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1.
Steven Soter  Alan Harris 《Icarus》1977,30(1):192-199
The shape of a close planetary satellite is distorted from a self-gravitating sphere into a triaxial ellipsoid maintained by tidal and centrifugal forces. Using the family of Roche ellipsoids calculated by Chandrasekhar, it should be possible in some cases to determine the density of an inner satellite by an accurate measurement of its shape alone. The equilibrium figure of Phobos is expected to be the most extreme of any satellite. The shape of Phobos as observed by Mariner 9 approaches but appears not to be a Roche ellipsoid, although the uncertainties of measurement remain too large to exclude the possibility. In any case, Phobos is so small that even the low mechanical strength of an impact-compressed regolith is sufficient to maintain substantial departures from the equipotential figure. If larger close satellites, particularly Amalthea, are found to be Roche ellipsoids, their densities can be estimated immediately from the data presented.Asteroids of size comparable to Phobos and Deimos appear to have more irregular shapes than the Martian satellites. This may reflect the absence of a deep regolith on those asteroids due to the low effective escape velocity for impact ejecta. For Phobos and Deimos, on the other hand, ejecta will tend to remain in orbit about Mars until swept up again by the satellite, contributing to a deeper equilibrium layer of debris.  相似文献   

2.
M. Noland  J. Veverka 《Icarus》1976,28(3):401-403
Using Mariner 9 results on the shapes, rotation periods and photometric functions of Phobos and Deimos we calculate approximate orbital lightcurves for the two Martian satellites. The prediction is that both Phobos and Deimos should show orbital brightness fluctuations detectable from Earth. For Phobos the detectable amplitude is predicted to be about 0.1 mag; for Deimos, 0.2 mag.  相似文献   

3.
Peter Thomas 《Icarus》1979,40(2):223-243
Viking Orbiter images have provided nearly complete coverage of the two satellites of Mars and have been used to construct maps of the surface features of Phobos and Deimos. The satellites have radically different appearances although nearly all features on both objects were formed directly or indirectly by impact cratering. Phobos has an extensive network of linear depressions (grooves) that probably were formed indirectly by the largest impact recorded on Phobos. Deimos lacks grooves as well as the large number of ridges that occur on Phobos. Craters on Deimos have substantial sediment fill; those on Phobos have none. Evidence of downslope movement of debris is prominent on Deimos but is rare on Phobos. Many of the differences between Phobos and Deimos may be caused by modest differences in mechanical properties. However, the lack of a very large crater on Deimos may be responsible for its lack of grooves.  相似文献   

4.
P. Thomas  J. Veverka 《Icarus》1977,30(3):595-597
The preliminary conclusion of the Mariner 9 Television Team that the surfaces of Phobos and Deimos are saturated with craters larger than 0.2 km in diameter is reconsidered on the basis of more extensive and uniform crater counts. For Phobos, it is verified that the surface appears saturated with craters larger than 1 km in diameter. For craters smaller than 1 km, the data points fall below the saturation curve, and it is not clear that all the departure can be explained in terms of loss of resolution. For Deimos, because of the paucity of craters visible in the Mariner 9 images, a statistically meaningful crater density curve cannot be constructed. Definitive crater density curves for subkilometer craters can only be established once additional imagery at a resolution of better than 100 m is obtained. Such imagery will be provided by the 1976 Viking Orbiters.  相似文献   

5.
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   

6.
The numerous problems related to the origin and evolution of Phobos and Deimos, as well as to specific features of their topography, are readily accounted for in the context of a concept presupposing the possibility of detonation (or burning) of electrolyzed ices.The explosion of an icy asteroid of mass m A \> 1023 g within the gravitational sphere of Mars resulted in the capture of secondary fragments into satellite orbits and the formation of a ring of icy and rocky particles. The motion of satellites in the ring reduced the eccentricities of their orbits and rendered their mutual collisions impossible. The thick regolith of Deimos is the material captured from the ring.The impact responsible for the Stickney crater on Phobos initiated a detonation in the material in the crater, and the detonation, in its turn, ignited the products of electrolysis in the bulk of the satellite. Phobos lost its regolith because of detonation-induced acceleration. As a result of the burning out of Phobos's ices, its density somewhat exeeds that of Deimos.Different grooves on Phobos have differing origins. The grooves of groups B, E, D (as specified by P. Thomas et al., J. Geophys. Res., 84, 8457–8477, 1979) are due to fracturing caused by the Sickney event; group C (which is normal to the minor axis of the Phobos ellipsoid) reflects the layered nature of the parent asteroid; while the closely arranged group A grooves, which are normal to Phobos's major axis, were formed during the contraction of the satellite as a result of the loss of burnt-out ices. A number of conclusions are drawn which can be tested by future missions to the satellites.  相似文献   

