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1.
Julie M. Groenleer 《Icarus》2008,193(1):158-181
The original model developed to explain cycloidal cracks on Europa interprets cycloids as tensile fractures that grow in a curved path in response to the constantly rotating diurnal tidal stress field. Cusps form when a new cycloid crack segment propagates at an angle to the first in response to a rotation of the principal tidal stress orientation during a period of no crack growth. A recent revised model states that a cycloid cusp forms through the creation of a secondary fracture called a tailcrack at the tip of an existing cycloid segment during shearing motion induced by the rotating tidal stress field. As the tailcrack propagates away from the cusp, it becomes the next cycloid segment in the chain. The qualitative tailcrack model uniquely accounts for the normal and shear stresses that mechanically must resolve onto the tip of an existing cycloid segment at the instant of cusp formation. In this work, we provide a quantitative framework and test of the hitherto purely conceptual tailcrack model. We first present a relative age sequence inferred from geologic mapping of multiply cross-cutting cycloids in Europa's trailing hemisphere and place this into the context of the global stress history. The age sequence requires a cumulative minimum of 630° of shell reorientation due to nonsynchronous rotation to account for the observed range of orientations of cycloids of different ages. We determined the back-rotated longitudes of formation of two cycloid chain examples and used mathematical modeling of europan tidal stresses to show that the tailcrack model for cusp formation is not only viable, but places constraints on the overall development of a cycloid chain by controlling the timing of cusp development within Europa's orbit. For all cusps analyzed, the exact ratio of resolved shear to normal stress required to form the cusp angles by a process of tailcracking, as governed by the principles of linear elastic fracture mechanics, is produced at the tip of a shearing cycloid segment during Europa's orbit. Cusp formation occurs after the point in the orbit at which the maximum tensile principal tidal stress occurs, implying that tensile tidal stresses are not directly responsible for cusp development. Instead, cusps develop when a tailcrack forms at the tip of a cycloid segment in response to the highly perturbed stress field induced during concomitant opening and shearing at the tip of the cycloid segment. 相似文献
2.
Alyssa Rose Rhoden Burkhard Militzer Eric M. Huff Terry A. Hurford Michael Manga Mark A. Richards 《Icarus》2010,210(2):770-784
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. 相似文献
3.
Cycloidal crack patterns on Europa are influenced by tides induced by orbital eccentricity, which in turn is driven by the Laplace orbital resonance. Their shapes potentially record the location of their formation (relative to the direction of Jupiter), as well as the parameters of crack formation. Hoppa et al. [Hoppa, G., Tufts, B.R., Greenberg, R., Geissler, P., 1999a. Icarus 141, 287-298] modeled several cycloid chains using a fixed set of material parameters, but some details did not fit. We now allow material parameters to vary for each arc of an observed cycloid. In general, with minimal variation of model parameters between the arcs, fits are greatly improved. Furthermore, accounting for tidal stress accumulated during non-synchronous rotation, in addition to diurnal stress, allows even better fits. Even with the added freedom in the model our fits allow us to better constrain the location where each cycloid may have formed. Our results support Hoppa et al.'s finding that only a few cracks form ridges per cycle of non-synchronous rotation in the region examined, probably because cracking relieves built up stress until further substantial rotation occurs. 相似文献
4.
Scott T. Marshall 《Icarus》2005,177(2):341-366
Although a single model currently exists to explain the development of curved Europan cycloids, there have been no systematic studies of the range of morphologies and quantifiable geometric parameters of cycloidal features. We address variations in geometry along individual cycloid segments, characterizing differences in cusp styles and angles, and addressing the morphologic aspects of cycloid segments and cusps. In so doing, we illustrate how geometric and morphologic evidence imply a formation mechanism that differs from the existing model in several aspects. The current model states that cycloids are initiated as tensile fractures that grow in a curved path in response to rotating diurnal tidal stresses on Europa. However, the geometry of a cycloid cusp necessitates that shear stress was resolved onto the existing cycloid segment by the rotating diurnal stresses at the instant of cusp formation. Furthermore, we observe that cycloid cusps have a strikingly similar geometry to tailcracks that developed at the tips of many ridge-like strike-slip faults on Europa in response to shearing at the fault tip. We suggest that this similarity in geometries can be attributed to an identical formation mechanism whereby cycloid cusps form by a tailcracking process. We therefore present a revised, mechanically-based model for cycloid formation that retains the basic premise that crack growth is governed by diurnal stresses, but describes the development of cycloid cusps in response to resolved shear stresses at the tips of existing cycloid segments. The ratio of normal to shear stress at the time of tailcrack formation dictates the cusp angle and, over longer time periods, influences the morphologic evolution of the cycloid segment as it is repeatedly reworked by tidal stresses. 相似文献
5.
