The equilibrium figures of Phobos and other small bodies

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.     

Motion of blocks on the surface of Phobos: New constraints for the formation of grooves

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.     

Dynamics of Mars-orbiting dust: Effects of light pressure and planetary oblateness

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.     

Life near the Roche limit: Behavior of ejecta from satellites close to planets

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.     

Detecting crater ejecta‐blanket boundaries and constraining source crater regions for boulder tracks and elongated secondary craters on Eros

Abstract– We present results of a numerical model of the dynamics of ejecta emplacement on asteroid 433 Eros. Ejecta blocks represent the coarsest fraction of Eros’ regolith and are important, readily visible, “tracer particles” for crater ejecta‐blanket units that may be linked back to specific source craters. Model results show that the combination of irregular shape and rapid rotation of an asteroid can result in markedly asymmetric ejecta blankets (and, it follows, ejecta block spatial distribution), with locally very sharp/distinct boundaries. We mapped boulder number densities in NEAR‐Shoemaker MSI images across a portion of a predicted sharp ejecta‐blanket boundary associated with the crater Valentine and confirm a distinct and real ejecta‐blanket boundary, significant at least at the 3‐sigma level. Using our dynamical model, we “back track” the landing trajectories of three ejecta blocks with associated landing tracks in an effort to constrain potential source regions where those blocks were ejected from Eros’ surface in impact events. The observed skip distances of the blocks upon landing on Eros’ surface and the landing speeds and elevation angles derived from our model allow us to estimate the coefficient of restitution, ε, of Eros’ surface for impacts of 10‐m‐scale blocks at approximately 5 m s^?1 impact speeds. We find mean values of ε of approximately 0.09–0.18.     

Mass-Wasting Processes on the Surface of Phobos

This paper considers morphologic signatures of mass-wasting processes on the surface of Phobos. Two types of downslope movement of material are distinguished: (i) intracrater volume landslides inside impact craters and (ii) downslope near-surface movement of material. Crater statistics for the Stickney area (based on new images of Phobos) showed that the landslide in the crater Stickney could have been formed after resurfacing of the outer rim of the crater in the process of meteorite bombardment. An estimate of the volume of the landslide in Stickney (1–2 km³) and simulation of its movement allowed us to classify the landslide as a long-runout one. The possibility of forming a hummocky topographic relief to the east of Stickney due to the crater ejecta and the emplacement of the frontal part of the long-runout landslide is discussed.     

Tidal rigidity of phobos

The Martian satellites Phobos and Deimos move along nearly circular coplanar, stable orbits and have created surfaces older than ～ 10⁹ years. The accretion hypothesis suggests that their primordial orbits were also very regular. However, tides raised on Mars and Phobos can substantially alter the semimajor axis a of Phobos' orbit over time. The effect of the Martian tidal torque alone on Phobos' orbit implies that the primordial e was ～0.1 to 0.2 about 4.6 × 10⁹ years ago if the present observed e = 0.015 is naively interpreted as a tidally damped remnant. Significant tidal friction in Phobos reduces the time scale for Phobos to achieve a crossing orbit with Deimos to less than 10⁹ years and permits the primodial e to approach unity. The consequences of orbital intersections cannot easily be resolved by assuming either a catastrophic origin for both satellites (namely, that both are fragments of a common parent body fractured by an impact) or that they were captured sequentially by Mars. Either hypothesis is difficult to accept, given that Deimos' orbit, which is only slightly affected by tides, is now so regular. An alternative scenario is proposed in this paper in which the observed e of Phobos results from several gravitational resonance excitations within the last 10⁹ years, assuming tidal friction in Phobos has had only a small effect on its orbit. In facr, both the primordial e and the inclination i may have been much smaller than presently observed. The constraints imposed on tidal friction in Phobos by both the apparent age of Phobos' surface (> 10⁹yrs) and the above scenario can be satisfied only of μQ > 10¹²dynes/cm². Since the Q factor is ～10², the rigidity μ > 10¹⁰dynes/cm². Thus Phobos should have substantial internal strength.     

Phobos,Deimos, and the Moon: Size and distribution of crater ejecta blocks

The size and radial distributions of ejecta blocks around craters (D = 0.8 to 10 km) on Phobos and Deimos have been compared to those around lunar craters (D = 0.2 to 3.5 km). The radial distribution of blocks was found to be similar on Phobos and the Moon, but more dispersed on Deimos. For the best imaged crater on Deimos (D = 800 m), the size distributions of blocks and the fraction of excavated volume present as blocks are similar to those on the Moon. The wider dispersal of blocks on Deimos is consistent with other findings on the spread of finer ejecta over the satellite.     