7.
The distribution of ejecta from impact craters significantly affects the surface characters of satellites and asteroids. In order to understand better the distinctive features seen on Phobos, Deimos, and Amalthea, we study the dynamics of nearby debris but include several factors — planetary tides plus satellite rotation and nonspherical shape-that complicate the problem. We have taken several different approaches to investigate the behavior of ejecta from satellites near planets. For example, we have calculated numerically the usual pseudoenergy (Jacobi) integral. This is done in the framework of a restricted three-body problem where we model the satellites as triaxial ellipsoids rather than point masses as in past work. Iso-contours of this integral show that Deimos and Amalthea are entirely enclosed by their Roche lobes, and the surfaces of their model ellipsoids lie nearly along equipotentials. Presumably this was once also the case for Phobos, before tidal evolution brought it so close to Mars. Presently the surface of Phobos overflows its Roche lobe, except for the regions within a few kilometers of the sub- and anti-Mars points. Thus most surface material on Phobos is not energetically bound: nevertheless it is retained by the satellite because local gravity has an inward component everywhere. Similar situations probably prevail for the newly discovered satellite of Jupiter (J14) and for the several objects found just outside Saturn's rings. We have also examined the fate of crater ejecta from the satellites of Mars by numerical integration of trajectories for particles leaving their surfaces in the equatorial plane. The ejecta behavior depends dramatically on the longitude of the primary impact, as well as on the speed and direction of ejection. Material thrown farther than a few degrees of longitude remains in flight for an appreciable time. Over intervals of an hour or more, the satellites travel through substantial arcs of their orbits, so that the Coriolis effect then becomes important. For this reason the limit of debris deposition is elongated toward the west while debris thrown to the east escapes at lower ejection velocities. We display some typical trajectories, which include many interesting special effects, such as loops, cusps, “folded” ejecta blankets, and even a temporary satellite of Deimos. Besides being important for understanding the formation of surface features on satellites, our work is perhaps pertinent to regolith development on small satellites and asteroids, and also to the budgets of dust belts around planets.  相似文献   

8.
We re-assess expected properties of the presumed dust belt of Mars formed by impact ejecta from Deimos. Previous studies have shown that dynamics of Deimos particles are dominated by two perturbing forces: radiation pressure (RP) and Mars’ oblateness (J2). At the same time, they have demonstrated that lifetimes of particles, especially of grains about ten of micrometers in size, may reach more than 104 years. On such timescales, the Poynting-Robertson drag (PR) becomes important. Here we provide a study of the dynamics under the combined action of all three perturbing forces. We show that a PR decay of the semimajor axes leads to an adiabatic decrease of amplitudes and periods of oscillations in orbital inclinations predicted in the framework of the underlying RP+J2 problem. Furthermore, we show that smallest of the long-lived Deimos grains (radius≈5- may reach a chaotic regime, resulting in unpredictable and abrupt changes of their dynamics. The particles just above that size (≈10-) should be the most abundant in the Deimos torus. Our dynamical analysis, combined with a more accurate study of the particle lifetimes, provides corrections to earlier predictions about the dimensions and geometry of the Deimos torus. In addition to a population, appreciably inclined and shifted towards the Sun, the torus should contain a more contracted, less asymmetric, and less tilted component between the orbits of Phobos and Deimos.  相似文献   

9.
The origin of Phobos and Deimos is considered with a view to accounting for the existence of very small satellites with circular orbits in the Martian equatorial plane, and simultaneously for the suspected angular momentum deficiency of the Mars system. All models considered failed to satisfy at least one requirement, and the problem is considered more puzzling than is at first apparent. The Martian angular momentum deficiency, if physically significant, may be unrelated to the present satellites' origin, but might relate to a large ancient satellite, long ago destroyed. Accretion onto Mars of large amounts of asteroidal dust brought in by Poynting-Robertson drag may have some bearing on the angular momentum problem.  相似文献   

