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1.
Solar light gets scattered at cloud top level in Venus’ atmosphere, in the visible range, which corresponds to the altitude of 67 km. We present Doppler velocity measurements performed with the high resolution spectrometer MTR of the Solar telescope THEMIS (Teide Observatory, Canary Island) on the sodium D2 solar line . Observations lasted only 49 min because of cloudy weather. However, we could assess the instrumental velocity sensitivity, per pixel of 1 arcsec, and give a value of the amplitude of zonal wind at equator at .  相似文献   

2.
An explosion on Comet 17P/Holmes occurred on 2007 October 23, projecting particulate debris of a wide range of sizes into the interplanetary medium. We observed the comet using the mid-Infrared Spectrograph (5-40 μm), on 2007 November 10 and 2008 February 27, and the imaging photometer (24 and 70 μm), on 2008 March 13, on board the Spitzer Space Telescope. The 2007 November 10 spectral mapping revealed spatially diffuse emission with detailed mineralogical features, primarily from small crystalline olivine grains. The 2008 February 27 spectra, and the central core of the 2007 November 10 spectral map, reveal nearly featureless spectra, due to much larger grains that were ejected from the nucleus more slowly. Optical images were obtained on multiple dates spanning 2007 October 27-2008 March 10 at the Holloway Comet Observatory and 1.5-m telescope at Palomar Observatory. The images and spectra can be segmented into three components: (1) a hemispherical shell fully 28′ on the sky in 2008 March, due to the fastest (262 m s−1), smallest (2 μm) debris, with a mass ; (2) a ‘blob’ or ‘pseudonucleus’ offset from the true nucleus and subtending some 10′ on the sky, due to intermediate speed (93 m s−1) and size (8 μm) particles, with a total mass ; and (3) a ‘core’ centered on the nucleus due to slower (9 m s−1), larger (200 μm) ejecta, with a total mass . This decomposition of the mid-infrared observations can also explain the temporal evolution of the millimeter-wave flux. The orientation of the leading edge of the ejecta shell and the ejecta ‘blob,’ relative to the nucleus, do not change as the orientation of the Sun changes; instead, the configuration was imprinted by the orientation of the initial explosion. The distribution and speed of ejecta implies an explosion in a conical pattern directed approximately in the solar direction on the date of explosion. The kinetic energy of the ejecta >1021 erg is greater than the gravitational binding energy of the nucleus. We model the explosion as being due to crystallization and release of volatiles from interior amorphous ice within a subsurface cavity; once the pressure in the cavity exceeded the surface strength, the material above the cavity was propelled from the comet. The size of the cavity and the tensile strength of the upper layer of the nucleus are constrained by the observed properties of the ejecta; tensile strengths on >10 m scale must be greater than 10 kPa (or else the ejecta energy exceeds the binding energy of the nucleus) and they are plausibly 200 kPa. The appearance of the 2007 outburst is similar to that witnessed in 1892, but the 1892 explosion was less energetic by a factor of about 20.  相似文献   

