Libration Amplitude Research Articles

Dynamical stability analysis of the HD 202206 system and constraints to the planetary orbits

Long-term precise Doppler measurements with the CORALIE spectrograph revealed the presence of two massive companions to the solar-type star HD202206. Although the three-body fit of the system is unstable, it was shown that a 5:1 mean motion resonance exists close to the best fit, where the system is stable. We present here an extensive dynamical study of the HD202206 system aiming at constraining the inclinations of the two known companions, from which we derive possible ranges of value for the companion masses. We study the long term stability of the system in a small neighborhood of the best fit using Laskar's frequency map analysis. We also introduce a numerical method based on frequency analysis to determine the center of libration mode inside a mean motion resonance. We find that acceptable coplanar configurations are limited to inclinations to the line of sight between 30 and 90 degrees. This limits the masses of both companions to roughly twice the minimum. Non coplanar configurations are possible for a wide range of mutual inclinations from 0 to 90 degrees, although $\Delta\Omega = 0 [\pi]$ configurations seem to be favored. We also confirm the 5:1 mean motion resonance to be most likely. In the coplanar edge-on case, we provide a very good stable solution in the resonance, whose $\chi^2$ does not differ significantly from the best fit. Using our method to determine the center of libration, we further refine this solution to obtain an orbit with a very low amplitude of libration, as we expect dissipative effects to have dampened the libration.

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.

Axisymmetric simulations of libration-driven fluid dynamics in a spherical shell geometry

We report on axisymmetric numerical simulations of rapidly rotating spherical shells in which the axial rotation rate of the outer shell is modulated in time. This allows us to model planetary bodies undergoing forced longitudinal libration. In this study we systematically vary the Ekman number, 10−7≤E≲10−4, which characterizes the ratio of viscous to Coriolis forces in the fluid, and the libration amplitude, Δϕ. For libration amplitudes above a certain threshold, Taylor–Görtler vortices form near the outer librating boundary, in agreement with the previous laboratory experiments of Noir et al. [Phys. Earth Planet. Inter. 173, 141 (2009)]. At the lowest Ekman numbers investigated, we find that the instabilities remain spatially localized at onset in the equatorial region. In addition, nonzero time-averaged azimuthal (zonal) velocities are observed for all parameters studied. The zonal flow is characterized by predominantly retrograde flow in the interior, with a stronger prograde jet in the outer equatorial region. The magnitude of the zonal flow scales as the square of the librational forcing, ϵ2, where ϵ=Δϕf and f is the dimensionless libration frequency defined as the ratio between the libration frequency and the mean angular rotation rate. In addition, the zonal flow is primarily independent of the Ekman number, implying that the zonal flow does not depend on the viscosity of the fluid. The simulations show that the zonal flow is driven by nonlinearities in the Ekman boundary layer; it is not driven by Taylor–Görtler vortices or by inertial waves in the fluid interior. Application of our results suggests that many librating bodies in the solar system are above the onset for centrifugal instabilities, with values up to ∼30 times supercritical. However, the spatial localization of the instabilities at onset in our simulations suggests that their effects are limited on the global dynamics of librating bodies. We find that the zonal flows driven by libration in axisymmetric spherical shells are unlikely to produce significant planetary magnetic fields, but will likely generate nonzero mean torques on the bounding surfaces.

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.

Experimental study of libration-driven zonal flows in a straight cylinder

Forced longitudinal librations are oscillatory perturbations of the rotation rate of a planet resulting from a gravitational coupling with orbital partners. In the present study we report the first experimental evidence that a librating cylindrical container can viscously drive mean azimuthal flows in the liquid interior, hereafter referred to as zonal flows. Using a novel laser Doppler velocimetry system, the current work extends upon the study of libration-driven flows by Noir et al. (2009). We investigate the different mechanisms underlying the zonal flow generation. It is found that zonal flows in the interior result primarily from non-linearities in the Ekman boundary layer. Furthermore, the zonal flow scales as the square of the libration amplitude and is independent of the Ekman number. This scaling implies that forced longitudinal libration in an axisymmetric container (purely viscous coupling) will drive unobservably small zonal flows at planetary conditions. Thus, purely viscous librational coupling will not generate significant energy dissipation in a planetary fluid layer. It follows that any observed phase lag between the gravitational forcing and the orbital response of a planet requires non-viscous coupling mechanisms to account for the energy dissipation.