10.
The density of craters larger than 1 km in diameter has been determined for the entire surface of Phobos, and half that of Deimos. Densities of craters as small as 10 m on Phobos and 5 m on Deimos have been measured for small areas of the satellites. On both objects, crater densities are similar and yield plots which have slopes close to -1.9 on both incremental and cumulative log-log graphs. These densities are close to those expected to obtain under equilibrium conditions. They are also near the maximum predicted, based on the fragmentation lifetimes of the two objects: that is, the densities are near to the maximum possible before such objects are likely to suffer an impact severe enough to disrupt them. While the observed crater densities cannot be converted to absolute ages in any rigorous fashion, they can be understood if the flux at Mars has been similar to that at the Moon and if the surfaces that we see today generally date back to the end of the period of heavy bombardment some 4 billion years ago. It is extremely unlikely that the surfaces are younger than 1 billion years. There are no large areas on Phobos for which crater densities differ by more than a factor of 3 from the average.  相似文献   

11.
We have observed the leading and trailing hemispheres of Phobos from 1.65 to 3.5 μm and Deimos from 1.65 to 3.12 μm near opposition. We find the trailing hemisphere of Phobos to be brighter than its leading hemisphere by 0.24±0.06 magnitude at 1.65 μm and brighter than Deimos by 0.98±0.07 magnitude at 1.65 μm. We see no difference larger than observational uncertainties in spectral slope between the leading and trailing hemispheres when the spectra are normalized to 1.65 μm. We find no 3-μm absorption feature due to hydrated minerals on either hemisphere to a level of ∼5-10% on Phobos and ∼20% on Deimos. When the infrared data are joined to visible and near-IR data obtained by previous workers, our data suggest the leading (Stickney-dominated) side of Phobos is best matched by T-class asteroids. The spectral slope of the trailing side of Phobos and leading side of Deimos are bracketed by the D-class asteroids. The best laboratory spectral matches to these parts of Phobos are mature lunar soils and heated carbonaceous chondrites. The lack of 3-μm absorption features on either side of Phobos argues against the presence of a large interior reservoir of water ice according to current models of Phobos' interior (F. P. Fanale and J. R. Salvail 1989, Geophys. Res. Lett.16, 287-290; Icarus88, 380-395).  相似文献   

12.
This paper contains a complete set of the best enhancements of Mariner 9 high resolution television pictures of Phobos and Deimos, consisting of 27 different views of Phobos, and 9 of Deimos. Pertinent data about the pictures are arranged in convenient tabular and graphical form.  相似文献   

13.
Robert A. Craddock 《Icarus》2011,211(2):1150-1161
Despite many efforts an adequate theory describing the origin of Phobos and Deimos has not been realized. In recent years a number of separate observations suggest the possibility that the martian satellites may have been the result of giant impact. Similar to the Earth–Moon system, Mars has too much angular momentum. A planetesimal with 0.02 Mars masses must have collided with that planet early in its history in order for Mars to spin at its current rate (Dones, L., Tremaine, S. [1993]. Science 259, 350–354). Although subject to considerable error, current crater-scaling laws and an analysis of the largest known impact basins on the martian surface suggest that this planetesimal could have formed either the proposed 10,600 by 8500-km-diameter Borealis basin, the 4970-km-diameter Elysium basin, the 4500-km-diameter Daedalia basin or, alternatively, some other basin that is no longer identifiable. It is also probable that this object impacted Mars at a velocity great enough to vaporize rock (>7 km/s), which is necessary to place large amounts of material into orbit. If material vaporized from the collision with the Mars-spinning planetesimal were placed into orbit, an accretion disk would have resulted. It is possible that as material condensed and dissipated beyond the Roche limit forming small, low-mass satellites due to gravity instabilities within the disk. Once the accretion disk dissipated, tidal forces and libration would have pulled these satellites back down toward the martian surface. In this scenario, Phobos and Deimos would have been among the first two satellites to form, and Deimos the only satellite formed—and preserved—beyond synchronous rotation. The low mass of Phobos and Deimos is explained by the possibility that they are composed of loosely aggregated material from the accretion disk, which also implies that they do not contain any volatile elements. Their orbital eccentricity and inclination, which are the most difficult parameters to explain easily with the various capture scenarios, are the natural result of accretion from a circum-planetary disk.  相似文献   

