Nicole J. Rappaport

Gravity Field, Shape, and Moment of Inertia of Titan

Titan Through to the Core Gravity measurements acquired from orbiting spacecraft can provide useful information about the interior of planets and their moons. Iess et al. (p. 1367; see the Perspective by Sohl) used gravity data from four flybys of the Cassini spacecraft past Saturns moon, Titan, to model the moons gravity field and probe its deep interior structure. Their analysis implies that Titan is a partially differentiated body with a core consisting of a mix of ice and rock or hydrated silicates. Analysis of gravity data reveals that Saturn’s moon Titan has a partially differentiated internal structure. Precise radio tracking of the spacecraft Cassini has provided a determination of Titan’s mass and gravity harmonics to degree 3. The quadrupole field is consistent with a hydrostatically relaxed body shaped by tidal and rotational effects. The inferred moment of inertia factor is about 0.34, implying incomplete differentiation, either in the sense of imperfect separation of rock from ice or a core in which a large amount of water remains chemically bound in silicates. The equilibrium figure is a triaxial ellipsoid whose semi-axes a, b, and c differ by 410 meters (a – c) and 103 meters (b – c). The nonhydrostatic geoid height variations (up to 19 meters) are small compared to the observed topographic anomalies of hundreds of meters, suggesting a high degree of compensation appropriate to a body that has warm ice at depth.

The Tides of Titan

Getting to Know Titan Gravity-field measurements provide information on the interior structure of planets and their moons. Iess et al. (p. 457; published online 28 June) analyzed gravity data from six flybys of Saturns moon, Titan, by the Cassini spacecraft between 2006 and 2011. The data suggest that Titans interior is flexible on tidal time scales with the magnitude of the observed tidal deformations being consistent with the existence of a global subsurface water ocean. Gravity measurements by the Cassini spacecraft suggest that Saturn’s moon Titan hosts a subsurface ocean. We have detected in Cassini spacecraft data the signature of the periodic tidal stresses within Titan, driven by the eccentricity (e = 0.028) of its 16-day orbit around Saturn. Precise measurements of the acceleration of Cassini during six close flybys between 2006 and 2011 have revealed that Titan responds to the variable tidal field exerted by Saturn with periodic changes of its quadrupole gravity, at about 4% of the static value. Two independent determinations of the corresponding degree-2 Love number yield k2 = 0.589 ± 0.150 and k2 = 0.637 ± 0.224 (2σ). Such a large response to the tidal field requires that Titan’s interior be deformable over time scales of the orbital period, in a way that is consistent with a global ocean at depth.

Hyperion's sponge-like appearance

Hyperion is Saturn’s largest known irregularly shaped satellite and the only moon observed to undergo chaotic rotation. Previous work has identified Hyperion’s surface as distinct from other small icy objects but left the causes unsettled. Here we report high-resolution images that reveal a unique sponge-like appearance at scales of a few kilometres. Mapping shows a high surface density of relatively well-preserved craters two to ten kilometres across. We have also determined Hyperion’s size and mass, and calculated the mean density as 544 ± 50 kg m-3, which indicates a porosity of >40 per cent. The high porosity may enhance preservation of craters by minimizing the amount of ejecta produced or retained, and accordingly may be the crucial factor in crafting this unusual surface.

Dynamics of Saturn's Dense Rings

The Cassini mission to Saturn opened a new era in the research of planetary rings, bringing data in unprecedented detail, monitoring the structure and properties of Saturns ring system. The question of ring dynamics is to identify and understand underlying physical processes and to connect them to the observations in terms of mathematical models and computer simulations. For Saturns dense rings important physical processes are dissipative collisions between ring particles, their motion in Saturns gravity field, their mutual self-gravity, and the gravitational interaction with Saturns moons, exterior to or embedded in the rings.

Chaotic motions of Prometheus and Pandora

Recent HST images of the Saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20◦. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 d at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.35 yr^−1 for satellite masses based on a nominal density of 1.3 g cm^−3. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 yr when their apses are anti-aligned. In this context we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occured shortly after their apsidal lines were anti-aligned.

SATURN'S RINGS: PRE-CASSINI STATUS AND MISSION GOALS

Theoretical and observational progress in studies of Saturns ring system since the mid-1980s is reviewed, focussing on advances in configuration and dynamics, composition and size distribution, dust and meteoroids, interactions of the rings with the planet and the magnetosphere, and relationships between the rings and various satellites. The Cassini instrument suite of greatest relevance to ring studies is also summarized, emphasizing how the individual instruments might work together to solve outstanding problems. The Cassini tour is described from the standpoint of ring studies, and major ring science goals are summarized.

Origin of chaos in the Prometheus–Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting resulting in resonance overlap which causes the chaos. A single degree of freedom model captures the essential features of the chaotic dynamics. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 deg yr^−1 and 3.1 deg yr^−1, respectively.

