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.     

Ammonium sulfate on Titan: Possible origin and role in cryovolcanism

We model the chemical evolution of Titan, wherein primordial NH₃ reacts with sulfate-rich brines leached from the silicate core during its hydration. The resulting differentiated body consists of a serpentinite core overlain by a high-pressure ice VI mantle, a liquid layer of aqueous ammonium sulfate, and a heterogeneous shell of methane clathrate, low-pressure ice Ih and solid ammonium sulfate. Cooling of the subsurface ocean results in underplating of the outer shell with ice Ih; this gravitationally unstable system can produce compositional plumes as ice Ih ascends buoyantly. Ice plumes may aid in advection of melt pockets through the shell and, in combination with surface topography, provide the necessary hydraulic pressure gradients to drive such melts to the surface. Moreover, contact between the magma and wall rock (methane clathrate) will allow some methane to dissolve in the magma, as well as eroding fragments of wall rock that can be transported as xenoliths. Upon rising to the clathrate decomposition depth (∼2 MPa, or 1700 m), the entrained xenoliths will break down to ice + methane gas, powering highly explosive eruptions with lava fountains up to several kilometers high. Hence we predict that Titan is being resurfaced by cryoclastic ash consisting of ice and ammonium sulfate (or its tetrahydrate), providing an abundance of sedimentary grains, a potential source of bedload for fluvial transport and erosion, and of sand-sized material for aeolian transport and dune-building. The infrared reflectance spectrum of ammonium sulfate makes it a plausible candidate for the 5 μm-bright material on Titan's surface.     

Coupling of thermal evolution and despinning of early Iapetus

The Cassini mission revealed two spectacular characteristics of Iapetus: (1) a geologically old and high equatorial ridge, which is unique in the Solar System and (2) a large flattening of 35 km consistent with the equilibrium figure for a hydrostatic body rotating with a period of 16 h, whereas the current spin period is 79.33 days. This study describes three-dimensional simulations of solid-state convection within an undifferentiated Iapetus. It investigates the implications for the evolution of the interior thermal structure and its spin rate and global shape using radially layered viscoelastic models. The role of the concentration in the short-lived radiogenic element [²⁶Al], just after accretion is completed, is specifically addressed. The first result is to show that whatever the [²⁶Al] value, convection occurs. As suggested by Castillo-Rogez et al. [Castillo-Rogez, J., Matson, D., Sotin, C., Johnson, T., Lunine, J., Thomas, P. [2007] Icarus, 190, 179-202], convection reduces the warming of the interior compared to the conductive evolution and therefore limits the conditions for despinning. In our calculations, two conceptual linear viscoelastic models are used. When considering a Maxwell rheology, the interior temperature (viscosity) never reaches a value high (low) enough to induce despinning. In order to promote dissipation at low temperature, a Burgers rheology, which includes an additional dissipation peak, is introduced. For favorable parameter values, this latter rheology leads to despinning. However, only models associated with large amounts of short-lived radiogenic elements lead to the observed flattening. This suggests that the accretion process needs to be completed shortly after the formation of CAIs (Calcium-Aluminum-rich Inclusions) (?4 Myr). For [²⁶Al] varying between 72 and 46 ppb, the observed flattening is obtained only for a limited range of initial spin period, between 9.5 and 10.2 h. For [²⁶Al] ranging between 30 and 15 ppb, initial spin rates smaller than 8.5 h are required. For smaller values of [²⁶Al], the body is too cold and viscous to acquire a significant flattening even if a rotation period close to the body disruption limit is considered. Even with a thin lithosphere during the early stage, our simulations show that Iapetus never reaches the equilibrium figure for a hydrostatic body due to the non-zero rigidity of the lithosphere. The 35 km value of the flattening is the result of the partial relaxation of an ancient larger flattening ranging between 45 and 80 km, depending on the evolution of the lithosphere thickness mainly controlled by the radiogenic content. A thin lithosphere is consistent with an early building of the equatorial ridge. The lithosphere thickening due to interior cooling can explain the preservation of the ridge throughout the remaining evolution of Iapetus.     