14.
M. Noland  J. Veverka 《Icarus》1977,30(1):212-223
At least three large areas on the surface of Phobos are covered by a dark material of complex texture which scatters light according to the Hapke-Irvine Law. The average 20° to 80° intrinsic and disc-integrated phase coefficients of this material are βi = 0.020 ± 0.001 mag/deg and β = 0.033 mag/deg, respectively. These values are slightly greater than the values found for Deimos in Paper II (preceding article). On the largest scale the surface of Phobos is rougher than the surface of Deimos, perhaps accounting for the slightly greater phase coefficients. Contrary to the situation on Deimos, no definite regions of intrinsically brighter material are apparent on Phobos. This difference could account for the slightly lower average reflectance of Phobos relative to Deimos. No evidence for large exposures of solid rock has been found in the three areas studied.  相似文献   

15.
The determination of the ephemeris of the Martian moons has benefited from observations of their plane-of-sky positions derived from images taken by cameras onboard spacecraft orbiting Mars. Images obtained by the Super Resolution Camera (SRC) onboard Mars Express (MEX) have been used to derive moon positions relative to Mars on the basis of a fit of a complete dynamical model of their motion around Mars. Since, these positions are computed from the relative position of the spacecraft when the images are taken, those positions need to be known as accurately as possible. An accurate MEX orbit is obtained by fitting two years of tracking data of the Mars Express Radio Science (MaRS) experiment onboard MEX. The average accuracy of the orbits has been estimated to be around 20–25 m. From these orbits, we have re-derived the positions of Phobos and Deimos at the epoch of the SRC observations and compared them with the positions derived by using the MEX orbits provided by the ESOC navigation team. After fit of the orbital model of Phobos and Deimos, the gain in precision in the Phobos position is roughly 30 m, corresponding to the estimated gain of accuracy of the MEX orbits. A new solution of the GM of the Martian moons has also been obtained from the accurate MEX orbits, which is consistent with previous solutions and, for Phobos, is more precise than the solution from the Mars Global Surveyor (MGS) and Mars Odyssey (ODY) tracking data. It will be further improved with data from MEX-Phobos closer encounters (at a distance less than 300 km). This study also demonstrates the advantage of combining observations of the moon positions from a spacecraft and from the Earth to assess the real accuracy of the spacecraft orbit. In turn, the natural satellite ephemerides can be improved and participate to a better knowledge of the origin and evolution of the Martian moons.  相似文献   

16.
《Planetary and Space Science》2006,54(9-10):844-854
It has long been suspected that Mars might be encircled by two faint rings, one originating from each of its moons Phobos and Deimos. Meteoroid impacts into these moons should release clouds of dust that quickly spread out to become rings; similar dust rings have been associated with several small inner moons of the gas giants. On May 28, 2001 Mars’ hypothetical ring plane appeared edge-on to Earth within weeks of its opposition, providing the best Earth-based opportunity to detect these rings in several decades. Using the Wide Field/Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, we obtained a set of deep exposures off the east and west limbs of Mars to search for these hypothetical rings. No rings were detected. This result limits normal optical depths to ∼3×10−8 for the Phobos ring and ∼10−7 for the Deimos ring. These limits fall at the low end of prior dynamical predictions and a factor of 1000 below previous observational limits. However, our limit for the Deimos ring is more tentative because of large uncertainties about this ring's expected shape, size and orientation. Our data set is also sensitive to small, previously undetected inner moons. No moons were detected down to a radius limit of 75–125 m. Longitudinal coverage of the region near and between Phobos and Deimos is 40–80% complete. We conclude by describing a promising opportunity for further Martian ring viewing in December 2007.  相似文献   

17.
Donald M. Hunten 《Icarus》1979,37(1):113-123
It is suggested that Phobos and Deimos are carbonaceous asteroids captured by drag in an extended protoatmosphere of solar composition. The time scales for regularization of the orbital parameters are estimated, and found to be of the order of a few years. The atmosphere is modeled as a slowly-rotating condensation in the solar nebula; the surface pressure should be a few tenths of a bar. Capture and evolution by such an atmosphere are found to be improbable. The odds are greatly improved if the atmosphere is rapidly rotating or if the pressure is 1 to 2 orders of magnitude greater. Escape of the atmosphere, after removal of the nebular pressure, takes a few years, depending on the solar heat input. But it relaxes much more quickly to a state with negligible density at satellite altitudes. This relaxation is taken as the event that leaves the satellites in stable orbits. Previous candidates presumably were added to the solid body of Mars, and later ones were not captured.  相似文献   

