The origin of chaotic behaviour in the Miranda-Umbriel 3 : 1 resonances

We have investigated the pericentric resonances through which Miranda and Umbriel are believed to have passed when, due to tidal evolution, their orbital mean motions reached a 3 : 1 commensurability. Our investigation is based upon a perturbative treatment. The predictions of this theory are in good agreement with the results of numerical integrations concerning both the extend of the chaotic layers generated by the separatrices of the primary resonances and the location of the secondary resonances. The effect of tidal evolution is discussed on the bases of the adiatatic invariant theory and its extension to separatrix crossing. We recover qualitatively the mean features of the numerical experiments of Tittermore and Wisdom (1988–1989), Dermott et al (1988) and Malhotra and Dermott (1989).     

Adiabatic chaos in the Prometheus–Pandora system

The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical–experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.     

Rotational dynamics of planetary satellites: A survey of regular and chaotic behavior

The problem of observability of chaotic regimes in the rotation of planetary satellites is studied. The analysis is based on the inertial and orbital data available for all satellites discovered up to now. The Lyapunov spectra of the spatial chaotic rotation and the full range of variation of the spin rate are computed numerically by integrating the equations of the rotational motion; the initial data are taken inside the main chaotic layer near the separatrices of synchronous resonance in phase space. The model of a triaxial satellite in a fixed elliptic orbit is adopted. A short Lyapunov time along with a large range of variation of the spin rate are used as criteria for observability of the chaotic motion. Independently, analysis of stability of the synchronous state with respect to tilting the axis of rotation provides a test for the physical opportunity for a satellite to rotate chaotically. Finally, a calculation of the times of despinning due to tidal evolution shows whether a satellite's spin could evolve close to the synchronous state. Apart from Hyperion, already known to rotate chaotically, only Prometheus and Pandora, the 16th and 17th satellites of Saturn, pass all these four tests.     

The control networks of the satellites of Uranus

Control networks of the five large satellites of Uranus have been established photogrammetrically from pictures taken by the Voyager 2 spacecraft. The control networks cover the illuminated southern hemisphere of each satellite. Coordinates are listed for 103 points on Miranda, 52 points on Ariel, 43 points on Umbriel, 46 points on Titania, and 34 points on Oberon; some points are identified on the U.S. Geological Survey maps of these satellites. Miranda is ellipsoidal in shape with radii of 241, 235 and 232 km. Mean radii are 579 km for Ariel, 586 km for Umbriel, 790 km for Titania, and 762 km for Oberon.     

Tidal dissipation,orbital evolution,and the nature of Saturn's inner satellites

Estimates of tidal damping times of the orbital eccentricities of Saturn's inner satellites place constraints on some satellite rigidities and dissipation functions Q. These constraints favor rock-like rather than ice-like properties for Mimas and probably Dione. Photometric and other observational data are consistent with relatively higher densities for these two satellites, but require lower densities for Tethys, Enceladus, and Rhea. This leads to a nonmonotonic density distribution for Saturn's inner satellites, apparently determined by different mass fractions of rocky materials. In spite of the consequences of tidal dissipation for the orbital eccentricity decay and implications for satellite compositions, tidal heating is not an important contributor to the thermal history of any Saturnian satellite.     

The formation of commensurabilities in satellite systems due to the action of tidal forces

The five types of resonance possible between a pair of satellites at a 21 commensurability are described. By a modification of the method usually used in the restricted three-body problem, phase-plane diagrams are constructed for these resonances for the more general case where both satellite masses are non-zero. These phase-plane diagrams are used to discuss the different types of motion possible at the five resonances.It is shown that tidal forces can drive a pair of satellites towards a commensurability, and at the 21 commensurability it is possible for the satellites to be captured into a libration at any of the five resonances, the probability of capture depending on the eccentricities, inclinations, and masses of the satellites. The tidal hypothesis provides a reasonable explanation of the origin of the commensurabilities between Mimas and Tethys, and between Enceladus and Dione, in the satellite system of Saturn.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972.     

Surfaces of section in the Miranda-Umbriel 3:1 inclination problem

The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermottet al. (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 inclination resonance between Miranda and Umbriel is analysed.     