The long-term stability of a possible aqueous ammonium sulfate ocean inside Titan

We model the thermal evolution of a subsurface ocean of aqueous ammonium sulfate inside Titan using a parameterized convection scheme. The cooling and crystallization of such an ocean depends on its heat flux balance, and is governed by the pressure-dependent melting temperatures at the top and bottom of the ocean. Using recent observations and previous experimental data, we present a nominal model which predicts the thickness of the ocean throughout the evolution of Titan; after 4.5 Ga we expect an aqueous ammonium sulfate ocean 56 km thick, overlain by a thick (176 km) heterogeneous crust of methane clathrate, ice I and ammonium sulfate. Underplating of the crust by ice I will give rise to compositional diapirs that are capable of rising through the crust and providing a mechanism for cryovolcanism at the surface. We have conducted a parameter space survey to account for possible variations in the nominal model, and find that for a wide range of plausible conditions, an ocean of aqueous ammonium sulfate can survive to the present day, which is consistent with the recent observations of Titan's spin state from Cassini radar data [Lorenz, R.D., Stiles, B.W., Kirk, R.L., Allison, M.D., del Marmo, P.P., Iess, L., Lunine, J.I., Ostro, S.J., Hensley, S., 2008. Science 319, 1649-1651].     

Cassini CIRS update on stratospheric ices at Titan's winter pole

A strong, broad spectral emission feature at 85° N latitude centered at 221 cm⁻¹ remains unidentified after candidate ices of H₂O and pure crystalline CH₃CH₂CN are unambiguously ruled out. A much shallower weak emission feature starts at 160 cm⁻¹ and blends into the strong feature at ∼190 cm⁻¹. This feature is consistent with one formed by an HCN ice cloud composed of ?5 μm radius particles that resides in the lower stratosphere somewhere below an altitude of 160 km. Titan's stratospheric aerosol appears to have a spectral emission feature at about 148 cm⁻¹. The aerosol abundance at 85° N is about a factor 2.2 greater than at 55° S.     

Thermal convection in ice-I shells of Titan and Enceladus

Cassini-Huygens observations have shown that Titan and Enceladus are geologically active icy satellites. Mitri and Showman [Mitri, G., Showman, A.P., 2005. Icarus 177, 447-460] and McKinnon [McKinnon, W.B., 2006. Icarus 183, 435-450] investigated the dynamics of an ice shell overlying a pure liquid-water ocean and showed that transitions from a conductive state to a convective state have major implications for the surface tectonics. We extend this analysis to the case of ice shells overlying ammonia-water oceans. We explore the thermal state of Titan and Enceladus ice-I shells, and also we investigate the consequences of the ice-I shell conductive-convective switch for the geology. We show that thermal convection can occur, under a range of conditions, in the ice-I shells of Titan and Enceladus. Because the Rayleigh number Ra scales with δ³/ηb, where δ is the thickness of the ice shell and ηb is the viscosity at the base of the ice-I shell, and because ammonia in the liquid layer (if any) strongly depresses the melting temperature of the water ice, Ra equals its critical value for two ice-I shell thicknesses: for relatively thin ice shell with warm, low-viscosity base (Onset I) and for thick ice shell with cold, high-viscosity base (Onset II). At Onset I, for a range of heat fluxes, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. Switches between these states can cause large, rapid changes in the ice-shell thickness. For Enceladus, we demonstrate that an Onset I transition can produce tectonic stress of ∼500 bars and fractures of several tens of km depth. At Onset II, in contrast, we demonstrate that zero equilibrium states exist for a range of heat fluxes. For a mean heat flux within this range, the satellite experiences oscillations in surface heat flux and satellite volume with periods of ∼50-800 Myr even when the interior heat production is constant or monotonically declining in time; these oscillations in the thermal state of the ice-I shell would cause repeated episodes of extensional and compressional tectonism.     

Laboratory studies of methane and ethane adsorption and nucleation onto organic particles: Application to Titan's clouds

Titan, Saturn's largest moon, has a thick nitrogen/methane atmosphere. The temperature and pressure conditions in Titan's atmosphere are such that the methane vapor should condense near the tropopause to form clouds. Several ground-based measurements have observed sparse cloud-like features in Titan's atmosphere, while the Cassini mission to Saturn has provided large scale images of the clouds. However, Titan's cloud formation conditions remain poorly constrained. Heterogeneous nucleation (from the vapor phase onto a solid or liquid aerosol surface) greatly enhances cloud formation relative to homogeneous nucleation. In order to elucidate the cloud formation mechanism near the tropopause, we have performed laboratory measurements of the adsorption of methane and ethane onto solid organic particles (tholins) representative of Titan's photochemical haze. We find that monolayers of methane adsorb onto tholin particles at saturation ratios less than unity. We also find that solid methane nucleates onto the adsorbed methane at a saturation ratio of S=1.07±0.008. This implies that Titan's methane clouds should form easily. This is consistent with recent measurements of the column of methane ruling out excessive methane supersaturation. In addition, we find ethane adsorbs onto tholin particles in a metastable phase prior to nucleation. However, ethane nucleation onto the adsorbed ethane occurs at a relatively high saturation ratio of S=1.36±0.08. These findings are consistent with the recent report of polar ethane clouds in Titan's lower stratosphere.     

