 kg) (Cohen and Taylor, 1999), its mean density is ρ̄=1236±38 kg/m3. It is in synchronous rotation with its orbital period of 4.5175 days, hence its equilibrium figure is determined by a static rotational and tidal distortion. The magnitude of the

Equilibrium theory

A synchronously rotating satellite in tidal and rotational equilibrium takes the shape of a tri-axial ellipsoid with dimensions a, b, and c (a>b>c). The long axis of the ellipsoid is along the planet–satellite line and the short axis is parallel to the rotation axis. The distortion of the satellite depends on the magnitude of the rotational and tidal forcing and the distribution of mass with radius inside the body. The distortion of the satellite and its internal mass distribution determine the

Rhea interior models

Consistent with the constraint provided by the single density datum ρ̄, we assume a simple two-layer model for Rhea consisting of a core of radius rc and density ρc surrounded by a mantle of density ρm. The mean density ρ̄ for this two-layer model is ρ̄=rcR3ρc−ρmm

Even for this simple model, there is only one equation in three unknowns. Therefore, assume that Rhea’s core is made up of material similar to Io’s mantle with a density ρc of 3250 kg/m3 (Anderson et al., 2001b) and an icy shell of

Mass determination

In this section, we focus on the problem of determining the satellite’s mass, neglecting for the moment higher order terms in the gravitational potential. The observable is the range rate q, or line of sight (LOS) Doppler. This is obtained by projecting the velocity vector along the Earth–spacecraft direction: q=mv−bv+r(t)vℓμtr(t)bwhere, as illustrated in Fig. 4, b is the spacecraft’s distance from the body’s baricenter, v is its velocity (all quantities refer to the closest approach time t

Flyby determination of C22

The Cassini mission will provide much improved values for Rhea’s mass GM and mean radius R (through imaging observations). This will result in a tighter density constraint than the one from the Pioneer and Voyager missions. However, in order that Rhea’s interior models be improved as well, a measurement of its gravity coefficient C22 must be made to an accuracy of 10−6 or better. Here we present an error analysis that shows that this measurement is feasible.

In general, the standard Legendre

Conclusions

The conclusions below were established using two- or three-way Allan deviations ranging from 2.4 (expected value) to 9×10−14 (worst case).

  • 1.

    The Cassini Rhea gravity science experiment is expected to determine C22 with an accuracy of ∼2×10−6, providing a very good experiment. This in turn will allow us to determine the size and density of Rhea’s core to within 16% in all plausible cases (see Fig. 3).

  • 2.

    In the best case, C22 would be determined with an accuracy of 1×10−6, providing an excellent

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