3.
4.
The Alice ultraviolet spectrograph onboard the New Horizons spacecraft observed two occultations of the bright star χ Ophiucus by Jupiter’s atmosphere on February 22 and 23, 2007 during the approach phase of the Jupiter flyby. The ingress occultation probed the atmosphere at 32°N latitude near the dawn terminator, while egress probed 18°N latitude near the dusk terminator. A detailed analysis of both the ingress and egress occultations, including the effects of molecular hydrogen, methane, acetylene, ethylene, and ethane absorptions in the far ultraviolet (FUV), constrains the eddy diffusion coefficient at the homopause level to be  cm2 s−1, consistent with Voyager measurements and other analyses (Festou, M.C., Atreya, S.K., Donahue, T.M., Sandel, B.R., Shemansky, D.E., Broadfoot, A.L. [1981]. J. Geophys. Res. 86, 5717-5725; Vervack Jr., R.J., Sandel, B.R., Gladstone, G.R., McConnell, J.C., Parkinson, C.D. [1995]. Icarus 114, 163-173; Yelle, R.V., Young, L.A., Vervack Jr., R.J., Young, R., Pfister, L., Sandel, B.R. [1996]. J. Geophys. Res. 101 (E1), 2149-2162). However, the actual derived pressure level of the methane homopause for both occultations differs from that derived by [Festou et al., 1981] and [Yelle et al., 1996] from the Voyager ultraviolet occultations, suggesting possible changes in the strength of atmospheric mixing with time. We find that at 32°N latitude, the methane concentration is  cm−3 at 70,397 km, the methane concentration is  cm−3 at 70,383 km, the acetylene concentration is  cm−3 at 70,364 km, and the ethane concentration is  cm−3 at 70,360 km. At 18°N latitude, the methane concentration is  cm−3 at 71,345 km, the methane concentration is  cm−3 at 71,332 km, the acetylene concentration is cm−3 at 71,318 km, and the ethane concentration is  cm−3 at 71,315 km. We also find that the H2 occultation light curve is best reproduced if the atmosphere remains cold in the microbar region such that the base of the thermosphere is located at a lower pressure level than that determined by in situ instruments aboard the Galileo probe (Seiff, A., Kirk, D.B., Knight, T.C.D., Young, R.E., Mihalov, J.D., Young, L.A., Milos, F.S., Schubert, G., Blanchard, R.C., Atkinson, D. [1998]. J. Geophys. Res. 103 (E10), 22857-22889) - the Sieff et al. temperature profile leads to too much absorption from H2 at high altitudes. However, this result is highly model dependent and non-unique. The observations and analysis help constrain photochemical models of Jupiter’s atmosphere.  相似文献   

5.
6.
We have completed a series of local N-body simulations of Saturn’s B and A rings in order to identify systematic differences in the degree of particle clumping into self-gravity wakes as a function of orbital distance from Saturn and dynamical optical depth (a function of surface density). These simulations revealed that the normal optical depth of the final configuration can be substantially lower than one would infer from a uniform distribution of particles. Adding more particles to the simulation simply piles more particles onto the self-gravity wakes while leaving relatively clear gaps between the wakes. Estimating the mass from the observed optical depth is therefore a non-linear problem. These simulations may explain why the Cassini UVIS instrument has detected starlight at low incidence angles through regions of the B ring that have average normal optical depths substantially greater than unity at some observation geometries [Colwell, J.E., Esposito, L.W., Srem?evi?, M., Stewart, G.R., McClintock, W.E., 2007. Icarus 190, 127-144]. We provide a plausible internal density of the particles in the A and B rings based upon fitting the results of our simulations with Cassini UVIS stellar occultation data. We simulated Cassini-like occultations through our simulation cells, calculated optical depths, and attempted to extrapolate to the values that Cassini observes. We needed to extrapolate because even initial optical depths of >4 (σ > 240 g cm−2) only yielded final optical depths no greater than 2.8, smaller than the largest measured B ring optical depths. This extrapolation introduces a significant amount of uncertainty, and we chose to be conservative in our overall mass estimates. From our simulations, we infer the surface density of the A ring to be , which corresponds to a mass of . We infer a minimum surface density of for Saturn’s B ring, which corresponds to a minimum mass estimate of . The A ring mass estimate agrees well with previous analyses, while the B ring is at least 40% larger. In sum, our lower limit estimate is that the total mass of Saturn’s ring system is 120-200% the mass of the moon Mimas, but significantly larger values would be plausible given the limitations of our simulations. A significantly larger mass for Saturn’s rings favors a primordial origin for the rings because the disruption of a former satellite of the required mass would be unlikely after the decay of the late heavy bombardment of planetary surfaces.  相似文献   

7.
We have used more than 4 years of Mars Express ion data to estimate the escape of heavy ions ( and ) from Mars. To take the limited field of view of the instrument into account, the data has been binned into spatial bins and angular bins to create average distribution functions for different positions in the near Mars space. The net escape flux for the studied low solar activity period, between May 2007 and May 2011, is 2.0 ± 0.2 × 1024 s−1. The escape has been calculated independently for four different quadrants in the YMSO − ZMSO plane, south, dusk, north and dawn. Escape is highest from the northern and dusk quadrants, 0.6 ± 0.1 × 1024 s−1, and smallest from the south and dawn quadrants, 0.4 ± 0.1 × 1024 s−1. The flux ratio of molecular ( and ) to O+ ions is 0.9 ± 0.1, averaged over all quadrants. The flux difference between the north and south quadrants is statistically significant, and is presumed to be due to the presence of significant crustal magnetic fields in the southern hemisphere, reducing the outflow. The difference between the dawn and dusk quadrants is likely due to the magnetic tension associated with the nominal Parker angle spiral, which should lead to higher average magnetic tension on the dusk side. The escape increases during periods of high solar wind flux and during times when co-rotating interaction regions (CIR) affect Mars. In the latter case the increase is a factor 2.4-2.9 as compared to average conditions.  相似文献   