Forced obliquity and moments of inertia of Titan

The obliquity of Titan is small, but certainly non-zero, and may be used to place constraints on Titan's internal structure. The measured gravity coefficients of Titan imply that it is non-hydrostatic and thus the normal Darwin-Radau approach to determining internal structure cannot be applied. However, if the obliquity is assumed to be tidally damped (that is, in a Cassini state) then combining the obliquity with the measured gravity coefficients allows Titan's moment of inertia to be determined without invoking hydrostatic equilibrium. For polar moment values in the range (0.3<C/MR²<0.4), tidally-damped obliquity values of (0.115°<|ε|<0.177°) result. If the inferred moment value exceeds 0.4, this strongly suggests the presence of a near-surface ice shell decoupled from the interior, probably by a subsurface ocean.     

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.     

On the maintenance of thermal wind balance and equatorial superrotation in Titan's stratosphere

Titan's atmospheric winds, like those on Venus, exhibit superrotation at high altitudes. Titan general circulation models have yielded conflicting results on whether prograde winds in excess of 100 m s⁻¹ at the 1 mbar level are possible based on known physical processes that drive wind systems. A comprehensive two-dimensional (2D) model for Titan's stratosphere was constructed to systematically explore the physical mechanisms that produce and maintain stratospheric wind systems. To ensure conservation of angular momentum in the limit of no net exchange of atmospheric angular momentum with the solid satellite and no external sources and sinks, the zonal momentum equation was solved in flux form for total angular momentum. The relationships among thermal wind balance, meridional circulation, and zonal wind were examined with numerical experiments over a range of values for fundamental input parameters, including planetary rotation rate, radius, internal friction due to wave stresses, and net radiative drive. The magnitude of mid-latitude jets is most sensitive to a single parameter, the planetary rotation rate and results from the conversion of planetary angular momentum to relative angular momentum by the meridional circulation, whereas the strength of meridional circulation is mainly determined by the magnitude of the radiative drive. For Titan's slowly rotating atmosphere, the meridional temperature gradient is vanishingly small, even when the radiative drive is enhanced beyond reasonable magnitudes, and can be inferred from zonal winds in gradient/thermal wind balance. In our 2D model large equatorial superrotation in Titan's stratosphere can be only produced through internal drag forcing by eddy momentum fluxes, which redistribute angular momentum within the atmosphere, while still conserving the total angular momentum of the atmosphere with time. We cannot identify any waves, such as gravitational or thermal tides, that are sufficiently capable of generating the required eddy forcing of >50 m s⁻¹ Titan-day⁻¹ to maintain peak prograde winds in excess of 100 m s⁻¹ at the 1 mbar level.     

Dissipation of Titan's south polar clouds

Nearly all adaptive optics images of Titan taken between December 2001 and November 2004 showed tropospheric clouds located within 30° of the south pole. We report here on a dissipation of Titan's south polar clouds observed in twenty-nine Keck and Gemini images taken between December 2004 and April 2005. The near complete lack of south polar cloud activity during this time, and subsequent resurgence months later at generally higher latitudes, may be the beginning of seasonal change in Titan's weather. The ∼5 month decrease in cloud activity may also have been caused by methane rainout from a large cloud event in October 2004. Understanding the seasonal evolution of Titan's clouds, and of any precipitation associated with them, is essential for interpreting the geological observations of fluid flow features observed over a wide range of Titan latitudes with the Cassini/Huygens spacecraft.     

Resurfacing of Titan by ammonia-water cryomagma

The Cassini Titan Radar Mapper observed on Titan several large features interpreted as cryovolcanic during the October 26, 2004 pass at high northern latitudes [Lopes, R.M.C., and 43 colleagues, 2007. Icarus 186, 395-412]. To date, models of ammonia-water resurfacing have not been tied to specific events or evolutionary stages of Titan. We propose a model of cryovolcanism that involves cracking at the base of the ice shell and formation of ammonia-water pockets in the ice. As these ammonia-water pockets undergo partial freezing in the cold ice shell, the ammonia concentration in the pockets increases, decreasing the negative buoyancy of the ammonia-water mixture. If the ice shell is contaminated by silicates delivered in impacts, the liquid-solid density difference would be even less. While the liquid cannot easily become buoyant relative to the surrounding ice, these concentrated ammonia-water pockets are sufficiently close to the neutral buoyancy point that large-scale tectonic stress patterns (tides, non-synchronous rotation, satellite volume changes, solid state convection, or subsurface pressure gradients associated with topography) would enable the ammonia to erupt effusively onto the surface. Rather than suggesting steady-state volcanism over the history of the Solar System, we favor a scenario where the cryovolcanic features could have been associated with episodic (potentially late) geological activity.     