Determination of spacecraft and phobos parameters of motion in the Phobos-Grunt project

For the needs of the upcoming flight to Phobos within the framework of the project Phobos-Grunt, a dynamical numerical theory of the motion of Phobos is developed on the basis of Earth-based and spacecraft (SC) optical measurements and Earth-based radio observations of the SC motion. The theory uses the most reliable astronomical constants. Within the framework of a unified dynamical model, an algorithm is proposed for the joint correction of Phobos and the spacecraft parameters of motion, among which are the secular acceleration of Phobos and its gravitational constant. The accuracy of the obtained ephemeris is estimated for the time of the SC arrival to Phobos.     

Search for Phobos and Deimos gas/dust tori using in situ observations from Mars Global Surveyor MAG/ER

More than 490 elliptical aerobraking and science phasing orbits made by Mars Global Surveyor (MGS) in 1997 and 1998 provide unprecedented coverage of the solar wind in the vicinity of the orbits of the martian moons Phobos and Deimos. We have performed a comprehensive survey of magnetic field perturbations in the solar wind to search for possible signatures of solar wind interaction with dust or gas escaping from the moons. A total of 1246 solar wind disturbance events were identified and their distribution was examined relative to Phobos, the Phobos orbit, and the Deimos orbit. We find that the spatial distribution of solar wind perturbations does not increase near or downstream of Phobos, Phobos’ orbit, or Deimos’ orbit, which would have been expected if there is significant outgassing or dust escape from the martian moons. Of the 1246 magnetic field perturbation events found in the MGS data set, 11 events were found within 2000 km of the Phobos orbit, while three events were found within 2000 km of the Deimos orbit. These events were analyzed in detail and found to likely have other causes than outgassing/dust escape from the martian moons. Thus we conclude that the amount of gas/dust escaping the martian moons is not significant enough to induce detectable magnetic field perturbations in the solar wind. In essence we have not found any clear evidence in the MGS magnetic field data for outgassing or dust escape from the martian moons.     

Accurate Mars Express orbits to improve the determination of the mass and ephemeris of the Martian moons

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.     

Phobos: Control network analysis

Initial analysis of the Mariner 9 high resolution pictures of Phobos surface features has been completed. A control network of 38 landmarks has been established and used to determine the physical size, shape, orientation, libration, and topography properties of Phobos. The results verified the synchronous rotation of Phobos and revealed a libration of approximately 5° in the orbit plane of Phobos. A preliminary map of Phobos, based on the control network analysis, is given.     

Spectral heterogeneity on Phobos and Deimos: HiRISE observations and comparisons to Mars Pathfinder results

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.     

Impact craters in the northern hemisphere of Mars: Layered ejecta and central pit characteristics

Abstract— Mars Global Surveyor (MGS) and Mars Odyssey data are being used to revise the Catalog of Large Martian Impact Craters. Analysis of data in the revised catalog provides new details on the distribution and morphologic details of 6795 impact craters in the northern hemisphere of Mars. This report focuses on the ejecta morphologies and central pit characteristics of these craters. The results indicate that single‐layer ejecta (SLE) morphology is most consistent with impact into an ice‐rich target. Double‐layer ejecta (DLE) and multiple‐layer ejecta (MLE) craters also likely form in volatile‐rich materials, but the interaction of the ejecta curtain and target‐produced vapor with the thin Martian atmosphere may be responsible for the large runout distances of these ejecta. Pancake craters appear to be a modified form of double‐layer craters where the thin outer layer has been destroyed or is unobservable at present resolutions. Pedestal craters are proposed to form in an icerich mantle deposited during high obliquity periods from which the ice has subsequently sublimated. Central pits likely form by the release of vapor produced by impact into ice‐soil mixed targets. Therefore, results from the present study are consistent with target volatiles playing a dominant role in the formation of crater morphologies found in the Martian northern hemisphere.     

Petrology and microstructure of distal impact ejecta from the Flinders Ranges,Australia

Abstract— The Acraman impact ejecta from Bunyeroo Gorge in the central Flinders Ranges consist of clast-bearing and sandy sublayers set in a shale host rock. A calculated transient crater diameter for the Acraman impact of at least 34 km was obtained from average thicknesses and estimated distances of the ejecta from the impact in the Gawler Ranges. The ejecta contain numerous grains of quartz and zircon that display impact-produced features, including one or more sets of decorated planar deformation features. There is also much unshocked material incorporated in the ejecta layer. The coarse-grained ejecta layer embedded within fine-grained sediments allowed easy passage for diagenetic fluids that produced a porous honeycomb structure in the clays and enhanced the content of elements such as Cu, Pb, Zn, and U. The clay fraction of the ejecta layers consists of vermiculite and kaolinite, probably formed from alteration and weathering of glassy components. It appears that quartz and zircon grains are the only remnants unaltered by diagenetic processes.     

