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Mass-spring model simulations are used to investigate past spin states of a viscoelastic Phobos and Deimos. From an initially tidally locked state, we find crossing of a spin-orbit resonance with Mars or a mean motion resonance with each other does not excite tumbling in Phobos or Deimos. However, once tumbling our simulations show that these moons can remain so for an extended period and during this time their orbital eccentricity can be substantially reduced. We attribute the tendency for simulations of an initially tumbling viscoelastic body to drop into spin-synchronous state at very low eccentricity to the insensitivity of the tumbling chaotic zone volume to eccentricity. After a tumbling body enters the spin synchronous resonance, it can exhibit long lived non-principal axis rotation and this too can prolong the period of time with enhanced tidally generated energy dissipation. The low orbital eccentricities of Phobos and Deimos could in part be due to spin excitation by nearly catastrophic impacts rather than tidal evolution following orbital resonance excitation.

A number of planetary spacecraft missions have carried instruments with sensors covering the ultraviolet (UV) wavelength range. However, there exists a general lack of relevant UV reflectance laboratory data to compare against these planetary surface remote sensing observations in order to make confident material identifications. To address this need, we have systematically analyzed reflectance spectra of carbonaceous materials in the 200–500 nm spectral range, and found spectral-compositional-structural relationships that suggest this wavelength region could distinguish between otherwise difficult-to-identify carbon phases. In particular (and by analogy with the infrared spectral region), large changes over short wavelength intervals in the refractive indices associated with the trigonal sp2 π–π* transition of carbon can lead to Fresnel peaks and Christiansen-like features in reflectance. Previous studies extending to shorter wavelengths also show that anomalous dispersion caused by the σ–σ* transition associated with both the trigonal sp2 and tetrahedral sp3 sites causes these features below λ = 200 nm. The peak wavelength positions and shapes of π–π* and σ–σ* features contain information on sp3/sp2, structure, crystallinity, and powder grain size. A brief comparison with existing observational data indicates that the carbon fraction of the surface of Mercury is likely amorphous and submicroscopic, as is that on the surface of the martian satellites Phobos and Deimos, and possibly comet 67P/Churyumov–Gerasimenko, while further coordinated observations and laboratory experiments should refine these feature assignments and compositional hypotheses. The new laboratory diffuse reflectance data reported here provide an important new resource for interpreting UV reflectance measurements from planetary surfaces throughout the solar system, and confirm that the UV can be rich in important spectral information.

We measured near-infrared (NIR) reflectance spectra of Phobos and Deimos, using the prism (0.7–2.52 μm) and long-wavelength cross dispersed (LXD: 1.9–4.2 μm) modes of NASA Infrared Telescope Facility (IRTF)’s SpeX instrument. The goal of this study is to investigate the surface composition of Phobos and Deimos and search for any mineralogical absorption signatures that may be present on their surfaces, especially in the LXD spectral range. Prism spectra of Phobos showed significant slope variation at shorter wavelengths (λ

Phobos is one of the two moons of Mars, the only other terrestrial planet to have companions. In spite of certain common orbital characteristics between Earth’s Moon and Phobos, such as almost circular, low-inclination, and synchronous orbits, the origin of the Martian moons remains to be understood. This unsettled state of affairs reflects a scarcity of data pertinent to its interior structure and bulk composition, both of which hold the key to solving the question of the provenance of the satellites. Drawing on the importance of interior structure as a means of providing further constraints on this problem, we construct a series of models of the interior of Phobos in accordance with current observations and determine their tidal deformation. The models include a homogeneous body, ice-rock mixtures, models with positive and negative density gradients, and layered models. To compute the deformation of Phobos precisely, we solve the three-dimensional elastostatic problem to obtain the full displacement field. For this, we rely on a higher-order spectral-element method and to account for a correct representation of shape and resulting displacement field, we accurately mesh the figure of Phobos by employing the digital terrain model of Willner et al. (2014). To enable us to further distinguish between models, we also rely on currently available geophysical data (e.g., magnitude of libration in longitude, mean density, gravity field, and moments of inertia). Our results show that the homogeneous, ice-rock mixture, and negative density gradient models are largely degenerate and therefore difficult to separate, but that models with a density increase with depth can be differentiated from the former model families. From a purely deformational point of view, we find that for positive gradient and layered models, the largest deformation occurs on the rim of the Stickney crater, rather than immediately at the sub-Mars point on Phobos, as in the case of the other models, where tidal forces are largest. These observations will be of considerable interest and should provide important anchoring points for the future exploration of Phobos as envisaged with the Martian Moons Exploration mission.