Plasma, plumes and rings: Saturn system dynamics as recorded in global color patterns on its midsize icy satellites

New global maps of the five inner midsize icy saturnian satellites, Mimas, Enceladus, Tethys, Dione, and Rhea, have been constructed in three colors (UV, Green and near-IR) at resolutions of 1 km/pixel. The maps reveal prominent global patterns common to several of these satellites but also three major color features unique to specific satellites or satellite subgroups. The most common features among the group are first-order global asymmetries in color properties. This pattern, expressed on Tethys, Dione and Rhea, takes the form of a ∼1.4-1.8 times enhancement in redness (expressed as IR/UV ratio) of the surface at the center of the trailing hemisphere of motion, and a similar though significantly weaker IR/UV enhancement at the center of the leading hemisphere. The peak in redness on the trailing hemisphere also corresponds to a known decrease in albedo. These double hemispheric asymmetries are attributable to plasma and E-ring grain bombardment on the trailing and leading hemispheres, respectively, for the outer three satellites Tethys, Dione and Rhea, whereas as E-ring bombardment may be focused on the trailing hemisphere of Mimas due to its orbital location interior to Enceladus. The maps also reveal three major deviations from these basic global patterns. We observe the previously known dark bluish leading hemisphere equatorial band on Tethys but have also discovered a similar band on Mimas. Similar in shape, both features match the surface patterns expected for irradiation of the surface by incident MeV electrons that drift in a direction opposite to the plasma flow. The global asymmetry on Enceladus is offset ∼40° to the west compared to the other satellites. We do not consider Enceladus in detail here, but the global distribution of bluish material can be shown to match the deposition pattern predicted for plume fallback onto the surface (Kempf, S., Beckmann, U., Schmidt, S. [2010]. Icarus 206, 446-457. doi:10.1016/j.icarus.2009.09.016). E-ring deposition on Enceladus thus appears to mask or prevent the formation of the lenses and hemispheric asymmetries we see on the other satellites. Finally, we observe a chain of discrete bluish splotches along the equator of Rhea. Unlike the equatorial bands of Tethys and Mimas, these splotches form a very narrow great circle ?10-km wide (north-to-south) and appear to be related to surface disruption, exposing fresh, bluish ice on older crater rims. This feature is unique to Rhea and may have formed by impact onto its surface of orbiting material.     

Some unsolved problems in evolutionary dynamics in the solar system

Several unsolved problems in the evolutionary histories leading to current dynamical configurations of the planets and their systems of satellites are discussed. These include the possibilities of rather tight constraints on the primordial rotation states of Mercury and Venus and the stabilizing mechanism for the latter's retrograde spin, a brief mention of the problem of origin of the moons of Earth and Mars, the excessive heat flow from Jupiter's satellite lo which is not compatible with an otherwise self-consistent model of origin of the Laplace three-body libration, the mechanism for the long history of resurfacing of Saturn's satellite Enceladus and the possibly short lifetime of the A ring and the mechanisms for resurfacing the satellites of Uranus, especially Ariel, if the high stability of the mean motion orbital resonances at the 2/1 commensurability involving Ariel and Umbriel precludes a long term occupancy of the resonance. Finally, excessive times of accumulation of the outer planets in current models may possibly be reducible from the effects of nebular gas drag.     

Occurrence of central peak craters on the Uranian satellites: Implications for surface structure and comparison with the Jovian and Saturnian systems

Craters with central peaks occur on the Uranian satellites Ariel, Umbriel, Titania, and Oberon; but do not occur on Miranda. The inelastic surface of Miranda is apparently due to the heavy tectonic reworking of its surface. A theory of expansion/contraction is proposed to explain the tectonic history of Miranda. The existence of central peak craters on the four largest satellites of Uranus implies that they have surface strengths similar to those of the Saturnian satellites and silicate bodies of the inner solar system which all have central peak craters. The absence of central peak craters on Miranda implies that it has an inelastic surface similar to those of the Jovian ice satellites Ganymede and Callisto whose surfaces do not contain central peak craters.     