Molecular Level Characterization of the Inorganic−Bioorganic Interface by Solid State NMR: Alanine on a Silica Surface, a Case Study

The molecular interface between bioorganics and inorganics plays a key role in diverse scientific and technological research areas including nanoelectronics, biomimetics, biomineralization, and medical applications such as drug delivery systems and implant coatings. However, the physical/chemical basis of recognition of inorganic surfaces by biomolecules remains unclear. The molecular level elucidation of specific interfacial interactions and the structural and dynamical state of the surface bound molecules is of prime scientific importance. In this study, we demonstrate the ability of solid state NMR methods to accomplish these goals. L-[1-(13)C,(15)N]Alanine loaded onto SBA-15 mesoporous silica with a high surface area served as a model system. The interacting alanine moiety was identified as the -NH(3)(+) functional group by (15)N{(1)H}SLF NMR. (29)Si{(15)N} and (15)N{(29)Si}REDOR NMR revealed intermolecular interactions between the alanine -NH(3)(+) and three to four surface Si species, predominantly Q(3), with similar internuclear N...Si distances of 4.0-4.2 A. Distinct dynamic states of the adsorbed biomolecules were identified by (15)N{(13)C}REDOR NMR, indicating both bound and free alanine populations, depending on hydration level and temperature. In the bound populations, the -NH(3)(+) group is surface anchored while the free carboxylate end undergoes librations, implying the carboxylate has small or no contributions to surface binding. When surface water clusters grow bigger with increased hydration, the libration amplitude of the carboxyl end amplifies, until onset of dissolution occurs. Our measurements provide the first direct, comprehensive, molecular-level identification of the bioorganic-inorganic interface, showing binding functional groups, geometric constraints, stoichiometry, and dynamics, both for the adsorbed amino acid and the silica surface.

2001 QR322: a dynamically unstable Neptune Trojan?

Since early work on the stability of the first Neptunian Trojan, 2001 QR322, suggested that it was a dynamically stable, primordial body, it has been assumed this applies to both that object, and its more recently discovered brethren. However, it seems that things are no longer so clear cut. In this work, we present the results of detailed dynamical simulations of the orbital behaviour of 2001 QR322. Using an ephemeris for the object that has significantly improved since earlier works, we follow the evolution of 19683 test particles, placed on orbits within the observational error ellipse of 2001 QR322's orbit, for a period of 1 Gyr. We find that majority of these "clones" of 2001 QR322 are dynamically unstable, exhibiting a near-exponential decay from both the Neptunian Trojan cloud (decay halflife ~550 Myr) and the Solar system (decay halflife ~590 Myr). The stability of the object within Neptune's Trojan cloud is found to be strongly dependent on the initial semi-major axis used, with those objects located at semimajor axis equal or greater than 30.30 AU being significantly less stable than those interior to this value, as a result of their having initial libration amplitudes very close to a critical threshold dividing regular and irregular motion, located at ~70-75 deg (full extent of angular motion). This result suggests that, if 2001 QR322 is a primordial Neptunian Trojan, it must be a representative of a population that was once significantly larger than that we see today, and adds weight to the idea that the Neptune Trojans may represent a significant source of objects moving on unstable orbits between the giant planets (the Centaurs).

The HARPS search for southern extra-solar planets

Precise radial-velocity measurements for data acquired with the HARPS spectrograph infer that three planets orbit the M4 dwarf star GJ876. In particular, we confirm the existence of planet "d", which orbits every 1.93785 days. We find that its orbit may have significant eccentricity (e=0.14), and deduce a more accurate estimate of its minimum mass of 6.3 Earth masses. Dynamical modeling of the HARPS measurements combined with literature velocities from the Keck Observatory strongly constrain the orbital inclinations of the "b" and "c" planets. We find that i_b = 48.9 degrees and i_c = 48.1 degrees, which infers the true planet masses of M_b = 2.64 Jupiter masses and M_c = 0.83 Jupiter masses, respectively. Radial velocities alone, in this favorable case, can therefore fully determine the orbital architecture of a multi-planet system, without the input from astrometry or transits. The orbits of the two giant planets are nearly coplanar, and their 2:1 mean motion resonance ensures stability over at least 5 Gyr. The libration amplitude is smaller than 2 degrees, suggesting that it was damped by some dissipative process during planet formation. The system has space for a stable fourth planet in a 4:1 mean motion resonance with planet "b", with a period around 15 days. The radial velocity measurements constrain the mass of this possible additional planet to be at most that of the Earth.