Deimos, one of the Martian moons, has numerous impact craters. However, it is unclear whether crater saturation has been reached on this satellite. To address this issue, we apply a statistical test known as nearest-neighbor analysis to analyze the crater distribution of Deimos. When a planetary surface such as the Moon is saturated with impact craters, the spatial distribution of craters is generally changed from random to more ordered. We measured impact craters on Deimos from Viking and HiRISE images and found (1) that the power law of the size-frequency distribution of the craters is approximately −1.7, which is significantly shallower than those of potential impactors, and (2) that the spatial distribution of craters over 30 m in diameter cannot be statistically distinguished from completely random distribution, which indicates that the surface of Deimos is inconsistent with a surface saturated with impact craters. Although a crater size-frequency distribution curve with a slope of −2 is generally interpreted as indicating saturation equilibrium, it is here proposed that two competing mechanisms, seismic shaking and ejecta emplacement, have played a major role in erasing craters on Deimos and are therefore responsible for the shallow slope of this curve. The observed crater density may have reached steady state owing to the obliterations induced by the two competing mechanisms. Such an occurrence indicates that the surface is saturated with impact craters despite the random distribution of craters on Deimos. Therefore, this work proposes that the age determined by the current craters on Deimos reflects neither the age of Deimos itself nor that of the formation of the large concavity centered at its south pole because craters should be removed by later impacts. However, a few of the largest craters on Deimos may be indicative of the age of the south pole event.

Impacts on planetary bodies can lead to both prompt secondary craters and projectiles that reimpact the target body or nearby companions after an extended period, producing so-called “sesquinary” craters. Here we examine sesquinary cratering on the moons of Mars. We model the impact that formed Voltaire, the largest crater on the surface of Deimos, and explore the orbital evolution of resulting high-velocity ejecta across 500 years using four-body physics and particle tracking. The bulk of mass transfer to Phobos occurs in the first 102 years after impact, while reaccretion of ejecta to Deimos is predicted to continue out to a 104 year timescale (cf. Soter, S. [1971]. Studies of the Terrestrial Planets. Cornell University). Relative orbital geometry between Phobos and Deimos plays a significant role; depending on the relative true longitude, mass transfer between the moons can change by a factor of five. Of the ejecta with a velocity range capable of reaching Phobos, 25–42% by mass reaccretes to Deimos and 12–21% impacts Phobos. Ejecta mass transferred to Mars is We find that the characteristic impact velocity of sesquinaries on Deimos is an order of magnitude smaller than those of background (heliocentric) hypervelocity impactors and will likely result in different crater morphologies. The time-averaged flux of Deimos material to Phobos can be as high as 11% of the background (heliocentric) direct-to-Phobos impactor flux. This relatively minor contribution suggests that spectrally red terrain on Phobos (Murchie, S., Erard, S. [1996]. Icarus 123, 63–86) is not caused by Deimos material. However the high-velocity ejecta mass reaccreted to Deimos from a Voltaire-sized impact is comparable to the expected background mass accumulated on Deimos between Voltaire-size events. Considering that the high-velocity ejecta contains only 0.5% of the total mass sent into orbit, sesquinary ejecta from a Voltaire-sized impact could feasibly resurface large parts of the Moon, erasing the previous geological record. Dating the surface of Deimos may be more challenging than previously suspected.

Although the two moons of Mars, Phobos and Deimos, have long been thought to be captured asteroids, recent observations of their compositions and orbits suggest that they may have formed from debris generated by one or more giant impacts of bodies with ~ 0.01 x target mass. Recent studies have both analytically estimated debris produced by giant impacts on Mars and numerically examined the evolution of circum-Mars debris disks. We perform a numerical study (Smoothed Particle Hydrodynamics simulation) of debris retention from giant impacts onto Mars, particularly in relation to a Borealis-scale giant impact (E ~ 3 x 10^29 J) capable of producing the Borealis basin. We find that a Borealis-scale impact is capable of producing a disk of mass ~ 5 x 10^20 kg (~ 1 - 4 % of the impactor mass), sufficient debris to form at least one of the martian moons according to recent numerical studies of martian debris disk evolution. While a Borealis-scale impact may generate sufficient debris to form both Phobos and Deimos, further studies of the debris disk evolution are necessary. Our results can serve as inputs for future studies of martian debris disk evolution., Comment: Accepted to Icarus