6.
Observations of the Europa environment using the Cassini UltraViolet Imaging Spectrograph (UVIS) show the presence of an extended atomic oxygen atmosphere in addition to the bound molecular oxygen atmosphere first detected by Hubble Space Telescope in 1994 [D.T. Hall, D.F. Strobel, P.D. Feldman, M.A. McGrath, H.A. Weaver, 1995, Detection of an oxygen atmosphere on Jupiter's moon Europa, Nature 373, 677-679]. The atomic oxygen measurement provides a direct constraint on the sputtering and loss of Europa's water ice surface and the interaction of Europa's atmosphere with Jupiter's magnetosphere. We derive a loss rate for O2 based on the emission rate of the OI 1356 Å multiplet. UVIS detected substantial variability in the oxygen emission from Europa's oxygen atmosphere that we attribute to the viewing geometry. B.H. Mauk, D.G. Mitchell, S.M. Krimigis, E.C. Roelof, C.P. Paranicas [2003, Energetic neutral atoms from a trans-Europa gas torus at Jupiter, Nature 421, 920-922] inferred the presence of a torus of neutral gas at Europa's orbit based on Cassini's energetic neutral atom (ENA) image of the Jupiter system acquired with the Magnetospheric Imaging Instrument (MIMI), with the most likely torus constituents being hydrogen and oxygen species sputtered from Europa. Cassini UVIS data rule out O and O2 as the possible torus species reported by Mauk et al. however, unless the torus density is so low that it is undetectable by UVIS (less than 8 atoms / cm3). The UVIS observations indicate the presence of atomic hydrogen and possibly other species, but a full analysis is deferred to a following paper. The hydrogen in the present observations shows a local-time asymmetry and complex spatial distribution. 相似文献
7.
Variations in diurnal tidal stress due to Europa’s eccentric orbit have been considered as the driver of strike-slip motion along pre-existing faults, but obliquity and physical libration have not been taken into account. The first objective of this work is to examine the effects of obliquity on the predicted global pattern of fault slip directions based on a tidal-tectonic formation model. Our second objective is to test the hypothesis that incorporating obliquity can reconcile theory and observations without requiring polar wander, which was previously invoked to explain the mismatch found between the slip directions of 192 faults on Europa and the global pattern predicted using the eccentricity-only model. We compute predictions for individual, observed faults at their current latitude, longitude, and azimuth with four different tidal models: eccentricity only, eccentricity plus obliquity, eccentricity plus physical libration, and a combination of all three effects. We then determine whether longitude migration, presumably due to non-synchronous rotation, is indicated in observed faults by repeating the comparisons with and without obliquity, this time also allowing longitude translation. We find that a tidal model including an obliquity of 1.2°, along with longitude migration, can predict the slip directions of all observed features in the survey. However, all but four faults can be fit with only 1° of obliquity so the value we find may represent the maximum departure from a lower time-averaged obliquity value. Adding physical libration to the obliquity model improves the accuracy of predictions at the current locations of the faults, but fails to predict the slip directions of six faults and requires additional degrees of freedom. The obliquity model with longitude migration is therefore our preferred model. Although the polar wander interpretation cannot be ruled out from these results alone, the obliquity model accounts for all observations with a value consistent with theoretical expectations and cycloid modeling. 相似文献
8.
A 100 km deep liquid water ocean probably underlies the icy exterior of Jupiter's satellite Europa. The long-term persistence of a liquid ocean beneath an ice shell presents a thermal conundrum: Is the temperature of the ocean equal to the freezing point of water at the bottom of the ice shell, or is it equal to the somewhat warmer temperature at which water attains its maximum density? We argue that most of the ocean is at the temperature of maximum density and that the bulk of the vigorously convecting ocean is separated from the bottom of the ice shell by a thin “stratosphere” of stably stratified water which is at the freezing point, and therefore buoyant. If Europa's subsurface water ocean is warm, it could explain the widespread geologic evidence for apparent melt-through events observed on its surface and may constrain the overall age of its surface. 相似文献
9.