Librational response of Enceladus

Physical librations could significantly contribute to Enceladus' geophysics through their influence on tidal stress. Therefore it is important to determine their behavior and the present paper is devoted to estimating Enceladus' libration in longitude. In a rotational model of Enceladus with no global ocean, we introduce the main perturbative terms of its orbital longitude and the tidal coupling. The main librations of Enceladus are related to indirect perturbations of the orbit of Enceladus by Dione (11 years and 3.7 years periods) with amplitudes of 933.4″ (1.14 km) and 676.6″ (827 m), respectively. These amplitudes are almost independent of the body's triaxiality. The third main libration is due to the direct gravitational attraction of Saturn and its period is equal to that of the mean anomaly of Enceladus with an amplitude between 93.1″ and 113.5″ (i.e., 112 and 139 m), depending on triaxiality. These amplitudes are consistent with the upper bound of 1.5° (6.6 km) inferred from observations with the Cassini‐Huygens spacecraft. The nonrigid body libration amplitudes due to tidal coupling are negligible. Nevertheless, tidal dissipation induces a small phase shift up to 0.57° corresponding to a displacement of Enceladus' figure of 1 m along the moon's equator at the mean anomaly period.

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.

Neptune Trojans and Plutinos: colors, sizes, dynamics, and their possible collisions

Neptune Trojans and Plutinos are two subpopulations of trans-Neptunian objects located in the 1:1 and the 3:2 mean motion resonances with Neptune, respectively, and therefore protected from close encounters with the planet. However, the orbits of these two kinds of objects may cross very often, allowing a higher collisional rate between them than with other kinds of trans-Neptunian objects, and a consequent size distribution modification of the two subpopulations. Observational colors and absolute magnitudes of Neptune Trojans and Plutinos show that i) there are no intrinsically bright (large) Plutinos at small inclinations, ii) there is an apparent excess of blue and intrinsically faint (small) Plutinos, and iii) Neptune Trojans possess the same blue colors as Plutinos within the same (estimated) size range do. For the present subpopulations we analyzed the most favorable conditions for close encounters/collisions and address any link there could be between those encounters and the sizes and/or colors of Plutinos and Neptune Trojans. We also performed a simultaneous numerical simulation of the outer Solar System over 1 Gyr for all these bodies in order to estimate their collisional rate. We conclude that orbital overlap between Neptune Trojans and Plutinos is favored for Plutinos with large libration amplitudes, high eccentricities, and small inclinations. Additionally, with the assumption that the collisions can be disruptive creating smaller objects not necessarily with similar colors, the present high concentration of small Plutinos with small inclinations can thus be a consequence of a collisional interaction with Neptune Trojans and such hypothesis should be further analyzed.

Phobos control point network, rotation, and shape

A new independent control point network for Phobos was computed from image data obtained by the SRC (Super Resolution Channel) on board the European Mars Express Mission. The network solution includes 3D coordinates of 665 surface control points and was used to observe the forced libration amplitude of Phobos. Based on the network control points a spherical harmonic function model to degree and order 17 was derived, from which volume, bulk density and moments of inertia were computed. The modeled forced libration amplitude agrees to our observation within the error bands, indicating a homogeneous mass distribution for Phobos. To bring both values into exact agreement with the observations, different mass distribution models were applied. It appears that the amplitude is relatively insensitive to a simple two-layer density model.

Accuracy of long-term forecasting geosynchronous satellite motion

The accuracy of forecasting geosynchronous satellite motion for 242-year term of forecast using a numerical model of artificial satellite motion taking into account the main perturbing factors including nonsphericity of the Earth’s gravitational field, attraction by the Moon and the Sun, tides inside the Earth, direct light pressure with allowance for the Earth’s shadow effect, and the Pointing–Robertson effect is considered. It is demonstrated that in this case, perturbations of the Earth’s gravitational field harmonics up to the 27th order must be considered. For regular motions, the maximum error in forecasting the geosynchronous satellite position ranges from 0.14 to 2400 km, the error in forecasting the long semiaxis ranges from 0.013 to 1100 m, and the error in forecasting the subsatellite point longitude ranges from 0.069″ to 3.4° depending on the libration amplitude. The accuracy of forecasting depends on the libration amplitude: the less the libration amplitude, the higher the accuracy of forecasting. For quasi-random trajectories, the integration period for which the errors in forecasting do not exceed values obtained for libration motion is determined by the frequency and proximity of the trajectory to unstable stationary points. For the examples considered, this period is about 200 years. The estimated MEGNO factor confirms the efficiency of the numerical model of artificial satellite motion used to investigate the stochastic properties of geosynchronous satellite motion.

