Theory of the rotation of Janus and Epimetheus

The saturnian coorbital satellites Janus and Epimetheus present a unique dynamical configuration in the Solar System, because of high-amplitude horseshoe orbits, due to a mass ratio of order unity. As a consequence, they swap their orbits every 4 years, while their orbital periods is about 0.695 days. Recently, Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) got observational informations on the shapes and the rotational states of these satellites. In particular, they detected an offset in the expected equilibrium position of Janus, and a large libration of Epimetheus.We here propose to give a three-dimensional theory of the rotation of these satellites in using these observed data, and to compare it to the observed rotations. We consider the two satellites as triaxial rigid bodies, and we perform numerical integrations of the system in assuming the free librations as damped.The periods of the three free librations we get, associated with the three dimensions, are respectively 1.267, 2.179 and 2.098 days for Janus, and 0.747, 1.804 and 5.542 days for Epimetheus. The proximity of 0.747 days to the orbital period causes a high sensitivity of the librations of Epimetheus to the moments of inertia. Our theory explains the amplitude of the librations of Janus and the error bars of the librations of Epimetheus, but not an observed offset in the orientation of Janus.     

Analytical description of physical librations of saturnian coorbital satellites Janus and Epimetheus

Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every 4 years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to Cassini ISS images. By a quasi-periodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long- and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results obtained for the short-period librations are studied with the help of an adiabatic-like approach.     

Analytical model of the long-period forced longitude librations of Mercury

The shaking of Mercury’s orbit by the planets forces librations in longitude in addition to those at harmonics of the orbital period that have been used to detect Mercury’s molten core. We extend the analytical formulation of Peale et al. (Peale, S.J., Margot, J.L., Yseboodt, M. [2009]. Icarus 199, 1-8) in order to provide a convenient means of determining the amplitudes and phases of the forced librations without resorting to numerical calculations. We derive an explicit relation between the amplitude of each forced libration and the moment of inertia parameter (B-A)/C_m. Far from resonance with the free libration period, the libration amplitudes are directly proportional to (B-A)/C_m. Librations with periods close to the free libration period of ∼12 years may have measurable (∼arcsec) amplitudes. If the free libration period is sufficiently close to Jupiter’s orbital period of 11.86 years, the amplitude of the forced libration at Jupiter’s period could exceed the 35 arcsec amplitude of the 88-day forced libration. We also show that the planetary perturbations of the mean anomaly and the longitude of pericenter of Mercury’s orbit completely determine the libration amplitudes.While these signatures do not affect spin rate at a detectable level (as currently measured by Earth-based radar), they have a much larger impact on rotational phase (affecting imaging, altimetry, and gravity sensors). Therefore, it may be important to consider planetary perturbations when interpreting future spacecraft observations of the librations.     

Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn

The Cassini spacecraft collects high resolution images of the Saturnian satellites and reveals the surface of these new worlds. Tiscareno et?al. succeeded to determine the Epimetheus rotation from the Cassini Imaging Science Subsystem data, initiating studies on the rotation of Epimetheus and its companion Janus (Tiscareno et?al., Icarus 204:254?C261, 2009; Noyelles, Icarus 207:887?C902, 2010; Robutel et?al., Icarus 211:758?C769, 2011). Especially, Epimetheus is characterized by its horseshoe shape orbit and the presence of the swap has to be introduced explicitly into rotational models. During its journey in the Saturnian system, Cassini spacecraft accumulates the observational data of the other satellites and it will be possible to determine the rotational parameters of several of them. To prepare these future observations, we built rotational models of the coorbital (also called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L ₄ and L ₅ Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital of Dione. The goal of this study is to understand how the departure from the Keplerian motion induced by the perturbations of the coorbital body, influences the rotation of these satellites. To this aim, we introduce explicitly the perturbation in the rotational equations by using the formalism developed by érdi (Celest Mech 15:367?C383, 1977) to represent the coorbital motions, and so we describe the rotational motion of the coorbitals, Janus and Epimetheus included, in compact form.     