8.
We present new and definitive results of Cassini plasma spectrometer (CAPS) data acquired during passage through Saturn's inner plasmasphere by the Cassini spacecraft during the approach phase of the Saturn orbit insertion period. This analysis extends the original analysis of Sittler et al. [2005. Preliminary results on Saturn's inner plasmasphere as observed by Cassini: comparison with Voyager. Geophys. Res. Lett. 32, L14S07, doi:10.1029/2005GL022653] to L∼10 along with also providing a more comprehensive study of the interrelationship of the various fluid parameters. Coincidence data are sub-divided into protons and water group ions. Our revised analysis uses an improved convergence algorithm which provides a more definitive and independent estimate of the spacecraft potential ΦSC for which we enforce the protons and water group ions to co-move with each other. This has allowed us to include spacecraft charging corrections to our fluid parameter estimations and allow accurate estimations of fluctuations in the fluid parameters for future correlative studies. In the appendix we describe the ion moments algorithm, and minor corrections introduced by not weighting the moments with sinθ term in Sittler et al. [2005] (Correction offset by revisions to instruments geometric factor). Estimates of the spacecraft potential and revised proton densities are presented. Our total ion densities are in close agreement with the electron densities reported by Moncuquet et al. [2005. Quasi-thermal noise spectroscopy in the inner magnetosphere of Saturn with Cassini/RPWS: electron temperatures and density. Geophys. Res. Lett. 32, L20S02, doi:10.1029/2005GL022508] who used upper hybrid resonance (UHR) emission lines observed by the radio and plasma wave science (RPWS) instrument. We show a positive correlation between proton temperature and water group ion temperature. The proton and thermal electron temperatures track each with both having a positive radial gradient. These results are consistent with pickup ion energization via Saturn's rotational electric field. We see evidence for an anti-correlation between radial flow velocity VR and azimuthal velocity Vφ, which is consistent with the magnetosphere tending to conserve angular momentum. Evidence for MHD waves is also present. We show clear evidence for outward transport of the plasma via flux tube interchange motions with the radial velocity of the flow showing positive radial gradient with functional dependence for 4<L<10 (i.e., if we assume to be diffusive transport then DLLD0L11 for fixed stochastic time step δt). Previous models with centrifugal transport have used DLLD0L3 dependence. The radial transport seems to begin at Enceladus’ L shell, L∼4, where we also see a minimum in the W+ ion temperature . For the first time, we are measuring the actual flux tube interchange motions in the magnetosphere and how it varies with radial distance. These observations can be used as a constraint with regard to future transport models for Saturn's magnetosphere. Finally, we evaluate the thermodynamic properties of the plasma, which are all consistent with the pickup process being the dominant energy source for the plasma.  相似文献   

9.
In November 2005, we observed the moons of Mars using the Arecibo 2380-MHz (13-cm) radar, obtaining a result for the OC radar albedo of Phobos (0.056±0.014) consistent with its previously reported radar albedo and implying an upper bound on its near-surface bulk density of . We detected Deimos by radar for the first time, finding its OC radar albedo to be 0.021±0.006, implying an upper bound on its near-surface density of , consistent with a high-porosity regolith. We briefly discuss reasons for these low radar albedos, Deimos' being possibly the lowest of any Solar System body yet observed by radar.  相似文献   