Photometric study of the major satellites of Uranus

In this paper, we analyze the results of ground-based and space-born photometric observations of the major satellites of Uranus—Miranda, Ariel, Umbriel, Titania, and Oberon. All sets of photometric observations of the satellites available in the literature were examined for uniformity and systematic differences and summarized to a unified set by wavelength ranging from 0.25 to 2.4 μm. This set covers the interval of phase angles from 0.034° to 35°. The compound phase curves of brightness of the satellites in the spectral bands at 0.25, 0.41, 0.48, 0.56, 0.75, 0.91, 1.4, and 1.8 μm, which include a pronounced opposition surge and linear part, were constructed. For each satellite, the geometric albedo was found in different spectral bands taking into account the brightness opposition effect, and its spectral dependence was studied. It has been shown that the reflectance of the satellites linearly depends on the wavelength at different phase angles, but has different spectral gradients. The parameters of the phase functions of brightness, including the amplitude and the angular width of the brightness opposition surge, the phase coefficient, and the phase angle at which the nonlinear increase in brightness starts, were determined and their dependences on wavelength and geometric albedo were analyzed. Our investigations show that, in their optical properties, the satellites Miranda and Ariel, Titania and Oberon, and Umbriel present three types of surfaces. The observed parameters of the brightness opposition effect for the Uranian satellites, some ice satellites of Jupiter and Saturn, and the E-and S-type asteroids are analyzed and compared within the framework of the coherent backscattering and mutual shadowing mechanisms.     

天王星卫星两种定标方法测定结果的比较

利用新发表的高精度、高密度天体测量星表UCAC2,对天王星的五颗主要卫星的CCD观测图像重新进行量测,采用不同方法作定标归算,并使用两种理论模型(GUST86和GUST06模型)计算卫星的理论位置。对不同方法所得到的卫星位置的O-C结果的分析和比较表明,本文获得的卫星位置精度,除天卫五(Miranda)有显著提高,其他4颗卫星的位置精度基本相同。本文中天卫一和天卫三的结果与"亮卫星定标法"的结果在精度上相当,天卫二的位置精度与其他天王星卫星的位置精度具有较好的一致性,这从另一方面证明了我们的"亮卫星定标法"的可靠性。此外我们还获得了天卫四的位置与精度。     

Shapes and gravitational moments of satellites and asteroids

The shapes and gravitational moments of tidally and rotationally distorted satellites with nonuniform internal density distributions are calculated. Spacecraft determinations of the radii and (a) the gravitational moments of some satellites of Jupiter and Saturn, particularly Io, Ganymede and Titan or (b) the shapes of some others, particularly Mimas and Tethys, could provide unambiguo3s evidence of either internal differentiation or orbital evolution. The shapes of rotationally distorted asteroids are discussed briefly.     

Modeling global impact effects on middle-sized icy bodies: applications to Saturn's moons

Disrupted terrains that form as a consequence of giant impacts may help constrain the internal structures of planets, asteroids, comets and satellites. As shock waves and powerful seismic stress waves propagate through a body, they interact with the internal structure in ways that may leave a characteristic impression upon the surface. Variations in peak surface velocity and tensile stress, related to landform degradation and surface rupture, may be controlled by variations in core size, shape and density. Caloris Basin on Mercury and Imbrium Basin on the Moon have disturbed terrain at their antipodes, where focusing is most intense for an approximately symmetric spheroid. Although, the icy saturnian satellites Tethys, Mimas, and Rhea possess giant impact structures, it is not clear whether these structures have correlated disrupted terrains, antipodal or elsewhere. In anticipation of high-resolution imagery from Cassini, we investigate antipodal focusing during giant impacts using a 3D SPH impact model. We first investigate giant impacts into a fiducial 1000 km diameter icy satellite with a variety of core radii and compositions. We find that antipodal disruption depends more on core radius than on core density, suggesting that core geometry may express a surface signature in global impacts on partially differentiated targets. We model Tethys, Mimas, and Rhea according to their image-derived shapes (triaxial for Tethys and Mimas and spherical for Rhea), varying core radii and densities to give the proper bulk densities. Tethys shows greater antipodal values of peak surface velocity and peak surface tensile stress, indicating more surface damage, than either Mimas or Rhea. Results for antipodal and global fragmentation and terrain rupture are inconclusive, with the hydrocode itself producing global disruption at the limits of model resolution but with peak fracture stresses never exceeding the strength of laboratory ice.     