Cassini spectra and photometry 0.25-5.1 μm of the small inner satellites of Saturn

The nominal tour of the Cassini mission enabled the first spectra and solar phase curves of the small inner satellites of Saturn. We present spectra from the Visual Infrared Mapping Spectrometer (VIMS) and the Imaging Science Subsystem (ISS) that span the 0.25-5.1 μm spectral range. The composition of Atlas, Pandora, Janus, Epimetheus, Calypso, and Telesto is primarily water ice, with a small amount (∼5%) of contaminant, which most likely consists of hydrocarbons. The optical properties of the “shepherd” satellites and the coorbitals are tied to the A-ring, while those of the Tethys Lagrangians are tied to the E-ring of Saturn. The color of the satellites becomes progressively bluer with distance from Saturn, presumably from the increased influence of the E-ring; Telesto is as blue as Enceladus. Janus and Epimetheus have very similar spectra, although the latter appears to have a thicker coating of ring material. For at least four of the satellites, we find evidence for the spectral line at 0.68 μm that Vilas et al. [Vilas, F., Larsen, S.M., Stockstill, K.R., Gaffley, M.J., 1996. Icarus 124, 262-267] attributed to hydrated iron minerals on Iapetus and Hyperion. However, it is difficult to produce a spectral mixing model that includes this component. We find no evidence for CO₂ on any of the small satellites. There was a sufficient excursion in solar phase angle to create solar phase curves for Janus and Telesto. They bear a close similarity to the solar phase curves of the medium-sized inner icy satellites. Preliminary spectral modeling suggests that the contaminant on these bodies is not the same as the exogenously placed low-albedo material on Iapetus, but is rather a native material. The lack of CO₂ on the small inner satellites also suggests that their low-albedo material is distinct from that on Iapetus, Phoebe, and Hyperion.     

Librations of the Galilean satellites: The influence of global internal liquid layers

The four Galilean satellites are thought to harbor one or even two global internal liquid layers beneath their surface layer. The iron core of Io and Ganymede is most likely (partially) liquid and also the core of Europa may be liquid. Furthermore, there are strong indications for the existence of a subsurface ocean in Europa, Ganymede, and Callisto. Here, we investigate whether libration observations can be used to prove the existence of these liquid layers and to constrain the thickness of the overlying solid layers. For Io, the presence of a small liquid core increases the libration of the mantle by a few percent with respect to an entirely solid Io and mantle libration observations could be used to determine the mantle thickness with a precision of several tens of kilometers given that the libration amplitude can be measured with a precision of 1 m. For Europa, Ganymede, and Callisto, the presence of a water ocean close to the surface increases by at least an order of magnitude the ice shell libration amplitude with respect to an entirely solid satellite. The shell libration depends essentially on the shell thickness and to a minor extent on the density difference between the ocean and the ice shell. The possible presence of a liquid core inside Europa and Ganymede has no noticeable influence on their shell libration. For a precision of several meters on the libration measurements, in agreement with the expected accuracy with the NASA/ESA EJSM orbiter mission to Europa and Ganymede, an error on the shell thickness of a few tens kilometers is expected. Therefore, libration measurements can be used to detect liquid layers such as Io’s core or water subsurface oceans in Europa, Ganymede, and Callisto and to constrain the thickness of the overlying solid surface layers.     

Constraints on Europa’s rotational dynamics from modeling of tidally-driven fractures

Cycloids, arcuate features observed on Europa’s surface, have been interpreted as tensile cracks that form in response to diurnal tidal stress caused by Europa’s orbital eccentricity. Stress from non-synchronous rotation may also contribute to tidal stress, and its influence on cycloid shapes has been investigated as well. Obliquity, fast precession, and physical libration would contribute to tidal stress but have often been neglected because they were expected to be negligibly small. However, more sophisticated analyses that include the influence of Jupiter’s other large satellites and the state of Europa’s interior indicate that perhaps these rotational parameters are large enough to alter the tidal stress field and the formation of tidally-driven fractures. We test tidal models that include obliquity, fast precession, stress due to non-synchronous rotation, and physical libration by comparing how well each model reproduces observed cycloids. To do this, we have designed and implemented an automated parameter-searching algorithm that relies on a quantitative measure of fit quality, which we use to identify the best fits to observed cycloids. We then apply statistical techniques to determine the tidal model best supported by the data. By incorporating obliquity, fits to observed southern hemisphere cycloids improve, and we can reproduce equatorial and equator-crossing cycloids. Furthermore, we find that obliquity plus physical libration is the tidal model best supported by the data. With this model, the obliquities range from 0.32° to 1.35°. The libration amplitudes are 0.72–2.44°, and the libration phases are −6.04° to 17.72° with one outlier at 84.5°. The variability in obliquity is expected if Europa’s ice shell is mechanically decoupled from the interior, and the libration amplitudes are plausible in the presence of a subsurface ocean. Indeed, the presence of a decoupling ocean may result in feedbacks that cause all of these rotational parameters to become time-variable.     