CHAOTIC DIFFUSION OF RESONANT KUIPER BELT OBJECTS

We carried out extensive numerical orbit integrations to probe the long-term chaotic dynamics of the two strongest mean motion resonances of Neptune in the Kuiper belt, the 3:2 (Plutinos) and 2:1 (Twotinos). Our primary results include a computation of the relative volumes of phase space characterized by large- and small-resonance libration amplitudes, and maps of resonance stability measured by mean chaotic diffusion rate. We find that Neptune's 2:1 resonance has weaker overall long-term stability than the 3:2 -- only ~15% of Twotinos are projected to survive for 4 Gyr, compared to ~27% of Plutinos, based on an extrapolation from our 1-Gyr integrations. We find that Pluto has only a modest effect, causing a ~4% decrease in the Plutino population that survives to 4 Gyr. Given current observational estimates, and assuming an initial distribution of particles proportional to the local phase space volume in the resonance, we conclude that the primordial populations of Plutinos and Twotinos formerly made up more than half the population of the classical and resonant Kuiper Belt. We also conclude that Twotinos were originally nearly as numerous as Plutinos; this is consistent with predictions from early models of smooth giant planet migration and resonance sweeping of the Kuiper Belt, and provides a useful constraint for more detailed models.

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 k 2 / Q (assumed constant). Enceladus’ evolution after escape from the second-order e-Enceladus e-Dione resonance requires that ( k 2 / 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 ( k 2 / Q ) Enceladus > 1.2 × 10 - 4 , assuming that Q Saturn < 10 5 . Dione’s present-day eccentricity indicates that ( k 2 / 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.

The rotation of Janus and Epimetheus

Epimetheus, a small moon of Saturn, has a rotational libration (an oscillation about synchronous rotation) of 5.9 ° ± 1.2 ° , placing Epimetheus in the company of Earth’s Moon and Mars’ Phobos as the only natural satellites for which forced rotational libration has been detected. The forced libration is caused by the satellite’s slightly eccentric orbit and non-spherical shape. Detection of a moon’s forced libration allows us to probe its interior by comparing the measured amplitude to that predicted by a shape model assuming constant density. A discrepancy between the two would indicate internal density asymmetries. For Epimetheus, the uncertainties in the shape model are large enough to account for the measured libration amplitude. For Janus, on the other hand, although we cannot rule out synchronous rotation, a permanent offset of several degrees between Janus’ minimum moment of inertia (long axis) and the equilibrium sub-Saturn point may indicate that Janus does have modest internal density asymmetries. The rotation states of Janus and Epimetheus experience a perturbation every 4 years, as the two moons “swap” orbits. The sudden change in the orbital periods produces a free libration about synchronous rotation that is subsequently damped by internal friction. We calculate that this free libration is small in amplitude (<0.1°) and decays quickly (a few weeks, at most), and is thus below the current limits for detection using Cassini images.

Quasi-critical orbits for artificial lunar satellites

We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J2 and C22 terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the incli- nation and the argument of pericenter do not remain both constant at the same time, as is the case when only the J2 term is taken into account. Instead, there exist quasi-critical solutions, for which the argument of pericenter librates around a constant value. These solutions are represented by smooth curves in phase space, which determine the dependence of the quasi- critical inclination on the initial nodal phase. The amplitude of libration of both argument of pericenter and inclination would be quite large for a non-rotating Moon, but is reduced to <0 ◦ .1 for both quantities, when a uniform rotation of the Moon is taken into account. The values of J2, C22 and the rotation rate strongly affect the quasi-critical inclination and the libration amplitude of the argument of pericenter. Examples for other celestial bodies are given, showing the dependence of the results on J2, C22 and rotation rate.

On the evolution of mean motion resonances through stochastic forcing: fast and slow libration modes and the origin of HD 128311