E. PierazzoC.F. Chyba 《Icarus》2002,157(1):120-127
Jupiter's moon Europa may harbor an ocean beneath its ice cover, but the composition of that ocean and the overlying ice is nearly entirely unknown. Regardless of uncertainties in models for Europa's formation, we estimate lower limits for Europa's inventory of biogenic elements (such as C, N, O, and P) by investigating the contribution to the inventory of impact events over Europa's geologic history. A series of high-resolution hydrocode simulations were carried out over a range of comet densities (1.1, 0.8, and 0.6 g/cm3, corresponding to porosities between 0 and 45%) and impact velocities (16, 21.5, 26.5, and 30.5 km/s). We found that at typical impact velocities on Europa most impactor material reaches escape velocity, and it is assumed to be lost from Europa. For a nonporous comet, some fraction (20% or higher) of the projectile is retained by Europa even at the highest impact velocity modeled, 30.5 km/s. For porous comets, however, a significant fraction of the projectile (above 25%) is retained only for the lowest impact velocity modeled, 16 km/s. Integrated over solar system history, this suggests that 1 to 10 Gt of carbon could have been successfully delivered to Europa's surface by impacts of large comets (around 1 km in diameter). This is a few times more carbon than is contained in the procaryotic biomass of the upper 200 meters of the Earth's oceans, but about 2 orders of magnitude less if the whole depth of the oceans is considered. Therefore, regardless of its initial formation conditions, Europa should have a substantial inventory of “biogenic” elements, with implications for the chemistry of its oceans, ice cover, and the possibility of life. 相似文献
10.
Richard Greenberg Gregory V. Hoppa Paul Geissler Alyssa Sarid B.R. Tufts 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):35-47
Theoretical predictions of non-synchronous rotation and of polar wander on Europa have been tested by comparing tectonic features observed in Voyager and Galileo spacecraft images with tidal stresses. Evidence for non-synchronous rotation comes from studying changes in global scale lineaments formed over time, from the character of strike-slip faults, and from comparison of distinctively shaped cycloidal cracks with the longitudes at which such shapes should have formed, in theory. The study of cycloids constrains the rotation period (relative to the direction of Jupiter) to less than 250 000 years, while direct comparison of the orientation of Europa in Voyager and Galileo images shows the rotation is slow, with a period of >12 000 years. Comparison of strike-slip faults with their theoretical locations of formation provides evidence for substantial polar wander, supported by the distribution of various thermally produced features. 相似文献
11.
Near-infrared observations of Europa's disk-integrated opposition surge by Cassini VIMS, first published in Fig. 4 of Brown et al. (2003, Icarus, 164, 461), have now been modeled with the commonly used Hapke photometric function. The VIMS data set emphasizes observations at 16 solar phase angles from 0.4° to 0.6°—the first time the <1° phase “heart” of Europa's opposition surge has been observed this well in the near-IR. This data set also provides a unique opportunity to examine how the surge is affected by changes in wavelength and albedo: at VIMS wavelengths of 0.91, 1.73, and 2.25 μm, the geometric albedo of Europa is 0.81, 0.33, and 0.18, respectively. Despite this factor-of-four albedo range, however, the slope of Europa's phase curve at <1° phase is similar at all three wavelengths (to within the error bars) and this common slope is similar to the phase coefficient seen in visible-light observations of Europa. The two components of the opposition surge—involving different models of the physical cause of the surge—are the Shadow Hiding Opposition Effect (SHOE) and the Coherent Backscatter Opposition Effect (CBOE). Because of sparse VIMS phase coverage, it is not possible to constrain all the surge parameters at once in a Hapke function that has both SHOE and CBOE; accordingly, we performed separate Hapke fits for SHOE-only and CBOE-only surges. At 2.25 μm, where VIMS data are somewhat noisy, both types of surges can mimic the slope of the VIMS phase curve at <1° phase. At 0.91 and 1.73 μm, however—where VIMS data are “cleaner”—CBOE does a noticeably poorer job than SHOE of matching the VIMS phase coefficient at <1° phase; in particular, the best CBOE fit insists on having a steeper phase-curve slope than the data. This discrepancy suggests that Europa's near-IR opposition surge cannot be explained by CBOE alone and must have a significant SHOE component, even at wavelengths where Europa is bright. 相似文献
12.