10.
Ground-based high angular-resolution images of asteroid (2) Pallas at near-infrared wavelengths have been used to determine its physical properties (shape, dimensions, spatial orientation and albedo distribution).We acquired and analyzed adaptive optics (AO) J/H/K-band observations from Keck II and the Very Large Telescope taken during four Pallas oppositions between 2003 and 2007, with spatial resolution spanning 32-88 km (image scales 13-20 km/pixel). We improve our determination of the size, shape, and pole by a novel method that combines our AO data with 51 visual light-curves spanning 34 years of observations as well as archived occultation data.The shape model of Pallas derived here reproduces well both the projected shape of Pallas on the sky (average deviation of edge profile of 0.4 pixel) and light-curve behavior (average deviation of 0.019 mag) at all the epochs considered. We resolved the pole ambiguity and found the spin-vector coordinates to be within 5° of [longitude, latitude] = [30°, −16°] in the Ecliptic J2000.0 reference frame, indicating a high obliquity of about 84°, leading to high seasonal contrast. The best triaxial-ellipsoid fit returns ellipsoidal radii of , and . From the mass of Pallas determined by gravitational perturbation on other minor bodies , [Michalak, G., 2000. Astron. Astrophys. 360, 363-374], we derive a density of significantly different from the density of C-type (1) Ceres of [Carry, B., Dumas, C., Fulchignoni, M., Merline, W.J., Berthier, J., Hestroffer, D., Fusco, T., Tamblyn, P., 2008. Astron. Astrophys. 478 (4), 235-244]. Considering the spectral similarities of Pallas and Ceres at visible and near-infrared wavelengths, this may point to fundamental differences in the interior composition or structure of these two bodies.We define a planetocentric longitude system for Pallas, following IAU guidelines. We also present the first albedo maps of Pallas covering ∼80% of the surface in K-band. These maps reveal features with diameters in the 70-180 km range and an albedo contrast of about 6% with respect to the mean surface albedo.  相似文献   

11.
We report on direct wind measurements in Venus’ mesosphere (90-115 km), performed in support of Venus Express, and based on CO millimeter observations. Most observations, sampling the CO(2-1) and CO(1-0) lines, were acquired with the IRAM 30-m telescope, over four distinct periods: (i) Summer 2006; (ii) May-June 2007, in association with the coordinated ground-based campaign; (iii) August 2007 inferior conjunction and (iv) September 2007. In the latter period, additional measurements (CO(3-2)) were obtained with the APEX 12-m telescope. Overall, the measurements indicate a large body of temporal variability of the Venus mesospheric field, but general features emerge: (i) winds strongly increase with altitude within the mesosphere, by a factor of 2-3 over a decade in pressure; (ii) many, but not all, of our observations can be viewed as the superposition of zonal retrograde and subsolar-to-antisolar (SSAS) flows of comparable speeds, typically 30-50 m/s near 0.1 mbar () and 90-120 m/s near 0.01 mbar () (iii) the wind field was very stable over three consecutive observing days in May-June 2007, but much more variable on a similar time base in August 2007 (iv) at a resolution, the nightside wind field appears very complex, with evidence that the SSAS flow does not reach high latitudes, and possible evidence for additional meridional winds. Our Summer 2006 observations, which sample Venus’ dayside, seem to suggest that a prograde zonal flow is superimposed to the SSAS circulation for this period. This surprising result, which implies a pre-midnight convergence of the wind field, requires confirmation, and fruitful comparisons may be obtained from the analysis of motions in the O2 emission images, as observed by Venus Express.  相似文献   

12.
13.
We present high-speed CCD photometry of Comet 9P/Tempel 1 during the Deep Impact event on 2005 July 4 UT. Approximately 2 h and 50 min of R-band data were acquired at Mount Laguna Observatory with a temporal resolution of 5.5 s. The flux increased by 9% in the first minute after impact. This was followed by a more gradual two-part linear rise, with a change in slope at 9.2 min post-impact, at which time the rate of brightening increased from ∼ to ∼. An analysis of the light curve obtained with the guide camera on the United Kingdom Infrared Telescope and yields very similar results. These findings are mildly in disagreement with the 3-part linear rise found by Fernández et al. (2007) in that we do not find any evidence for a change at 4 min post-impact. We interpret the linear rise phase as due to solar illumination of the edge of an expanding optically thick dust ejecta plume. After approximately 20 min, the light curves begin to flatten out, perhaps coincident with the start of the transition to becoming optically thin. In the large apertures (>10) the light curve continues to gradually rise until the end of the observations. In smaller apertures, the light curves reach a peak at approximately 50 min, then decrease back towards the pre-impact flux level. The drop in flux in the smaller apertures may be caused by the ejecta expanding beyond the edge of the photometric aperture, and if so, we can use this timescale to infer an expansion velocity of ∼, consistent with previous published estimates.  相似文献   

