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A. V. Krivov L. L. Sokolov V. V. Dikarev 《Celestial Mechanics and Dynamical Astronomy》1995,63(3-4):313-339
This paper deals with dynamics of impact ejecta from Phobos and Deimos initially on near-circular equatorial orbits around Mars. For particles emitted in a wide size regime of 1 micron and greater, and taking into account the typical particle lifetimes to be less than 100 years, the motion is governed by two perturbing forces: solar radiation pressure and influence of Mars' oblateness. The equations of motion of particles in Lagrangian non-singular elements are deduced and solved, both analytically and numerically, for different-sized ejecta. We state that the coupled effect of both forces above is essential so that on no account can the oblateness of Mars are be neglected. The dynamics of grains prove to be quite different for the ejecta of Phobos and Deimos. For Deimos, the qualitative results are relatively simple and imply oscillations of eccentricity and long-term variations of orbital inclination, with amplitudes and periods both depending on grain size. For Phobos, the dynamics are shown to be much more complicated, and we discuss it in detail. We have found an intriguous peculiar behavior of debris near 300 µm in size. Another finding is that almost all the Phobos ejecta with radii less than 30 µm (against the values of 5 to 20 µm adopted earlier by many authors) should be rapidly lost by collisions with martian surface. The results of the paper may be the base for constructing an improved model of dust belts that presumably exist around Mars. 相似文献
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Georges Balmino 《Celestial Mechanics and Dynamical Astronomy》1994,60(3):331-364
The spherical harmonic coefficients of the gravitational potential of an homogeneous body are analytically derived from the harmonics describing its shape. General formulas are given as well as detailed expressions up to the fifth order of the topography harmonics. The volume, surface and inertia tensor of the body are obtained as by-products. The case of a triaxial ellipsoid is given as example and used for numerical checking. Another numerical scheme for verification is provided. The application to Phobos is made and the convergence of the expressions for the harmonics is numerically established.
Résumé Les harmoniques du champ de gravitation d'un corps homogène de forme donnée sont calculés analytiquement à partir des harmoniques du développement en série du rayon vecteur exprimant la forme de la surface du corps. Outre la formule générale, des expressions détaillées, au cinquième ordre des harmoniques du rayon vecteur, sont données sous une forme bien adaptée à la programmation. Le volume, la surface et le tenseur d'inertie du corps sont calculés analytiquement `a partir des formules générales. Le cas de l'ellipsoide triaxial est pris comme test des formules établies. Un autre test numérique est fourni dans le cas le plus général. Ceci est appliqué à Phobos, et la convergence des expressions fournissant les harmoniques est numériquement démontrée.相似文献
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M. Giuranna T.L. Roush T. Duxbury R.C. Hogan C. Carli A. Geminale V. Formisano 《Planetary and Space Science》2011,59(13):1308-1325
The origin of the Martian satellites presents a puzzle of long standing. Addressing the composition of Phobos will help constrain theories of its formation. Visible and near-infrared spectra of Phobos lack deep absorption features, making the compositional interpretation a tricky task. PFS/MEx and TES/MGS observations in the thermal infrared show several spectral features that can be used to investigate the composition of the surface. Our results show that the majority of the spectra are consistent with the presence of phyllosilicates, particularly in the area northeast of Stickney. This area corresponds to the “blue” region as defined by Murchie et al. (1999). Analysis of PFS and TES observations in the “red” region defined by Murchie et al. (1999) are consistent with tectosilicates, especially feldspars/feldspathoids. We discuss several physical and chemical mechanisms that can act to eliminate or reduce the strength of bands in the VIS/NIR spectra, with possibly little or no effect in the mid-IR. Comparison of the TES and PFS data to the meteorites shows that no class of chondritic meteorites provide significant agreement with the spectral features observed. The lack of consistency of the PFS and TES spectra to analogs of ultraprimitive materials (organic residues) suggests that an origin via capture of a transneptunian object is not supported by these observations, although it cannot be completely ruled out. Derived surface temperatures from PFS and TES data are in very good agreement with brightness temperatures derived from Viking orbiter measurements, Earth-based observations, and values predicted by numerical models. Our results show that the surface temperature of Phobos varies with solar incidence angle and heliocentric distance, reconciling the different results.We collect and summarize the compositional clues for the origin of Phobos discussed in this paper, including our results. Currently, the most likely scenario is the in-situ formation of Phobos, although a capture of achrondrite-like meteorites is not ruled out. 相似文献
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A great many Martian bow shock and magnetic pile-up boundary crossings have been identified in the Phobos 2 and Mars Global Surveyor, MGS, data. From these observations the positions and shapes of the bow shock and magnetic pile-up boundary, MPB, have been derived and modelled, using curve-fitting techniques. The models thus derived separately from the Phobos 2 and MGS data sets do not differ drastically, despite the different time and space data coverages. The purpose of the paper is therefore to show the results obtained from the mixing of the Phobos 2 and MGS data bases and to compare the derived bow shock and MPB models with the ones obtained previously. The underlying objective was to see whether it was possible to determine improved bow shock and MPB models or not. The answer is definitely yes, and particularly for the MPB, thanks to the complementary nature of the observations. The boundaries crossed close to the subsolar direction or mostly far downstream by Phobos 2 indeed allow a better coverage of the Martian space environment to be considered. Nevertheless, in order to reduce the domination of the overabundant MGS data set and/or the crossings that are close to Mars (x>−4 RM, i.e. x>−13 562 km) weighting factors have been introduced. 相似文献