Coupled thermal-orbital evolution models of Europa and Io are presented. It is assumed that Io, Europa, and Ganymede evolve in the Laplace resonance and that tidal dissipation of orbital energy is an internal heat source for both Io and Europa. While dissipation in Io occurs in the mantle as in the mantle dissipation model of Segatz et al. (1988, Icarus 75, 187), two models for Europa are considered. In the first model dissipation occurs in the silicate mantle while in the second model dissipation occurs in the ice shell. In the latter model, ice shell melting and variations of the shell thickness above an ocean are explicitly included. The rheology of both the ice and the rock is cast in terms of a viscoelastic Maxwell rheology with viscosity and shear modulus depending on the average temperature of the dissipating layer. Heat transfer by convection is calculated using a parameterization for strongly temperature-dependent viscosity convection. Both models are consistent with the present orbital elements of Io, Europa, and Ganymede. It is shown that there may be phases of quasi-steady evolution with large or small dissipation rates (in comparison with radiogenic heating), phases with runaway heating or cooling and oscillatory phases during which the eccentricity and the tidal heating rate will oscillate. Europa's ice thickness varies between roughly 3 and 70 km (dissipation in the silicate layer) or 10 and 60 km (dissipation in the ice layer), suggesting that Europa's ocean existed for geological timescales. The variation in ice thickness, including both convective and purely conductive phases, may be reflected in the formation of different geological surface features on Europa. Both models suggest that at present Europa's ice thickness is several tens of km thick and is increasing, while the eccentricity decreases, implying that the satellites evolve out of resonance. Including lithospheric growth in the models makes it impossible to match the high heat flux constraint for Io. Other heat transfer processes than conduction through the lithosphere must be important for the present Io. 相似文献
13.
In this study we present a semi-analytical Maxwell-viscoelastic model of the variable tidal stress field acting on Europa’s surface. In our analysis, we take into account surface stresses induced by the small eccentricity of Europa’s orbit, the non-zero obliquity of Europa’s spin axis - both acting on a diurnal 3.55-days timescale - and the reorientation of the ice shell as a result of non-synchronous rotation (NSR). We assume that Europa’s putative ocean is covered by an ice shell, which we subdivide in a low-viscous and warm lower ice layer (asthenosphere, viscosity 1012-1017 Pa s), and a high-viscous and cold upper ice layer (lithosphere, viscosity 1021 Pa s).Viscoelastic relaxation influences surface stresses in two ways: (1) through viscoelastic relaxation in the lithosphere and (2) through the viscoelastic tidal response of Europa’s interior. The amount of relaxation in the lithosphere is proportional to the ratio between the period of the forcing mechanism and the Maxwell time of the high-viscous lithosphere. As a result, this effect is only relevant to surface stresses caused by the slow NSR mechanism. On the other hand, the importance of the viscoelastic response on surface stresses is proportional to the ratio between the relaxation time (τj) of a given viscoelastic mode j and the period of the forcing function. On a diurnal timescale the fast relaxation of transient modes related to the low viscosity of the asthenosphere can alter the magnitude and phase shift of the diurnal stress field at Europa’s surface. The effects are largest, up to 20% in magnitude and 7° in phase for ice rigidities lower than 3.487 GPa, when the relaxation time of the aforementioned transient modes approaches the inverse of the average angular rate of Europa’s orbit. On timescales relevant for NSR (>104 years) the magnitude and phase shift of NSR surface stresses can be affected by viscoelastic relaxation of the ocean-ice boundary. This effect, however, becomes only important when the behavior of the lithosphere w.r.t. NSR approaches the fluid limit, i.e. for strong relaxation in the lithosphere. The combination of NSR and diurnal stresses for different amounts of viscoelastic relaxation of NSR stresses in the lithosphere leads to a large variety of global stress fields that can explain the formation of the large diversity of lineament morphologies observed on Europa’s surface. Variation of the amount of relaxation in the lithosphere is likely due to changes in the spin rate of Europa and/or the rheological properties of the surface.In addition, we show that a small obliquity(<1°) can have a considerable effect on Europa’s diurnal stress field. A non-zero obliquity breaks the symmetric distribution of stress patterns with respect to the equator, thereby affecting the magnitude and orientation of the principal stresses at the surface. As expected, increasing the value of Europa’s obliquity leads to larger diurnal stresses at the surface, especially when Europa is located 90° away from the nodes formed by the intersection of its orbital and equatorial planes. 相似文献
14.