Asteroid (596) Scheila was the first object for which the immediate aftermath of an inter-asteroidal collision was observed. In December 2010, the 113 km-sized asteroid was impacted by a smaller asteroid of less than 100 m in diameter. The scale of the impactor was established by observations of fading ejecta plumes. Comparison of the lightcurves obtained before and after the impact allowed us to assess how much of Scheila’s surface was altered. Cratering physics based on the impactor size suggests that the size of the affected area is larger than expected, (effective radii of 3.5–10 km depending on the change in the albedo of the surface). Similar but more localized albedo changes have been observed on Vesta and the martian moons, but are not understood. Empirical laws describing ejecta blankets however indicate that at distances between 3.5 and 10 km from the crater, Scheila’s surface would be covered by a thin layer 2 mm to 2 cm thick. This dusting, possibly mixed with bright impactor material may be enough to explain to observed brightness increase. Our results show that sub-critical impacts may play a significant role in processing the surfaces of asteroids. The large effect of small impacts on asteroidal lightcurves complicate shape modeling.

Absorption features on Phobos and Deimos in the visible/near infrared wavelength region (0.4–3.9 μm) are mapped using observations from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM). Fe 2+ electronic absorptions diagnostic of olivine and pyroxene are not detected. A broad absorption centered around 0.65 μm within the red spectral units of both moons is detected, and this feature is also evident in telescopic, Pathfinder, and Phobos-2 observations of Phobos. A 2.8 μm metal–OH combination absorption on both moons is also detected in the CRISM data, and this absorption is shallower in the Phobos blue unit than in the Phobos red unit and Deimos. The strength, position, and shape of both of the 0.65 μm and 2.8 μm absorptions are similar to features seen on red-sloped, low-albedo primitive asteroids. Two end-member hypotheses are presented to explain the spectral features on Phobos and Deimos. The first invokes the presence of highly desiccated Fe-phyllosilicate minerals indigenous to the bodies, and the second invokes Rayleigh scattering and absorption of small iron particles formed by exogenic space weathering processing, coupled with implantation of H from solar wind. Both end-member hypotheses may play a role, and in situ exploration will be needed to ultimately determine the underlying causes for the pair of spectral features observed on Phobos and Deimos.

We reconsider two scenarios for the formation of Phobos and Deimos from a circum-martian accretion disk of debris: the strong tide regime for which accretion occurs close to the planet at the Roche limit and the weak tide regime for which accretion occurs farther from the planet. We assume a disk with an initial mass of 10 18 kg (Craddock, R.A. [2011]. Icarus 211, 1150–1161). In the strong tide regime, the disk loses its material by viscous spreading inward to and outward from the planet. When outward moving material crosses the Roche limit, small-sized moonlets are accreted from gravitational instabilities with a shape and density similar to Phobos and Deimos. Due to the gravitational torque exerted by the disk, the moonlets migrate away from the planet, though they cannot reach the synchronous orbit (lying at 6 Mars’ radii). After the disk has lost most of its mass they rapidly fall back onto Mars due to the tidal decay of their orbits. Although, the total mass of moonlets is comparable to the mass of Phobos, their survival time does not exceed 200 Ma, which is incompatible with the formation of Phobos and Deimos early in Mars’ history. In the weak tide regime, moonlets can accrete near the synchronous orbit with the mass of Deimos in a disk of up to 10 18 kg (similarly to planetary embryos formation in the protoplanetary disk). A Phobos-mass embryo can also be formed in the same disk but closer to Mars (at 3–4 Mars’ radii) so that it rapidly falls back onto Mars by tidal decay of its orbit. However, several embryos may accrete together in the disk (similarly to the final stage of terrestrial planet formation), and Phobos and Deimos may be the last two remnants of those bodies formed near the synchronous distance to Mars. Further investigations are still needed to understand such accretion mechanism within a circum-martian disk primarily extending below the synchronous orbit.

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 4500km-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.

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.