Photometric observations of 107P/Wilson-Harrington

We present lightcurve observations and multiband photometry for 107P/Wilson-Harrington using five small- and medium-sized telescopes. The lightcurve has shown a periodicity of 0.2979 day (7.15 h) and 0.0993 day (2.38 h), which has a commensurability of 3:1. The physical properties of the lightcurve indicate two models: (1) 107P/Wilson-Harrington is a tumbling object with a sidereal rotation period of 0.2979 day and a precession period of 0.0993 day. The shape has a long axis mode (LAM) of L₁:L₂:L₃ = 1.0:1.0:1.6. The direction of the total rotational angular momentum is around λ = 310°, β = −10°, or λ = 132°, β = −17°. The nutation angle is approximately constant at 65°. (2) 107P/Wilson-Harrington is not a tumbler. The sidereal rotation period is 0.2979 day. The shape is nearly spherical but slightly hexagonal with a short axis mode (SAM) of L₁:L₂:L₃ = 1.5:1.5:1.0. The pole orientation is around λ = 330°, β = −27°. In addition, the model includes the possibility of binary hosting. For both models, the sense of rotation is retrograde. Furthermore, multiband photometry indicates that the taxonomy class of 107P/Wilson-Harrington is C-type. No clear rotational color variations are confirmed on the surface.     

Saturn’s icy satellites investigated by Cassini-VIMS: II. Results at the end of nominal mission

We report the detailed analysis of the spectrophotometric properties of Saturn’s icy satellites as derived by full-disk observations obtained by visual and infrared mapping spectrometer (VIMS) experiment aboard Cassini. In this paper, we have extended the coverage until the end of the Cassini’s nominal mission (June 1st 2008), while a previous paper (Filacchione, G., and 28 colleagues [2007]. Icarus 186, 259-290, hereby referred to as Paper I) reported the preliminary results of this study.During the four years of nominal mission, VIMS has observed the entire population of Saturn’s icy satellites allowing us to make a comparative analysis of the VIS-NIR spectral properties of the major satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Hyperion, Iapetus) and irregular moons (Atlas, Prometheus, Pandora, Janus, Epimetheus, Telesto, Calypso, Phoebe). The results we discuss here are derived from the entire dataset available at June 2008 which consists of 1417 full-disk observations acquired from a variety of distances and inclinations from the equatorial plane, with different phase angles and hemispheric coverage. The most important spectrophotometric indicators (as defined in Paper I: I/F continua at 0.55 μm, 1.822 μm and 3.547 μm, visible spectral slopes, water and carbon dioxide bands depths and positions) are calculated for each observation in order to investigate the disk-integrated composition of the satellites, the distribution of water ice respect to “contaminants” abundances and typical regolith grain properties. These quantities vary from the almost pure water ice surfaces of Enceladus and Calypso to the organic and carbon dioxide rich Hyperion, Iapetus and Phoebe. Janus visible colors are intermediate between these two classes having a slightly positive spectral slope. These results could help to decipher the origins and evolutionary history of the minor moons of the Saturn’s system. We introduce a polar representation of the spectrophotometric parameters as function of the solar phase angle (along radial distance) and of the effective longitude interval illuminated by the Sun and covered by VIMS during the observation (in azimuth) to better investigate the spatial distribution of the spectrophotometric quantities across the regular satellites hemispheres. Finally, we report the observed spectral positions of the 4.26 μm band of the carbon dioxide present in the surface material of three outermost moons Hyperion, Iapetus and Phoebe.     