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Tadashi Yokoyama 《Planetary and Space Science》2002,50(1):63-77
Due to the tides, the orbits of Phobos and Triton are contracting. While their semi major axes are decreasing, several possibilities of secular resonances involving node, argument of the pericenter and mean motion of the Sun will take place. In the case of Mars, if the obliquity (ε), during the passage through some resonances, is not so small, very significant variations of the inclination will appear. In one case, capture is almost certain provided that ε?20°. For Triton there are also similar situations, but capture seems to be not possible, mainly because in S1 state, Triton's orbit is sufficiently inclined (far) with respect to the Neptune's equator. Following Chyba et al. (Astron. Astrophys. 219 (1989) 123), a simplified equation that gives the evolution of the inclination versus the semi major axis, is derived. The time needed for Triton crash onto Neptune is longer than that one obtained by these authors, but the main difference is due to the new data used here. In general, even in the case of non-capture passages, some significant jumps in inclination and in eccentricities are possible. 相似文献
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Robert A. Werner 《Celestial Mechanics and Dynamical Astronomy》1994,59(3):253-278
A polyhedron can model irregularly shaped objects such as asteroids, comet nuclei, and small planetary satellites. With minor effort, such a model can incorporate important surface features such as large craters. Here we develop closed-form expressions for the exterior gravitational potential and acceleration components due to a constant-density polyhedron. An equipotential surface of Phobos is illustrated. 相似文献
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N. Thomas R. Stelter A. Ivanov N.T. Bridges K.E. Herkenhoff A.S. McEwen 《Planetary and Space Science》2011,59(13):1281-1292
The High-Resolution Imaging Science Experiment (HiRISE) onboard Mars Reconnaissance Orbiter (MRO) has been used to observe Phobos and Deimos at spatial scales of around 6 and 20 m/px, respectively. HiRISE (McEwen et al., JGR, 112, CiteID E05S02, DOI: 10.1029/2005JE002605, 2007) has provided, for the first time, high-resolution colour images of the surfaces of the Martian moons. When processed, by the production of colour ratio images for example, the data show considerable small-scale heterogeneity, which might be attributable to fresh impacts exposing different materials otherwise largely hidden by a homogenous regolith. The bluer material that is draped over the south-eastern rim of the largest crater on Phobos, Stickney, has been perforated by an impact to reveal redder material and must therefore be relatively thin. A fresh impact with dark crater rays has been identified. Previously identified mass-wasting features in Stickney and Limtoc craters stand out strongly in colour. The interior deposits in Stickney appear more inhomogeneous than previously suspected. Several other local colour variations are also evident.Deimos is more uniform in colour but does show some small-scale inhomogeneity. The bright “streamers” (Thomas et al., Icarus, 123, 536–556,1996) are relatively blue. One crater to the south-west of Voltaire and its surroundings appear quite strongly reddened with respect to the rest of the surface. The reddening of the surroundings may be the result of ejecta from this impact.The spectral gradients at optical wavelengths observed for both Phobos and Deimos are quantitatively in good agreement with those found by unresolved photometric observations made by the Imager for Mars Pathfinder (IMP; Thomas et al., JGR, 104, 9055–9068, 1999). The spectral gradients of the blue and red units on Phobos bracket the results from IMP. 相似文献
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Michel Hamelin 《Planetary and Space Science》2011,59(13):1293-1307
Although grooves are common on asteroids, on Phobos the grooves have been the subject of various formation hypotheses for two reasons: the fact that Phobos is orbiting around Mars close to the Roche limit, implies an unusual gravity environment as well as the presence of the huge crater impact, Stickney, which seems to be related at least to a family of grooves. Among many hypotheses, it has been suggested that the grooves could have been dug by rolling Stickney ejecta, but this hypothesis was questioned using two main arguments: no block was observed at the end of the grooves, nor do they run downslope. Thus, the study of surface and near surface dynamics on Phobos can clarify the soundness of these controversial arguments.The present study explores this idea by computing the trajectory of a test mass gliding on the surface of Phobos for any initial position and velocity. An ellipsoidal model of Phobos is used for both the gravity and surface geometry, and several orbiting distances from Mars are considered. It is shown that, due to the Phobos rotation, the trajectories generally do not run downslope even for velocities as low as ∼1 m/s. In consequence the corresponding argument against the rolling blocks hypothesis is not applicable. This hypothesis, however, is clearly ruled out for the sets of parallel grooves in the polar regions because of the curvature of the computed trajectories. On the contrary the trajectories issued from the rim of Stickney close to the equator, with velocities of a few m/s, show similitude with the corresponding groove patterns, in particular for the east–west asymmetry. In some conditions the trajectories leave the surface, which may account for regions free of grooves and for trails without blocks at the end. Consequently, the rolling block hypothesis cannot be rejected outright until further analysis is carried out. Damping of the motion on the regolith is simulated introducing a solid damping coefficient in the equations. A relatively small but not unrealistic coefficient of ∼0.1 accounts for the length of the long main western hypothetic block trails. The simulations with damping confirm that the trajectories turn downslope only at the very end for velocities ?1 m/s, but valuable comparison with the observations requires a better model. 相似文献
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