Many new small moons of the giant planets have been discovered recently. In parallel, satellites of several asteroids, e.g., Ida, have been found. Strikingly, a majority of these new-found planetary moons are estimated to have very low densities, which, along with their hypothesized accretionary origins, suggests a rubble internal structure. This, coupled to the fact that many asteroids are also thought to be particle aggregates held together principally by self-gravity, motivates the present investigation into the possible ellipsoidal shapes that a rubble-pile satellite may achieve as it orbits an aspherical primary. Conversely, knowledge of the shape will constrain the granular aggregate's orbit—the closer it gets to a primary, both primary's tidal effect and the satellite's spin are greater. We will assume that the primary body is sufficiently massive so as not to be influenced by the satellite. However, we will incorporate the primary's possible ellipsoidal shape, e.g., flattening at its poles in the case of a planet, and the proloidal shape of asteroids. In this, the present investigation is an extension of the first classical Darwin problem to granular aggregates. General equations defining an ellipsoidal rubble pile's equilibrium about an ellipsoidal primary are developed. They are then utilized to scrutinize the possible granular nature of small inner moons of the giant planets. It is found that most satellites satisfy constraints necessary to exist as equilibrated granular aggregates. Objects like Naiad, Metis and Adrastea appear to violate these limits, but in doing so, provide clues to their internal density and/or structure. We also recover the Roche limit for a granular satellite of a spherical primary, and employ it to study the martian satellites, Phobos and Deimos, as well as to make contact with earlier work of Davidsson [Davidsson, B., 2001. Icarus 149, 375–383]. The satellite's interior will be modeled as a rigid-plastic, cohesion-less material with a Drucker–Prager yield criterion. This rheology is a reasonable first model for rubble piles. We will employ an approximate volume-averaging procedure that is based on the classical method of moments, and is an extension of the virial method [Chandrasekhar, S., 1969. Ellipsoidal Figures of Equilibrium. Yale Univ. Press, New Haven] to granular solid bodies.

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 1.6 ± 0.3 g cm −3 . 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 1.1 ± 0.3 g cm −3 , 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.

With the collection of six years of MGS tracking data and three years of Mars Odyssey tracking data, there has been a continual improvement in the JPL Mars gravity field determination. This includes the measurement of the seasonal changes in the gravity coefficients (e.g., J ¯ 2 , J ¯ 3 , C ¯ 21 , S ¯ 21 , C ¯ 31 , S ¯ 31 ) caused by the mass exchange between the polar ice caps and atmosphere. This paper describes the latest gravity field MGS95J to degree and order 95. The improvement comes from additional tracking data and the adoption of a more complete Mars orientation model with nutation, instead of the IAU 2000 model. Free wobble of the Mars' spin axis, i.e. polar motion, has been constrained to be less than 10 mas by looking at the temporal history of C ¯ 21 and S ¯ 21 . A strong annual signature is observed in C ¯ 21 , and this is a mixture of polar motion and ice mass redistribution. The Love number solution with a subset of Odyssey tracking data is consistent with the previous liquid outer core determination from MGS tracking data [Yoder et al., 2003. Science 300, 299–303], giving a combined solution of k 2 = 0.152 ± 0.009 using MGS and Odyssey tracking data. The solutions for the masses of the Mars' moons show consistency between MGS, Odyssey, and Viking data sets; Phobos GM = ( 7.16 ± 0.005 ) × 10 −4 km 3 / s 2 and Deimos GM = ( 0.98 ± 0.07 ) × 10 −4 km 3 / s 2 . Average MGS orbit errors, determined from differences in the overlaps of orbit solutions, have been reduced to 10-cm in the radial direction and 1.5 m along the spacecraft velocity and normal to the orbit plane. Hence, the ranging to the MGS and Odyssey spacecraft has resulted in position measurements of the Mars system center-of-mass relative to the Earth to an accuracy of one meter, greatly reducing the Mars ephemeris errors by several orders of magnitude, and providing mass estimates for Asteroids 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, and 324 Bamberga.

We have observed the leading and trailing hemispheres of Phobos from 1.65 to 3.5 micrometers and Deimos from 1.65 to 3.12 micrometers near opposition. We find the trailing hemisphere of Phobos to be brighter than its leading hemisphere by 0.24 plus or minus 0.06 magnitude at 1.65 micrometers and brighter than Deimos by 0.98 plus or minus 0.07 magnitude at 1.65 micrometers. 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 micrometers. We find no 3-micrometer absorption feature due to hydrated minerals on either hemisphere to a level of approximately 5-10% on Phobos and approximately 20% on Deimos. When the infrared data are joined to visible and nearby 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-micrometer 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.