Ballistic capture into distant retrograde orbits around Phobos: an approach to entering orbit around Phobos without a critical maneuver near the moon

This paper discusses an approach for designing missions to Phobos that do not require a critical maneuver in proximity of the moon. A low-energy transfer is designed that utilizes the aspherical mass distribution of Phobos to capture a spacecraft into a distant retrograde orbit (DRO) for the mission duration. The process for generating stable DROs in the Mars–Phobos system is discussed along with the method for generating and surveying a set of ballistic capture trajectories (BCTs) for DROs with altitudes between 0.5 and 14 km above Phobos. Statistical analysis of the BCT set reveals options for designing a mission to the desired DRO. This approach can be used in any three-body system when a significant perturbation is present, such as Phobos’ aspherical co-rotating gravity field.     

Mercurian impact ejecta: Meteorites and mantle

Abstract— We have examined the fate of impact ejecta liberated from the surface of Mercury due to impacts by comets or asteroids, in order to study 1) meteorite transfer to Earth, and 2) reaccumulation of an expelled mantle in giant‐impact scenarios seeking to explain Mercury's large core. In the context of meteorite transfer during the last 30 Myr, we note that Mercury's impact ejecta leave the planet's surface much faster (on average) than other planets in the solar system because it is the only planet where impact speeds routinely range from 5 to 20 times the planet's escape speed; this causes impact ejecta to leave its surface moving many times faster than needed to escape its gravitational pull. Thus, a large fraction of Mercurian ejecta may reach heliocentric orbit with speeds sufficiently high for Earth‐crossing orbits to exist immediately after impact, resulting in larger fractions of the ejecta reaching Earth as meteorites. We calculate the delivery rate to Earth on a time scale of 30 Myr (typical of stony meteorites from the asteroid belt) and show that several percent of the high‐speed ejecta reach Earth (a factor of 2–3 less than typical launches from Mars); this is one to two orders of magnitude more efficient than previous estimates. Similar quantities of material reach Venus. These calculations also yield measurements of the re‐accretion time scale of material ejected from Mercury in a putative giant impact (assuming gravity is dominant). For Mercurian ejecta escaping the gravitational reach of the planet with excess speeds equal to Mercury's escape speed, about one third of ejecta reaccretes in as little as 2 Myr. Thus collisional stripping of a silicate proto‐Mercurian mantle can only work effectively if the liberated mantle material remains in small enough particles that radiation forces can drag them into the Sun on time scale of a few million years, or Mercury would simply re‐accrete the material.     

Results of TV imaging of Phobos (Experiment VSK-Fregat)

From February to March 1989 the Phobos 2 spacecraft took 37 TV images of Phobos at a distance of 190-1100 km. These images complement Mariner-9 and Viking data by providing higher-resolution coverage of a large region West of the crater Stickney (40-160 degrees W) and by providing disk-resolved measurements of surface brightness at a greater range of wavelengths and additional phase angles. These images have supported updated mapping and characterization of large craters and grooves, and have provided additional observations of craters' and grooves' bright rims. Variations in surface visible/near-infrared color ratio of almost a factor of 2 have been recognized; these variations appear to be associated with the ejecta of specific large impact craters. Updated determinations of satellite mass and volume allow calculation of a more accurate value of bulk density, 1.90 +/- 0.1 g cm-3. This is significantly lower than the density of meteoritic analogs to Phobos' surface, suggesting a porous interior perhaps containing interstitial ice.     

The nature and emplacement of distal aqueous-rich ejecta deposits from Hale crater,Mars

Hale crater formed in the Early to Middle Amazonian and is one of the best preserved large craters on Mars. We focus on the emplacement of previously mapped distal continuous ejecta and newly recognized discontinuous distal ejecta deposits reaching up to 450 km northeast of Hale. The distal continuous ejecta deposits are typically tens of meters thick, likely water-rich, and subsequent dewatering of some resulted in flow along gradients of 10 m km^-1 for distances of tens of kilometers. The discontinuous distal ejecta are typically <10 m thick with volumes generally <0.5 km³ and embay Hale secondaries, which occur up to ~600 km from Hale. Both continuous and discontinuous distal ejecta deposits are typically smooth at scales of tens to hundreds of meters, relatively dark-toned, devoid of eolian bedforms, inferred to be mostly fine-grained, and were likely emplaced within hours to 1–2 days after impact. The occurrence of well-preserved discontinuous distal ejecta at Hale is unusual compared to other large Martian craters and could be due to impact into an ice-rich substrate that enabled their formation and (or) their survival after minimal postimpact degradation relative to older craters. The pristine nature of distal continuous and discontinuous distal deposits at Hale and the preservation of associated secondaries imply (1) low erosion rates after the Hale impact, comparable to those estimated elsewhere during the Amazonian; (2) the impact did not significantly influence long-term global or regional scale geomorphic activity or climate; and (3) the Hale impact occurred after late alluvial fan activity in Margaritifer Terra.