Spin states and climates of eccentric exoplanets

The known extrasolar planets exhibit a wide range of orbital eccentricities e. This has a profound influence on their rotations and climates. Because of tides in their interiors, mostly solid exoplanets are expected eventually to despin to a state of spin-orbit resonance, where the orbital period is some integer or half-integer times the rotation period. The most important of these resonances is the synchronous state, where the planet's spin period exactly equals its orbital period (like Earth's Moon, and indeed most of the regular satellites in the Solar System). Such planets seem doomed to roast on one side and freeze on the other. However, synchronous planets rock back and forth by an angle of ∼2Arcsine with respect to the sub-stellar point. For e=0.055 (as for the Moon), this optical libration amounts to only ∼6°; but for a synchronous planet with e=0.50, for example, it would rise to ∼59°. This greatly expands the temperate “twilight zone” near the terminator and considerably improves the planet's prospects for habitability. For e?0.72389, the optical libration exceeds 90°; for such planets, the sector of permanent night vanishes, while the sunniest region splits in two. Furthermore, the synchronous state is not the only possible spin resonance. For example, Mercury (with e≈0.206) has an orbital period exactly 1.5 times its rotation period. A terrestrial exoplanet with e=0.40, say, is liable to have an orbital period of 2.0, 2.5, or 3.0 times its spin period. The corresponding insolation patterns are generally complicated, and all different from the synchronous state. Yet these non-synchronous resonances also protect certain longitudes from the worst extremes of temperature and solar radiation, and improve the planet's habitability, compared to non-resonant rotation. These results also have implications for the direct detectability of extrasolar planets, and the interpretation of their thermal emissions.     

Iapetus' geophysics: Rotation rate, shape, and equatorial ridge

Iapetus has preserved evidence that constrains the modeling of its geophysical history from the time of its accretion until now. The evidence is (a) its present 79.33-day rotation or spin rate, (b) its shape that corresponds to the equilibrium figure for a hydrostatic body rotating with a period of ∼16 h, and (c) its high, equatorial ridge, which is unique in the Solar System. This paper reports the results of an investigation into the coupling between Iapetus' thermal and orbital evolution for a wide range of conditions including the spatial distributions with time of composition, porosity, short-lived radioactive isotopes (SLRI), and temperature. The thermal model uses conductive heat transfer with temperature-dependent conductivity. Only models with a thick lithosphere and an interior viscosity in the range of about the water ice melting point can explain the observed shape. Short-lived radioactive isotopes provide the heat needed to decrease porosity in Iapetus' early history. This increases thermal conductivity and allows the development of the strong lithosphere that is required to preserve the 16-h rotational shape and the high vertical relief of the topography. Long-lived radioactive isotopes and SLRI raise internal temperatures high enough that significant tidal dissipation can start, and despin Iapetus to synchronous rotation. This occurred several hundred million years after Iapetus formed. The models also constrain the time when Iapetus formed because the successful models are critically dependent upon having just the right amount of heat added by SLRI decay in this early period. The amount of heat available from short-lived radioactivity is not a free parameter but is fixed by the time when Iapetus accreted, by the canonical concentration of ²⁶Al, and, to a lesser extent, by the concentration of ⁶⁰Fe. The needed amount of heat is available only if Iapetus accreted between 2.5 and 5.0 Myr after the formation of the calcium aluminum inclusions as found in meteorites. Models with these features allow us to explain Iapetus' present synchronous rotation, its fossil 16-h shape, and the context within which the equatorial ridge arose.     

Recent orbital evolution and the internal structures of Enceladus and Dione

We study the orbital behavior of Saturn’s satellites Enceladus and Dione during their passage through the 2:1 mean-motion resonances to constrain their interior structures, parameterized by the quantity k₂/Q (assumed constant). Enceladus’ evolution after escape from the second-order e-Enceladus e-Dione resonance requires that (k₂/Q)_Enceladus<8×10^-4, for that Q_Saturn>18,000. This result is in agreement with [Meyer, J., Wisdom, J., 2008b. Icarus 193, 213-223]. The present-day libration amplitude of Enceladus requires that (k₂/Q)_Enceladus>1.2×10^-4, assuming that Q_Saturn<10⁵. Dione’s present-day eccentricity indicates that (k₂/Q)_Dione?3×10^-4 for Q_Saturn>18,000. Assuming Maxwellian viscoelastic behavior, we find that for Enceladus a convective ice shell overlying an ocean is too dissipative to match the orbital constraints. We conclude that a conductive shell overlying an ocean is more likely, and discuss the implications of this result. Dione’s ice shell is also likely to be conductive, but our results are less constraining.     

Grooves on small saturnian satellites and other objects: Characteristics and significance

High-resolution images from the Cassini Imaging Science Subsystem (ISS) show parallel sets of grooves on Epimetheus and Pandora. Grooves have previously been observed on other satellites and asteroids, including Phobos, Gaspra, Ida, Eros, and minor occurrences on Phoebe. Sets of parallel grooves are so far observed only on satellites known or likely to be subject to significant tidal stresses, such as forced librations. Grooves on asteroids and on satellites not subject to significant forced librations occur in more globally disorganized patterns that may reflect impacts, varying internal structures, or even thermal stresses. The patterns and individual morphologies of grooves on the tidally-affected satellites suggest fracturing in weak materials due to tidal stresses and forced librations.     