14.
We present new analysis of HST images of (47171) 1999 TC36 that confirm it as a triple system. Fits to the point-spread function (PSF) consistently show that the apparent primary is itself composed of two similar-sized components. The two central components, A1 and A2, can be consistently identified in each of nine epochs spread over 7 years of time. In each instance, the component separation, ranging from 0.023 ± 0.002 to 0.031 ± 0.003 arcsec, is roughly one half of the Hubble Space Telescope’s diffraction limit at 606 nm. The orbit of the central pair has a semi-major axis of a  867 km with a period of P ∼ 1.9 days. These orbital parameters yield a system mass that is consistent with Msys = 12.75 ± 0.06 × 1018 kg derived from the orbit of the more distant secondary, component B. The diameters of the three components are . The relative sizes of these components are more similar than in any other known multiple in the Solar System. Taken together, the diameters and system mass yield a bulk density of . HST photometry shows that component B is variable with an amplitude of ?0.17 ± 0.05 magnitudes. Components A1 and A2 do not show variability larger than 0.08 ± 0.03 magnitudes approximately consistent with the orientation of the mutual orbit plane and tidally distorted equilibrium shapes. The system has high specific angular momentum of J/J′ = 0.93, comparable to most of the known transneptunian binaries.  相似文献   

15.
16.
We propose a new scenario for compound chondrule formation named as “fragment-collision model,” in the framework of the shock-wave heating model. A molten cm-sized dust particle (parent) is disrupted in the high-velocity gas flow. The extracted fragments (ejectors) are scattered behind the parent and the mutual collisions between them will occur. We modeled the disruption event by analytic considerations in order to estimate the probability of the mutual collisions assuming that all ejectors have the same radius. In the typical case, the molten thin () layer of the parent surface will be stripped by the gas flow. The stripped layer is divided into about 200 molten ejectors (assuming that the radius of ejectors is 300 μm) and then they are blown away by the gas flow in a short period of time (). The stripped layer is leaving from the parent with the velocity of depending on the viscosity, and we assumed that the extracted ejectors have a random velocity Δv of the same order of magnitude. Using above values, we can estimate the number density of ejectors behind the parent as . These ejectors occupy ∼9% of the space behind the parent in volume. Considering that the collision rate (number of collisions per unit time experienced by an ejector) is given by Rcoll=σcollnv, where σcoll is the cross-section of collision [e.g., Gooding, J.K., Keil, K., 1981. Meteoritics 16, 17-43], we obtain by substituting above values. Since most collisions occur within the short duration () before the ejectors are blown away, we obtain the collision probability of Pcoll∼0.36, which is the probability of collisions experienced by an ejector in one disruption event. The estimated collision probability is about one order of magnitude larger than the observed fraction of compound chondrules. In addition, the model predictions are qualitatively consistent with other observational data (oxygen isotopic composition, textural types, and size ratios of constituents). Based on these results, we concluded that this new model can be one of the strongest candidates for the compound chondrule formation. It should be noted that all collisions do not necessarily lead to the compound chondrule formation. The formation efficiency and the future works which should be investigated in the forthcoming paper are also discussed.  相似文献   

17.
Stéfan Renner  Bruno Sicardy 《Icarus》2005,174(1):230-240
Hubble Space Telescope (HST) images of Prometheus and Pandora show longitude discrepancies of about 20° with respect to the Voyager ephemerides, with an abrupt change in mean motion at the end of 2000 (French et al., 2003, Icarus 162, 143-170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07). These discrepancies are anti-correlated and arise from chaotic interactions between the two moons, occurring at interval of 6.2 yr, when their apses are anti-aligned (Goldreich and Rappaport, 2003a, Icarus 162, 391-399). This behavior is attributed to the overlap of four 121:118 apse-type mean motion resonances (Goldreich and Rappaport, 2003b, Icarus 166, 320-327). We study the Prometheus-Pandora system using a Radau-type integrator taking into account Saturn's oblateness up to and including terms in J6, plus the effects of the major satellites. We first confirm the chaotic behavior of Prometheus and Pandora. By fitting the numerical integrations to the HST data (French et al., 2003, Icarus 162, 143-170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07), we derive the satellite masses. The resulting GM values (with their standard 3-σ errors) for Prometheus and Pandora are respectively and . Using the nominal shape of the two moons (Thomas, 1989, Icarus 77, 248-274), we derive Prometheus and Pandora's densities, 0.40+0.03−0.07 and 0.49+0.05−0.09 g cm−3, respectively. Our numerical fits also enable us to constrain the time of the latest apse anti-alignment in 2000. Finally, using our fit, we predict the orbital positions of the two satellites during the Cassini tour, and provide a lower limit of the uncertainties due to chaos. These uncertainties amount to about 0.2° in mean longitude at the arrival of the Cassini spacecraft in July 2004, and to about 3° in 2008, at the end of the nominal tour.  相似文献   