The effect of YORP on Itokawa

The effect of solar radiation on the near-term rotation rate of Asteroid Itokawa via the YORP effect is predicted using the detailed shape model, rotation pole, mass estimate, and optical properties derived from the Hayabusa mission to Itokawa. Based on these estimates Itokawa is decelerating at a rate which will halve its rotation rate in only 50-90 thousand years, a large deceleration that should be detectable in a future appartion. The implications of such a large deceleration for Itokawa's past history are discussed and related to possible seismic shaking.     

The effect of a dense atmosphere on the tidally induced potential of Titan

The effect of the dense atmosphere of Titan on the tidal variations of the external gravitational potential of degree two is quantified. The atmospheric tides perturb the external gravitational potential of Titan in two ways. First, the atmosphere itself contributes directly to the external gravitational potential with a period of 15.945 days. Second, the variable loading of the atmosphere induces mass redistribution within Titan, which also changes the external gravitational potential. It is shown that the relative atmospheric contributions to the tides are most likely less than 2% and vanish almost completely for the most plausible models with a subsurface ocean. This suggest that atmospheric tidal perturbations will contribute only negligibly to Cassini measurements of Titan's gravitational field so that the tidal Love numbers derived from these observations can be directly interpreted in terms of the satellite's interior.     

Evolution of Mercury's obliquity

Mercury has a near-zero obliquity, i.e. its spin axis is nearly perpendicular to its orbital plane. The value of the obliquity must be known precisely in order to constrain the size of the planet's core within the framework suggested by Peale [Peale, S.J., 1976. Nature 262, 765-766]. Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] have suggested that Mercury's obliquity varies on thousand-year timescales due to planetary perturbations, potentially ruining the feasibility of Peale's experiment. We use a Hamiltonian approach (free of energy dissipation) to study the spin-orbit evolution of Mercury subject to secular planetary perturbations. We can reproduce an obliquity evolution similar to that of Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] if we integrate the system with a set of initial conditions that differs from the Cassini state. However the thousand-year oscillations in the obliquity disappear if we use initial conditions corresponding to the equilibrium position of the Cassini state. This result indicates that planetary perturbations do not force short-period, large amplitude oscillations in the obliquity of Mercury. In the absence of excitation processes on short timescales, Mercury's obliquity will remain quasi-constant, suggesting that one of the important conditions for the success of Peale's experiment is realized. We show that interpretation of data obtained in support of this experiment will require a precise knowledge of the spin-orbit configuration, and we provide estimates for two of the critical parameters, the instantaneous Laplace plane orientation and the orbital precession rate from numerical fits to ephemeris data. Finally we provide geometrical relationships and a scheme for identifying the correct initial conditions required in numerical integrations involving a Cassini state configuration subject to planetary perturbations.     

Stability of methane clathrate hydrates under pressure: Influence on outgassing processes of methane on Titan

We have conducted high-pressure experiments in the H₂O-CH₄ and H₂O-CH₄-NH₃ systems in order to investigate the stability of methane clathrate hydrates, with an optical sapphire-anvil cell coupled to a Raman spectrometer for sample characterization. The results obtained confirm that three factors determine the stability of methane clathrate hydrates: (1) the bulk methane content of the samples; (2) the presence of additional gas compounds such as nitrogen; (3) the concentration of ammonia in the aqueous solution. We show that ammonia has a strong effect on the stability of methane clathrates. For example, a 10 wt.% NH₃ solution decreases the dissociation temperature of methane clathrates by 14-25 K at pressures above 5 MPa. Then, we apply these new results to Titan’s conditions. Dissociation of methane clathrate hydrates and subsequent outgassing can only occur in Titan’s icy crust, in presence of locally large amounts of ammonia and in a warm context. We propose a model of cryomagma chamber within the crust that provides the required conditions for methane outgassing: emplacement of an ice plume triggers the melting (if solid) or heating (if liquid) of large ammonia-water pockets trapped at shallow depth, and the generated cryomagmas dissociate surrounding methane clathrate hydrates. We show that this model may allow for the outgassing of significant amounts of methane, which would be sufficient to maintain the presence of methane in Titan’s atmosphere for several tens of thousands of years after a large cryovolcanic event.     