The influence of Mercury’s inner core on its physical libration

As Mercury orbits the Sun, gravitational torques on its equatorial elliptical shape give rise to a planetary libration. The amplitude of Mercury’s libration, as determined from Earth-based radar speckle pattern observations, suggests that only the mantle participates in the motion. This indicates a decoupling between the core and the mantle, and therefore that the outermost part of the core must be fluid. If a solid inner core is present at the center of Mercury, the equatorial elliptical shape of the latter may become misaligned with that of Mercury’s mantle, leading to an internal gravitational torque between the two. If this torque is large, it may participate in the dynamics of Mercury’s libration. The goal of this work is to determine whether Mercury’s observed librations can be used to place constraints on the properties of its inner core. We present a comparison between predicted and observed librations for a range of interior models of Mercury, with various inner core sizes and fluid core densities. We show that a marginally better fit to observations can be achieved for interior models that have an inner core radius larger than 400 km. However, the improvement in fit is small, and it is not possible to draw robust conclusions on the size of Mercury’s inner core on the basis of existing libration data. Nevertheless, our study demonstrates that the influence of the inner core on the libration of Mercury could be detected with a decade worth of accurate observations.     

Orbital evolution of small binary asteroids

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (?uk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary’s orbit, depending on the satellite’s shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary’s orbital as well the secondary’s rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary’s eccentricity (through the coupling between the orbit and the secondary’s spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a “flipped” secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary’s librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary’s librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.     

Elastic ice shells of synchronous moons: Implications for cracks on Europa and non-synchronous rotation of Titan

A number of synchronous moons are thought to harbor water oceans beneath their outer ice shells. A subsurface ocean frictionally decouples the shell from the interior. This has led to proposals that a weak tidal or atmospheric torque might cause the shell to rotate differentially with respect to the synchronously rotating interior. Applications along these lines have been made to Europa and Titan. However, the shell is coupled to the ocean by an elastic torque. As a result of centrifugal and tidal forces, the ocean would assume an ellipsoidal shape with its long axis aligned toward the parent planet. Any displacement of the shell away from its equilibrium position would induce strains thereby increasing its elastic energy and giving rise to an elastic restoring torque. In the investigation reported on here, the elastic torque is compared with the tidal torque acting on Europa and the atmospheric torque acting on Titan.Regarding Europa, it is shown that the tidal torque is far too weak to produce stresses that could fracture the ice shell, thus refuting an idea that has been widely advocated. Instead, it is suggested that the cracks arise from time-dependent stresses due to non-hydrostatic gravity anomalies from tidally driven, episodic convection in the satellite’s interior.Two years of Cassini RADAR observations of Titan’s surface have been interpreted as implying an angular displacement of ∼0.24° relative to synchronous rotation. Compatibility of the amplitude and phase of the observed non-synchronous rotation with estimates of the atmospheric torque requires that Titan’s shell be decoupled from its interior. We find that the elastic torque balances the seasonal atmospheric torque at an angular displacement ?0.05°, effectively coupling the shell to the interior. Moreover, if Titan’s surface were spinning faster than synchronous, the tidal torque tending to restore synchronous rotation would almost certainly be larger than the atmospheric torque. There must either be a problem with the interpretation of the radar observations, or with our basic understanding of Titan’s atmosphere and/or interior.     

A primordial origin for the atmospheric methane of Saturn’s moon Titan

The origin of Titan’s atmospheric methane is a key issue for understanding the origin of the saturnian satellite system. It has been proposed that serpentinization reactions in Titan’s interior could lead to the formation of the observed methane. Meanwhile, alternative scenarios suggest that methane was incorporated in Titan’s planetesimals before its formation. Here, we point out that serpentinization reactions in Titan’s interior are not able to reproduce the deuterium over hydrogen (D/H) ratio observed at present in methane in its atmosphere, and would require a maximum D/H ratio in Titan’s water ice 30% lower than the value likely acquired by the satellite during its formation, based on Cassini observations at Enceladus. Alternatively, production of methane in Titan’s interior via radiolytic reactions with water can be envisaged but the associated production rates remain uncertain. On the other hand, a mechanism that easily explains the presence of large amounts of methane trapped in Titan in a way consistent with its measured atmospheric D/H ratio is its direct capture in the satellite’s planetesimals at the time of their formation in the solar nebula. In this case, the mass of methane trapped in Titan’s interior can be up to ∼1300 times the current mass of atmospheric methane.     