18.
19.
We report on observations of the dust trail of Comet 67P/Churyumov-Gerasimenko (CG) in visible light with the Wide Field Imager at the ESO/MPG 2.2 m telescope at 4.7 AU before aphelion, and at with the MIPS instrument on board the Spitzer Space Telescope at 5.7 AU both before and after aphelion. The comet did not appear to be active during our observations. Our images probe large dust grains emitted from the comet that have a radiation pressure parameter β<0.01. We compare our observations with simulated images generated with a dynamical model of the cometary dust environment and constrain the emission speeds, size distribution, production rate and geometric albedo of the dust. We achieve the best fit to our data with a differential size distribution exponent of −4.1, and emission speeds for a β=0.01 particle of 25 m/s at perihelion and 2 m/s at 3 AU. The dust production rate in our model is on the order of 1000 kg/s at perihelion and 1 kg/s at 3 AU, and we require a dust geometric albedo between 0.022 and 0.044. The production rates of large (>) particles required to reproduce the brightness of the trail are sufficient to also account for the coma brightness observed while the comet was inside 3 AU, and we infer that the cross-section in the coma of CG may be dominated by grains of the order of .  相似文献   

20.
D.G. Korycansky  Erik Asphaug 《Icarus》2006,181(2):605-617
We present results of modeling rubble piles as collections of polyhedra. The use of polyhedra allows more realistic (irregular) shapes and interactions (e.g. collisions), particularly for objects of different sizes. Rotational degrees of freedom are included in the modeling, which may be important components of the motion. We solved the equations of rigid-body dynamics, including frictional/inelastic collisions, for collections of up to several hundred elements. As a demonstration of the methods and to compare with previous work by other researchers, we simulated low-speed collisions between km-scale bodies with the same general parameters as those simulated by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151]. High-speed collisions appropriate to present-day asteroid encounters require additional treatment of shock effects and fragmentation and are the subject of future work; here we study regimes appropriate to planetesimal accretion and re-accretion in the aftermath of catastrophic events. Collisions between equal-mass objects at low speeds () were simulated for both head-on and off-center collisions between rubble piles made of a power-law mass spectrum of sub-elements. Very low-speed head-on collisions produce single objects from the coalescence of the impactors. For slightly higher speeds, extensive disruption occurs, but re-accretion produces a single object with most of the total mass. For increasingly higher speeds, the re-accreted object has smaller mass, finally resulting in complete catastrophic disruption with all sub-elements on escape trajectories and only small amounts of mass in re-accreted bodies. Off-center collisions at moderately low speeds produce two re-accreted objects of approximately equal mass, separating at greater than escape speed. At high speed, complete disruption occurs as with the high-speed head-on collisions. Head-on collisions at low to moderate speeds result in objects of mostly oblate shape, while higher speed collisions produce mostly prolate objects, as do off-center collisions at moderate and high speeds. Collisions carried out with the same dissipative coefficients (coefficient of restitution ?n=0.8, zero friction) as used by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151] result in a value for specific energy for disruption , somewhat lower than the value of 2 J/kg found by them, while collisions with a lower coefficient of restitution and friction [?n=0.5, ?t=0, μ=0.5, similar to those used by Michel, et al. [Michel, P., Benz, W., Richardson, D.C., 2004. Planet. Space Sci. 52, 1109-1117] for SPH + N-body calculations] yield .  相似文献   

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