Gravity field and interior structure of Rhea
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 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 , 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 for this two-layer model is
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: where, 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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