Titan's Interior Structure

The goal of this chapter is to give a description of Titans interior that is consistent with the new constraints provided by the Cassini mission. As the Cassini mission proceeds into its first extended phase, the data obtained during the nominal mission suggest that Titan is at least partially differentiated. An ocean would be present some tens of kilometers below the surface. By comparison with the Galilean icy satellites Ganymede and Callisto, Titan would be composed of a metal/silicate rich core and a H2O rich outer layer. These conclusions are drawn from the interpretation of the gravity data, the geological data and the presence of a Schumann resonance which has been inferred from the measurement of electric signals during the descent of the Huygens probe into Titans atmosphere. Titans high eccentricity implies that the interior has not been very dissipative, there is little tidal heating available for internal dynamics, and the ice layer is cold, which can be achieved if the ocean under the ice layer contains ammonia. This paper also describes observations and interpretations which seem difficult to reconcile with our present understanding of Titans interior structure and evolution such as the shape of the planet or the obliquity. The last part of the chapter describes heat transfer models which suggest that the lower part of the ice crust could be convective. The NH3–H2o phase diagram indicates that the ocean is decoupled from the silicate-rich core by a layer of high-pressure ices. However, the interior model is largely uncertain because the interpretation of the data is still debated at present time. The additional information that will be acquired during the Cassini Solstice Mission should allow us to answer some of the questions.

OCCULTATION OBSERVATIONS OF SATURN'S B RING AND CASSINI DIVISION

The outer edge of Saturns B ring is strongly affected by the nearby 2:1 inner Lindblad resonance of Mimas and is distorted approximately into a centered elliptical shape, which at the time of the Voyager 1 and 2 encounters was oriented with its periapse toward Mimas. Subsequent observations have shown that the actual situation is considerably more complex. We present a complete set of historical occultation measurements of the B-ring edge, including the 1980 Voyager 1 and 1981 Voyager 2 radio and stellar occultations, the 1989 occultation of 28 Sgr, two independently analyzed occultations observed with the Hubble Space Telescope in 1991 and 1995, and a series of ring profiles from 12 diametric (ansa-to-ansa) occultations observed in 2005, using the Cassini Radio Science Subsystem (RSS). After making an approximate correction for systematic errors in the reconstructed spacecraft trajectories, we obtain orbit fits to features in the rings with rms residuals well under 1 km, in most cases. Fits to the B-ring edge in the RSS data reveal a systematic variation in the maximum optical depth at the very edge of the ring as a function of its orbital radius. We compare the B-ring measurements to an m = 2 distortion aligned with Mimas, and show that there have been substantial phase shifts over the past 25 years. Finally, we present freely precessing equatorial elliptical models for 16 features in the Cassini Division. The inner edges of the gaps are generally eccentric, whereas the outer edges are nearly circular, with ae < 0.5 km.

A procedure to analyze nonlinear density waves in Saturn's rings using several occultation profiles

Abstract Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturns rings that can be used in combination to analyze density waves. This paper establishes an accurate procedure of inversion of the wave profiles to reconstruct the wave kinematic parameters as a function of semi-major axis, in the nonlinear regime. This procedure is established using simulated data in the presence of realistic noise perturbations, to control the reconstruction error. It is then applied to the Mimas 5:3 density wave. There are two important concepts at the basis of this procedure. The first one is that it uses the nonlinear representation of density waves, and the second one is that it relies on a combination of optical depth profiles instead of just one profile. A related method to analyze density waves was devised by Longaretti and Borderies [Longaretti, P.-Y., Borderies, N., 1986. Icarus 67, 211–223] to study the nonlinear density wave associated with the Mimas 5:3 resonance, but the single photopolarimetric profile provided limited constraints. Other studies of density waves analyzing Cassini data [ Colwell, J.E., Esposito, L.W., 2007. Bull. Am. Astron. Soc. 39, 461 ; Tiscareno, M.S., Burns, J.A., Nicholson, P.D., Hedman, M.M., Porco, C.C., 2007. Icarus 189, 14–34] are based on the linear theory and find inconsistent results from profile to profile. Multiple cuts of the rings are helpful in a fundamental way to ensure the accuracy of the procedure by forcing consistency among the various optical depth profiles. By way of illustration we have applied our procedure to the Mimas 5:3 density wave. We were able to recover precisely the kinematic parameters from the radio experiment occultation data in most of the propagation region; a preliminary analysis of the pressure-corrected dispersion allowed us to determine new but still uncertain values for the opacity ( K ≃ 0.02 cm 2 / g ) and velocity dispersion of ( c 0 ≃ 0.6 cm/s ) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturns rings. It is very accurate and efficient in the far-wave region. However, improvements are required within the first wavelength. The ways in which this method can be used to establish diagnostics of ring physics are outlined.