Precession of the lunar core

Goldreich (Goldreich, P. [1967]. J. Geophys. Res. 72, 3135) showed that a lunar core of low viscosity would not precess with the mantle. We show that this is also the case for much of lunar history. But when the Moon was close to the Earth, the Moon’s core was forced to follow closely the precessing mantle, in that the rotation axis of the core remained nearly aligned with the symmetry axis of the mantle. The transition from locked to unlocked core precession occurred between 26.0 and 29.0 Earth radii, thus it is likely that the lunar core did not follow the mantle during the Cassini transition. Dwyer and Stevenson (Dwyer, C.A., Stevenson, D.J. [2005]. An Early Nutation-Driven Lunar Dynamo. AGU Fall Meeting Abstracts GP42A-06) suggested that the lunar dynamo needs mechanical stirring to power it. The stirring is caused by the lack of locked precession of the lunar core. So, we do not expect a lunar dynamo powered by mechanical stirring when the Moon was closer to the Earth than 26.0-29.0 Earth radii. A lunar dynamo powered by mechanical stirring might have been strongest near the Cassini transition.     

Observation of a tilt of Titan's middle-atmospheric superrotation

Maps of isotherms on surfaces of constant pressure in Titan's middle atmosphere encircle the poles but show an offset, implying that the mean zonal flow has an axis of symmetry that is tilted relative to the spin axis of the solid body. The effect is seen in both hemispheres around a consistent axis. Periodogram analysis of the temperature field shows that wavenumber one, the signal corresponding to the spin tilt, is the strongest wave component. We conjecture that the tilt of the atmospheric spin is due to a feedback between the flow and the solar heating. The spin adjusts itself to align the spin equator with the direction toward the Sun, and thereby maximizes the efficiency with which the meridional circulation pumps angular momentum upward to generate superrotation.     

Global and temporal variations in hydrocarbons and nitriles in Titan's stratosphere for northern winter observed by Cassini/CIRS

Mid-infrared spectra measured by Cassini's Composite InfraRed Spectrometer (CIRS) between July 2004 and January 2007 (Ls=293°-328°) have been used to determine stratospheric temperature and abundances of C₂H₂, C₃H₄, C₄H₂, HCN, and HC₃N. Over 65,000 nadir spectra with spectral resolutions of 0.5 and 2.5 cm⁻¹ were used to probe spatial and temporal composition variations in Titan's stratosphere. Cassini's 180° orbital transfer in mid-2006 allowed low emission angle observations of the north polar region for the first time in the mission and allowed us to probe the full latitude range. We present the first measurements of composition variations within the polar vortex, which display increasing abundances right up to 90° N. The lack of a homogeneous abundance-latitude variation within the vortex indicates limited horizontal mixing and suggests that subsidence is greatest at the vortex core. Contrary to numerical model predictions and tropospheric cloud observations, we do not see any evidence for a secondary circulation cell near the south pole, which suggests a single Hadley-type circulation in the stratosphere at this epoch. This difference can be reconciled if the secondary cell is restricted to altitudes below 100 km, where there is no sensitivity in our data. Temporal variations in composition were observed in the south, with volatile species becoming less abundant as the season progressed. The observed variations are compared to numerical model predictions and observations from Voyager.     

The librations, shape, and icy shell of Europa

Europa, the smallest of the Galilean satellites, has a young icy surface and most likely contains an internal ocean. The primary objective of possible future missions to Europa is the unambiguous detection and characterization of a subsurface ocean. The thickness of the overlying icy shell provides important information on the thermal evolution of the satellite and on the interaction between the ocean and the surface, the latter being fundamental for astrobiology. However, the thickness is not well known, and estimates range from several hundred of meters to some ten of kilometers. Here, we investigate the use of libration (rotation variation) observations to study the interior structure of Europa and in particular its icy shell. A dynamical libration model is developed, which includes gravitational coupling between the icy shell and the heavy solid interior. The amplitude of the main libration signal at 3.55 days (the orbital period) is shown to depend on Europa's shape and structure. Models of the interior structure of Europa are constructed and the equatorial flattening of the internal layers, which are key parameters for the libration, are calculated by assuming that Europa is in hydrostatic equilibrium. Europa's flattened shape is assumed to be due to rotation and permanent tides, and we extend the classical Radau equation for rotationally flattened bodies to include also tidal deformation. We show that the presence of an ocean increases the amplitude of libration by about 10%, depending mainly on the thickness of the icy shell. Therefore, libration observations offer possibility of detection of a subsurface ocean in Europa and estimation of the thickness of its overlying icy shell.