Long-period forcing of Mercury's libration in longitude

Planetary perturbations of Mercury's orbit lead to forced librations in longitude in addition to the 88-day forced libration induced by Mercury's orbital motion. The forced librations are a combination of many periods, but 5.93 and 5.66 years dominate. These two periods result from the perturbations by Jupiter and Venus respectively, and they lead to a 125-year modulation of the libration amplitude corresponding to the beat frequency. Other periods are also identified with Jupiter and Venus perturbations as well as with those of the Earth, and these and other periods in the perturbations cause several arc second fluctuations in the libration extremes. The maxima of these extremes are about 30″ above and the minima about 7″ above the superposed ∼^60″, 88-day libration during the 125-year modulation. Knowledge of the nature of the long-period forced librations is important for the interpretation of the details of Mercury's rotation state to be obtained from radar and spacecraft observations. We show that the measurement of the 88-day libration amplitude for the purposes of determining Mercury's core properties is not compromised by the additional librations, because of the latter's small amplitude and long period. If the free libration in longitude has an amplitude that is large compared with that of the forced libration, its ∼10-year period will dominate the libration spectrum with the 88-day forced libration and the long-period librations from the orbital perturbations superposed. If the free libration has an amplitude that is comparable to those of the long-period forced libration, it will be revealed by erratic amplitude, period and phase on the likely time span of a series of observations. However, a significant free libration component is not expected because of relatively rapid damping.     

Tectonics on Iapetus: Despinning, respinning, or something completely different?

Saturn’s moon Iapetus is unique in that it has apparently despun while retaining a substantial equatorial bulge. Stresses arising from such a non-hydrostatic shape should in principle cause surface deformation (tectonics). As part of a search for such a tectonic signature, lineaments (linear surface features) on Iapetus were mapped on both its bright and dark hemispheres. Lineament orientations were then compared to model stress patterns predicted for spin-down from a rotation period of 16.5 h (or less) to its present synchronous period, and for a range of lithospheric thicknesses. Many lineaments are straight segments of crater rimwalls, which may be faults or joints reactivated during complex crater collapse. Most striking are several large troughs on the bright, trailing hemisphere. These troughs appear to be extensional and are distinctive on that hemisphere, because the interior floors and walls of the troughs contain dark material. Globally, no specific evidence of strike slip or thrust offsets are seen, but this could be due to the age and degraded nature of any such features. We find that observed lineament orientations do not correlate with predicted patterns due to despinning on either hemisphere (the equatorial ridge was specifically excluded from this analysis, and is considered separately). Modest evidence for preferred orientations ±40° from north could be construed as consistent with respinning, which is not necessarily far-fetched. Assuming the rigidity of unfractured ice, predicted maximum lithospheric differential stresses from despinning range from ∼1 MPa to ∼160 MPa for the elastic spheroid and thin lithosphere limits, respectively (although it is only for thicker elastic lithospheres that we expect a nonhydrostatic state to be maintained over geologic time against lithospheric failure). The tectonic signature of despinning may have been obscured over time because the surface of Iapetus is very ancient, Iapetus’ thick lithosphere may have inhibited the full tectonic expression of despinning, or both. Several prominent lineaments strike E–W, and are thus parallel to the equatorial ridge (though not physically close to it), but a tectonic or volcanic origin for the ridge is highly problematic.     

Orbits and masses of Saturn's coorbital and F-ring shepherding satellites

We have obtained numerically integrated orbits for Saturn's coorbital satellites, Janus and Epimetheus, together with Saturn's F-ring shepherding satellites, Prometheus and Pandora. The orbits are fit to astrometric observations acquired with the Hubble Space Telescope and from Earth-based observatories and to imaging data acquired from the Voyager spacecraft. The observations cover the 38 year period from the 1966 Saturn ring plane crossing to the spring of 2004. In the process of determining the orbits we have found masses for all four satellites. The densities derived from the masses for Janus, Epimetheus, Prometheus, and Pandora in units of g cm⁻³ are , , , and , respectively.