Tim Van Hoolst

Titan’s obliquity as evidence of a subsurface ocean?

Abstract On the basis of gravity and radar observations with the Cassini spacecraft, the moment of inertiaof Titan and the orientation of Titan’s rotation axis have been estimated in recent studies. Accordingto the observed orientation, Titan is close to the Cassini state. However, the observed obliquity isinconsistent with the estimate of the moment of inertia for an entirely solid Titan occupying theCassini state. We propose a new Cassini state model for Titan in which we assume the presenceof a liquid water ocean beneath an ice shell and consider the gravitational and pressure torquesarising between the di erent layers of the satellite. With the new model, we nd a closer agreementbetween the moment of inertia and the rotation state than for the solid case, strengthening thepossibility that Titan has a subsurface ocean. 1 Introduction On the basis of Cassini radar images, [6] and [7] precisely measured the orientation of therotation axis of Titan. Using the orientation of the normal to the orbit of Titan given in the IAUrecommendations (Seidelmann et al. 2007), they determined the obliquity to be about 0:3

Chandler wobble and Free Core Nutation for Mars

Abstract The NetLander Ionospheric and Geodesic Experiment (NEIGE) of the 2007 NetLander/Mars Sample Return mission will allow the determination of Mars’ orientation parameters. Two normal rotational modes of Mars are studied here which can play an important role in these quantities: the Free Core Nutation (FCN) and the Chandler wobble (CW). The influence of various rheological and structural assumptions about the planet on the periods of these modes is investigated. Special attention is paid to the effects of inelasticity and the possible presence of a solid inner core. It is found that inelasticity has an almost negligible effect on the FCN period but can change the CW period by several days. The presence of an inner core, on the other hand, almost does not influence the CW period but can cause important changes to the FCN period. For the FCN, also nonhydrostatic effects can have a large impact on the period. These additional factors determining the FCN period, besides core size and density, certainly complicate the procedure for deriving information on the core of Mars such as the core radius, but more importantly offer the possibility to study and constrain a wide variety of inner core outer core and mantle properties.

Influence of an inner core on the long-period forced librations of Mercury

Abstract The planetary perturbations on Mercury’s orbit lead to long-period forced librations of Mercury’s mantle. These librations have previously been studied for a planet with two layers: a mantle and a liquid core. Here, we calculate how the presence of a solid inner core in the liquid outer core influences the long-period forced librations. Mantle–inner core coupling affects the long-period libration dynamics mainly by changing the free libration: first, it lengthens the period of the free libration of the mantle, and second, it adds a second free libration, closely related to the free gravitational oscillation between the mantle and inner core. The two free librations have periods between 2.5 and 18y depending on the internal structure. We show that large amplitude long-period librations of a few tens of arcsec are generated when the period of a planetary forcing approaches one of the two free libration periods. These amplitudes are sufficiently large to be detectable by spacecraft measurements of the libration of Mercury. The amplitudes of the angular velocity of Mercury’s mantle at planetary forcing periods are also amplified by the resonances, but remain much smaller than the current precision of Earth-based radar observations unless the period is very close to a free libration period. The inclusion of mantle–inner core coupling in the rotation model does not significantly improve the fit to the radar observations. This implies that it is not yet possible to determine the size of the inner core of Mercury on the basis of available observations of Mercury’s rotation rate. Future observations of the long-period librations may be used to constrain the interior structure of Mercury, including the size of its inner core.

The obliquity of Enceladus

Abstract The extraordinary activity at Enceladus’ warm south pole indicates the presence of an internal global or local reservoir of liquid water beneath the surface. While Tyler (Tyler, R.H. [2009]. Geophys. Res. Lett. 36(15), L15205; Tyler, R.H. [2011]. Icarus 211(1), 770–779) has suggested that the geological activity and the large heat flow of Enceladus could result from tidal heating triggered by a large obliquity of at least 0.05–0.1°, theoretical models of the Cassini state predict the obliquity to be two to three orders of magnitude smaller for an entirely solid and rigid Enceladus. We investigate the influence of an internal subsurface ocean and of tidal deformations of the solid layers on the obliquity of Enceladus. Our Cassini state model takes into account the external torque exerted by Saturn on each layer of the satellite and the internal gravitational and pressure torques induced by the presence of the liquid layer. As a new feature, our model also includes additional torques that arise because of the periodic tides experienced by the satellite. We find that the upper limit for the obliquity of a solid Enceladus is 4.5 × 10 - 4 degrees and is negligibly affected by elastic deformations. The presence of an internal ocean decreases this upper limit by 13.1%, elasticity attenuating this decrease by only 0.5%. For larger satellites, such as Titan, elastic effects could be more significant because of their larger tidal deformations. As a consequence, it appears that it is easier to reconcile the theoretical estimates of Titan’s obliquity with the measured obliquity than reported in previous studies wherein the solid layers or the entire satellite were assumed to be rigid. Since the obliquity of Enceladus cannot reach Tyler’s requirement, obliquity tides are unlikely to be the source of the large heat flow of Enceladus. More likely, the geological activity at Enceladus’ south pole results from eccentricity tides. Even in the most favorable case, the upper limit for the obliquity of Enceladus corresponds to about two meters at most at the surface of Enceladus. This is well below the resolution of Cassini images. Control point calculations cannot be used to detect the obliquity of Enceladus, let alone to constrain its interior from an obliquity measurement.

The long-period forced librations of Titan

A moon in synchronous rotation has longitudinal librations because of its nonspherical mass distribution and its elliptical orbit around the planet. We study the librations of Titan with periods of 14.7y and 29.5y and include deformation effects and the existence of a subsurface ocean. We take into account the fact that the orbit is not Keplerian and has other periodicities than the main period of orbital motion around Saturn due to perturbations by the Sun, other planets and moons. An orbital theory is used to compute the orbital perturbations due to these other bodies. We numerically evaluate the amplitude of the long-period librations for many interior structure models of Titan constrained by the mass, radius and gravity field. Measurements of the librations may give constraints on the interior structure of the icy satellites.

Rotation of Planets

In this part of the book we describe the rotation of planets and moons of the solar system. Besides providing information on the current rotation rate and orientation of these bodies, we discuss the changes in the rotation speed and orientation on both short and long timescales. We show how information on the planetary interior and dynamics can be determined from observations of changes in rotation and orientation and what we have learned so far.