18.
Construction of an accurate theory of orbits about a precessing and nutating oblate planet, in terms of osculating elements defined in a frame associated with the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2004, 2005, 2006a, b). Here we continue this line of research by combining that analytical machinery with numerical tools. Our model includes three factors: the J 2 of the planet, its nonuniform equinoctial precession described by the Colombo formalism, and the gravitational pull of the Sun. This semianalytical and seminumerical theory, based on the Lagrange planetary equations for the Keplerian elements, is then applied to Deimos on very long time scales (up to 1 billion years). In parallel with the said semianalytical theory for the Keplerian elements defined in the co-precessing equatorial frame, we have also carried out a completely independent, purely numerical, integration in a quasi-inertial Cartesian frame. The results agree to within fractions of a percent, thus demonstrating the applicability of our semianalytical model over long timescales. Another goal of this work was to make an independent check of whether the equinoctial-precession variations predicted for a rigid Mars by the Colombo model could have been sufficient to repel its moons away from the equator. An answer to this question, in combination with our knowledge of the current position of Phobos and Deimos, will help us to understand whether the Martian obliquity could have undergone the large changes ensuing from the said model (Ward 1973; Touma and Wisdom 1993, 1994; Laskar and Robutel 1993), or whether the changes ought to have been less intensive (Bills 2006; Paige et al. 2007). It has turned out that, for low initial inclinations, the orbit inclination reckoned from the precessing equator of date is subject only to small variations. This is an extension, to non-uniform equinoctial precession given by the Colombo model, of an old result obtained by Goldreich (1965) for the case of uniform precession and a low initial inclination. However, near-polar initial inclinations may exhibit considerable variations for up to ±10 deg in magnitude. This result is accentuated when the obliquity is large. Nevertheless, the analysis confirms that an oblate planet can, indeed, afford large variations of the equinoctial precession over hundreds of millions of years, without repelling its near-equatorial satellites away from the equator of date: the satellite inclination oscillates but does not show a secular increase. Nor does it show secular decrease, a fact that is relevant to the discussion of the possibility of high-inclination capture of Phobos and Deimos. We use the term “precession” in its general meaning, which includes any change of the instantaneous spin axis. So generally defined precession embraces the entire spectrum of spin-axis variations—from the polar wander and nutations through the Chandler wobble through the equinoctial precession.  相似文献   

19.
Recent Viking results indicate the Martian satellites are composed of carbonaceous chondritic material, suggesting that Phobos and Deimos were once asteroids captured by Mars. On the other hand, the low eccentricities and inclinations of their orbits on the equator of Mars argue against that hypothesis. This paper presents detailed calculations of the tidal evolution of Phobos and Deimos, considering dissipation in both Mars and its satellites simultaneously and using a new method applicable for any value of the eccentricity. In particular, including precession of the satellites' orbits indicates that they have always remained close to their Laplacian plane, so that the orbital planes of Phobos and Deimos switched from near the Martian orbital plane to the Martian equator once the perturbations due to the planetary oblateness dominated the solar perturbations, as they do presently. The results show that Deimos has been little affected by tides, but several billion (109) years ago, Phobos was in a highly eccentric orbit lying near the common plane of the solar system. This outcome is obtained for very reasonable values of dissipation inside Mars and inside Phobos. Implications for the origin of the Martian satellites are discussed.  相似文献   

20.
An extensive analysis of the motion of Phobos and Deimos from 1877 to 1973 has been fulfilled. The new values of the parameters of the orbital model first developed by Struve have been determined for both satellites. The new sets of the orbital parameters compete with the solutions of similar accuracy found by Wilkins and Sinclair. A secular acceleration in longitude of Phobos is found to be equal to +(0.107±0.011)×10?7 deg day?2. The value of the acceleration is little affected when one or another group of oppositions is omitted. The acceleration of Deimos is determined with great uncertainty: +(0.06±0.34)×10?9 deg day?2. Values found for the orbital parameters seem to be in good agreement since the mass, oblateness and coordinates of the pole of Mars inferred from the motion of each satellite have similar values in both cases.  相似文献   

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