Stagnant lid convection in the mid-sized icy satellites of Saturn

Thermal history models for the mid-sized saturnian satellites Mimas, Tethys, Dione, Iapetus, and Rhea have been calculated assuming stagnant lid convection in undifferentiated satellites and varying parameter values over broad ranges. Of all five satellites under consideration, only Dione, Rhea and Iapetus do show significant internal activities related to convective overturn for extended periods of time. The interiors of Mimas and Tethys do not convect or do so only for brief periods of time early in their thermal histories. Although we use lower densities than previous models, our calculations suggest higher interior temperatures but also thicker rigid shells above the convecting regions. Temperatures in the stagnant lid will allow melting of ammonia-dihydrate. Dione, Rhea and Iapetus may differentiate early and form early oceans, Iapetus only if ammonia is present. Mimas and Tethys with ammonia may differentiate if they accreted in an optically thick nebula with ambient temperatures around 250 K. Our models suggest that the outer shells of the satellites are largely primordial in composition even if the satellites differentiated. In these cases the deep interior may be layered with a pure ice shell underlain by an ammonia dihydrate layer and a rock core.     

Saturn's icy satellites: Thermal and structural models

Thermal histories of the small icy Saturnian satellites Mimas, Tethys, Dione, Rhea, and Iapetus are constructed by assuming that they formed as homogeneous ice-silicate mixtures. The models include effects of radiogenic and accretional heating, conductive and subsolidus convective heat transfer, and lithospheric growth. Accretional heating is unlikely to have melted the water ice in the interiors of these bodies and solid state creep of the predominately ice material precludes melting by radiogenic heating. Mimas is so small that its thermal evolution is essentially purely conductive; at present it is a cold, nearly isothermal body. Any subsolidus convection or thermal activity in Mimas would have been confined to a brief period in its early history and would have been due to a warm formation. The four largest satellites are big enough and contain sufficient heat-producing silicates that solid state convection beneath a rigid lithosphere is inevitable independent of initial conditions. Dione and Rhea have convective interiors for most of their thermal histories, while Tethys and Iapetus have mainly conductive thermal histories with early periods of convective 0activity. The thermal histories of the five satellites for the last 4 by are independent of initial conditions; at present they have cold, conductive interiors. The model thermal histories are qualitatively consistent with the appearances of these satellites: Mimas has an ancient heavily cratered surface, Tethys and probably Iapetus have both heavily cratered and more lightly cratered areas, and Dione and Rhea have extensively modified surfaces. Because of their similar sizes and densities, Mimas and Enceladus are expected to have similar surfaces and thermal histories, but instead Enceladus has the most modified surface of all the small icy Saturnian satellites. Our results suggest a heat source for Enceladus, in addition to radiogenic and accretional heating; tidal dissipation is a possibility. Because the water ice in these bodies does not melt, resurfacing must be accomplished by the melting of a low-melting-temperature minor component such as ammonia hydrate.     

The 3:1 mean motion resonance between Miranda and the inner Uranian satellites,Cressida and Desdemona

We build a simple dissipative analytical model considering an averaged restricted 3-body problem taking into account the effect of the oblateness of a planet on a small satellite and on its perturber. We apply this model to the inner Uranian system and we follow the dynamical evolution of the satellites Cressida or Desdemona, these latter being close to a 3:1 commensurability with the large satellite Miranda. Our analysis shows that the positions of the two inner satellites, on both sides of the exact resonance, are temporary, Cressida having already crossed the resonance, and Desdemona approaching the commensurability to jump over later on.     

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.     

Sinking, tidally stripped, galactic satellites

Tidally interacting galaxies offer an interesting field for the investigation of chaotic phenomena in stellar systems. When the galaxies are gravitationally bound, and one of them is much larger than the other, the latter can be regarded as a satellite of the former. The study of their dynamics is somewhat simplified in this case, which presents well observed examples in nature (e.g., globular clusters). Galactic satellites suffer orbital decay due to dynamical friction, a process that may be greatly enhanced in the presence of chaotic motions. Besides, the satellite is stripped by the field of tidal forces and, in the long run, it will disintegrate completely. Modern observations are able to show the signature of these processes taking place at present.     

Mapping of the icy Saturnian satellites: First results from Cassini-ISS

Images of the icy Saturnian satellites Mimas, Enceladus, Tethys, Dione, Rhea, Iapetus, and Phoebe, derived by the Voyager and Cassini cameras are used to produce new local high-resolution image mosaics as well as global mosaics [http://ciclops.org, http://photojournal.jpl.nasa.gov]. These global mosaics are valuable both for scientific interpretation and for the planning of future flybys later in the ongoing Cassini orbital tour. Furthermore, these global mosaics can be extended to standard cartographic products.