It has been claimed [Canup, R.M., Ward, W.R., 2002. Astron. J. 124, 3404-3423; Ward, W.R., 2003. In: AGU, Fall Meeting 2003] that a long-lived minimum mass circumplanetary gas disk is inconsistent with Jupiter's low obliquity. Here we find that while Jupiter's obliquity may constrain its characteristics it does not rule out a long-lived massive (compared to the mass of the Galilean satellites) disk. This is because the argument assumes a Solar System much like that of the present day with the one exception of a circumjovian disk which is then allowed to dissipate on a long timescale (106-107 yr). Given that the sequence of events in Solar System history that fit known constraints is non-unique, we choose for the sake of clarity of exposition the orbital architecture framework of Tsiganis et al. [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461], in which Jupiter and Saturn were once in compact, nearly coplanar orbits, and show that in this case Jupiter's low obliquity is consistent with the SEMM (solids-enhanced minimum mass) satellite formation model of Mosqueira and Estrada [Mosqueira, I., Estrada, P.R., 2003a. Icarus 163, 198-231; Mosqueira, I., Estrada, P.R., 2003b. Icarus 163, 232-255]. We suggest that a low inclination starting condition may apply, but stress that our SEMM satellite formation model could be compatible with Jupiter's obliquity even for mutually inclined giant planets. 相似文献
15.
This paper focuses on tenuous dust clouds of Jupiter's Galilean moons Europa, Ganymede and Callisto. In a companion paper (Srem?evi? et al., Planet. Space Sci. 51 (2003) 455-471) an analytical model of impact-generated ejecta dust clouds surrounding planetary satellites has been developed. The main aim of the model is to predict the asymmetries in the dust clouds which may arise from the orbital motion of the parent body through a field of impactors. The Galileo dust detector data from flybys at Europa, Ganymede and Callisto are compatible with the model, assuming projectiles to be interplanetary micrometeoroids. The analysis of the data suggests that two interplanetary impactor populations are most likely the source of the measured dust clouds: impactors with isotropically distributed velocities and micrometeoroids in retrograde orbits. Other impactor populations, namely those originating in the Jovian system, or interplanetary projectiles with low orbital eccentricities and inclinations, or interstellar stream particles, can be ruled out by the statistical analysis of the data. The data analysis also suggests that the mean ejecta velocity angle to the normal at the satellite surface is around 30°, which is in agreement with laboratory studies of the hypervelocity impacts. 相似文献
16.
The orientations of the albedo lineaments, bands, and lineations on Europa's surface have been compared in previous studies with the global stress fields set up by orbital eccentricity, orbital recession, and nonsynchronous rotation. Of these orbital and rotational effects, nonsynchronous rotation, combined with an offsetting of the tidal bulge, comes closest to providing agreement between the stress field generated and the lineation orientations, if the lineations trace tension or extension fractures (McEwen 1986.Nature321, 49–51). However, inferred minimum principal stress directions for a broad region of wedge-shaped bands near the anti-Jove point cannot satisfactorily be accounted for by any of the stress fields above, but are consistent with the stresses resulting from a rotation of Europa's ice shell about an axis through the sub- and anti-Jove points, clockwise as seen from the anti-Jove hemisphere (P. M. Schenk and W. B. McKinnon 1989.Icarus79, 75–100). Calculations by Ojakangas and Stevenson (1989.Icarus81, 220–241) of the thermal state of Europa's ice shell indicate that spatial variations in the thickness of the shell may cause it to undergo such a reorientation. We have investigated whether any reorientation of the shell about an axis through the sub- and anti-Jove points produces a stress field consistent with the full, global set of prominent lineations on Europa's surface. We find that no such reorientation provides a good fit between the lineations and plausible fracture orientations derived from the principal stress trajectories. Topographic ridges, identified in a limited zone south of the anti-Jove point, are roughly consistent with compression due to clockwise polar wander, but the orientations of these ridges may be strongly biased by illumination direction. Within the limitations of the presently available imagery, nonsynchronous rotation is still the most likely cause of the prominant fractures on Europa's surface, and the best specific, albeit regionally limited, tectonic evidence consistent with recent polar wander remains the wedge-shaped bands. 相似文献
17.