Aims. We clarify the response of extrasolar planetary systems in a 2:1 mean motion commensurability with masses ranging from the super Jovian range to the terrestrial range to stochastic forcing that could result from protoplanetary disk turbulence. The behaviour of the different libration modes for a wide range of system parameters and stochastic forcing magnitudes is investigated. The growth of libration amplitudes is parameterized as a function of the relevant physical parameters. The results are applied to provide an explanation of the configuration of the HD 128311 system. Methods. We first develop an analytic model from first principles without making the assumption that both eccentricities are small. We also perform numerical N-body simulations with additional stochastic forcing terms to represent the effects of putative disk turbulence. Results. We isolate two distinct libration modes for the resonant angles. These react to stochastic forcing in a different way and become coupled when the libration amplitudes are large. Systems are quickly destabilized by large magnitudes of stochastic forcing but some stability is imparted should systems undergo a net orbital migration. The slow mode, which mostly corresponds to motion of the angle between the apsidal lines of the two planets, is converted to circulation more readily than the fast mode which is associated with oscillations of the semi-major axes. This mode is also vulnerable to the attainment of small eccentricities which causes oscillations between periods of libration and circulation. Conclusions. Stochastic forcing due to disk turbulence may have played a role in shaping the configurations of observed systems in mean motion resonance. It naturally provides a mechanism for accounting for the HD 128311 system for which the fast mode librates and the slow mode is apparently near the borderline between libration and circulation.

The interior structure of Mercury and its core sulfur content

Depth-dependent interior structure models of Mercury are calculated for several plausible chemical compositions of the core and of the mantle. For those models, we compute the associated libration amplitude, obliquity, tidal deformation, and tidal changes in the external potential. In particular we study the relation between the interior structure parameters for five different mantle mineralogies and two different temperature profiles together with two extreme crust density values. We investigate the influence of the core light element concentration, temperature, and melting law on core state and inner and outer core size. We show that a sulfur concentration above 10 wt% is unlikely if the temperature at the core–mantle boundary is above 1850 K and the silicate shell at least 240 km thick. The interior models can only have an inner core if the sulfur weight fraction is below 5 wt% for core–mantle boundary temperature in the 1850–2200 K range. Within our modeling hypotheses, we show that with the expected precision on the moment of inertia the core size can be estimated to a precision of about 50 km and the core sulfur concentration with an error of about 2 wt%. This uncertainty can only be reduced when more information on the mantle mineralogy of Mercury becomes available. However, we show that the uncertainty on the core size estimation can be greatly reduced, to about 25 km, if tidal surface displacements and tidal variations in the external potential are considered.

An experimental and numerical study of librationally driven flow in planetary cores and subsurface oceans

Many planetary bodies undergo forced longitudinal librations [Williams, J.G., Boggs, D.H., Yoder, C.F., Ratcliff, J.T., Dickey, J.O., 2001. Lunar rotational dissipation in solid body and molten core. Journal of Geophysical Research-Planets 106 (E11), 27933–27968; Comstock, R.L., Bills, B.G., 2003. A solar system survey of forced librations in longitude. Journal of Geophysical Research-Planets 108 (E9); Margot, J.L., Peale, S.J., Jurgens, R.F., Slade, M.A., Holin, I.V., 2007. Large longitude libration of mercury reveals a molten core. Science 316 (5825), 710–714]. Yet few studies to date have investigated how longitudinal libration, the oscillatory motion of a planet around its rotation axis, couples with its interior planetary fluid dynamics [e.g., Aldridge, K.D., Toomre, A., 1969. Axisymmetric inertial oscillations of a fluid in a rotating spherical container. Journal of Fluid Mechanics 37, 307; Tilgner, A., 1999. Driven inertial oscillations in spherical shells. Physical Review E 59 (2), 1789–1794]. In this study, we investigate, via laboratory experiments, the viscously driven flow in a spherical librating fluid cavity. We focus on libration frequencies less than or equal to the planetary rotation frequency (frequency ratios f∗≤1), moderate rotation rates (Ekman numbers E=10−4 to 10−5) and a relatively broad range of librational amplitudes (libration amplitudes 10°≲Δϕ≲200°; Rossby numbers 0.03≲Ro≲5). In addition we model flow in three different core geometries: full sphere, rinner≃0.6router and rinner≃0.9router.Direct flow visualizations in the laboratory experiment allow us to identify three distinct librationally driven flow regimes. The transitions between these regimes are governed by critical values of the outer boundary layer Reynolds number, Re. For Re≲20 the flow is dominated by inertial modes. For 20≲Re≲120 the system becomes unstable to longitudinal rolls that form beneath the outer boundary. This laminar instability initiates near the equator and is qualitatively similar to Taylor-Görtler instabilities. For Re≳120 the flow in the vicinity of the outer boundary becomes turbulent.For several librating planets with an internal fluid layer, estimates of Re and f∗ lie in the range of values accessible in our laboratory experiment. Our results suggest that Mercury, Io, Europa and Titan may undergo boundary layer turbulence, whereas Earth’s moon, Callisto and Ganymede may become unstable to laminar longitudinal rolls.