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. 相似文献
18.
We address impact cratering on Io and Europa, with the emphasis on the origin of small craters on Europa as secondary to the primary impacts of comets on Io, Europa, and Ganymede. In passing we also address the origin of secondary craters generated by Zunil, a well-studied impact crater on Mars that is a plausible analog to impact craters on Io. At nominal impact rates, and taking volcanic resurfacing into account, we find that there should be 1.3 impact craters on Io, equally likely to be of any diameter between 100 m and 20 km. The corresponding model age of Europa's surface is between 60 and 100 Ma. This range of ages does not include a factor three uncertainty stemming from the uncertain sizes and numbers of comets. The mass of basaltic impact ejecta from Io to reach Europa is found to meet or exceed the micrometeoroid flux as a source of rock-forming elements to Europa's ice crust. To describe impact ejecta in more detail we adapt models for impact-generated spalls and Grady-Kipp fragments originally developed by Melosh. Our model successfully reproduces the observed size-number distributions of small craters on both Mars and Europa. However, the model predicts that a significant fraction of the 200-500 m diameter craters on Europa are not traditional secondary craters but are instead sesquinary craters caused by impact ejecta from Io that had gone into orbit about Jupiter. This prediction is not supported by observation, which implies that high speed spalls usually break up into smaller fragments that make smaller sesquinary craters. Iogenic basalts are also interesting because they provide stratigraphic horizons on Europa that in principle could be used to track historic motions of the ice, and they provide materials suitable to radiometric dating of Europa's surface. 相似文献
19.
As the obliquity of Mars is strongly chaotic, it is not possible to give a solution for its evolution over more than a few million years. Using the most recent data for the rotational state of Mars, and a new numerical integration of the Solar System, we provide here a precise solution for the evolution of Mars' spin over 10 to 20 Myr. Over 250 Myr, we present a statistical study of its possible evolution, when considering the uncertainties in the present rotational state. Over much longer time span, reaching 5 Gyr, chaotic diffusion prevails, and we have performed an extensive statistical analysis of the orbital and rotational evolution of Mars, relying on Laskar's secular solution of the Solar System, based on more than 600 orbital and 200,000 obliquity solutions over 5 Gyr. The density functions of the eccentricity and obliquity are specified with simple analytical formulas. We found an averaged eccentricity of Mars over 5 Gyr of 0.0690 with standard deviation 0.0299, while the averaged value of the obliquity is 37.62° with a standard deviation of 13.82°, and a maximal value of 82.035°. We find that the probability for Mars' obliquity to have reached more than 60° in the past 1 Gyr is 63.0%, and 89.3% in 3 Gyr. Over 4 Gyr, the position of Mars' axis is given by a uniform distribution on a spherical cap limited by the obliquity 58.62°, with the addition of a random noise allowing a slow diffusion beyond this limit. We can also define a standard model of Mars' insolation parameters over 4 Gyr with the most probable values 0.068 for the eccentricity and 41.80° for the obliquity. 相似文献
20.
We investigate the response of conductive and convective ice shells on Europa to variations of heat flux and interior tidal-heating rate. We present numerical simulations of convection in Europa's ice shell with Newtonian, temperature-dependent viscosity and tidal heating. Modest variations in the heat flux supplied to the base of a convective ice shell, ΔF, can cause large variations of the ice-shell thickness Δδ. In contrast, for a conductive ice shell, large ΔF involves relatively small Δδ. We demonstrate that, for a fluid with temperature-dependent viscosity, the heat flux undergoes a finite-amplitude jump at the critical Rayleigh number Racr. This jump implies that, for a range of heat fluxes relevant to Europa, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. We show that, as a result, modest variations in heat flux near the critical Rayleigh number can force the ice shell to switch between the thin, conductive and thick, convective configurations over a ∼107-year interval, with thickness changes of up to ∼10-30 km. Depending on the orbital and thermal history, such switches might occur repeatedly. However, existing evolution models based on parameterized-convection schemes have to date not allowed these transitions to occur. Rapid thickening of the ice shell would cause radial expansion of Europa, which could produce extensional tectonic features such as fractures or bands. Furthermore, based on interpretations for how features such as chaos and ridges are formed, several authors have suggested that Europa's ice shell has recently undergone changes in thickness. Our model provides a mechanism for such changes to occur. 相似文献