Ejecta features on the martian satellites are compared to models of ballistic emplacement and downslope motion. The asymmetric distribution of ejecta around the large crater Stickney on Phobos appears most easily explained if the crater were formed when Phobos was only slightly farther from Mars than at present (due to tidal evolution), where rotational and tidal effects allow spreading of low velocity material several kilometers to the east of the crater, but which do not allow a large fraction of the crater's ejecta to be launched into temporary Mars orbit. An additional condition needed to explain the distribution of Stickney's ejecta is that the crater excavation occurred in a gravity-dominated regime. The distribution of Stickney's ejecta is not closely related to the patterns of grooves nor to potential long-distance downslope motion. On Deimos, ejecta from a large impact near the south pole also appear to have been produced by cratering largely in the gravity regime. The morphology of older craters, evidence of ejecta ponding, and crater density data indicate that the ejecta from this large impact have been subject to significant redistribution downslope. This crater is much larger relative to Deimos than Stickney is to Phobos; the resulting greater ejecta cover and possibly much greater seismic shaking on Deimos may help explain the strikingly different appearances of the martian moons.

In this paper, we present modeling results of the presumed dust belts of Mars. We combine recently obtained theoretical results in dynamics of circumplanetary dust grains with up-to-date impact models and use a new numerical code to construct a three-dimensional, time-dependent, and size-dependent distribution of dust material. Our modeling is performed in two consecutive stages. First, for each grain size, we construct a relative spatial density distribution (i.e., a density distribution normalized to an arbitrary factor), which depends almost entirely on dust dynamics. We arrive at an extended set of data tables which quantitatively describe the asymmetric and season-dependent structure formed by different-sized grains. This step is done quite accurately using sophisticated dynamical models. Next, we model the dust production and loss rates in two conceivable formation scenarios to estimate absolute spatial dust densities. These results are uncertain by one or two orders of magnitude because the hypervelocity impact process is poorly characterized. We use the absolute spatial densities to estimate the normal and edge-on optical depths of the Phobos and Deimos tori and obtain values from 10−8to 10−5. Spacecraft data are required to substantially reduce these uncertainties.

Galileo's flyby of 243 Ida in August 1993 led to the discovery of a small satellite, Dactyl, some 85 km from the asteroid's center. From Earth at mean opposition, the satellite is a V = +20.3 mag object (some 6.7 magnitudes fainter than Ida). Forty-seven images of the satellite at 18 different observing times were played back, including one multicolor sequence in which the satellite is resolved adequately to distinguish surface markings (∼105 m/pxl) and three higher resolution single-color views (89, 39, and 24 m/pxl). The satellite, mean radius = 0.7 km, is an elongated, but not angular body with principal diameters of 1.6 × 1.4 × 1.2 km. In the highest resolution view, the longest axis points approximately in the direction of Ida, and its shortest axis is perpendicular to the orbital plane. The spin period is slow (> 8 hr?) and may be synchronous. The satellite shows no conspicuous sharp edges and is much less irregular in shape than Ida. Limb profiles are remarkably smooth over distances of 200–300 m. The geometric albedos of the two objects are similar (0.20 vs 0.21), as are the 0.4–1.0-μm colors. Like Ida, Dactyl is an S-asteroid, but has a slightly deeper 1-μm band than Ida (by 5–8%). While no identical regions (in color) are seen on Ida, the color difference is consistent with color variations reported within the Koronis family and may be due to a slightly higher pyroxene/olivine ratio on the satellite. More than a dozen craters ranging from ≲90 to 280 m diameter are visible in the best image (39 m/pxl at 47° phase). The largest contains an off-centered, positive relief feature some 75 m across. The image includes an intriguing crater chain, but no grooves, ridges, or sharp edges are evident. In terms of limb roughness, Dactyl is much smoother than Ida, but comparable to the two satellites of Mars, Phobos and Deimos. While the satellite's origin is uncertain, a likely scenario would have the satellite date from the breakup of the Koronis family. It is interesting that crater densities on the satellite are similar to those on Ida itself.

In this paper, we investigate the dynamics and steady-state behavior of the hypothetical circumplanetary dust rings associated with the two tiny satellites of Mars, Phobos and Deimos. These moonlets are subject to a flux of micrometeoroids which erodes their surfaces and ejects material into orbit around Mars. We study the detailed orbital dynamics of ejected material between a micrometer and a millimeter in radius and find that these grains are significantly perturbed by solar radiation pressure and Mars' oblateness. The coupling between these two forces forms rings that are vertically and azimuthally asymmetric as well as time-variable. Our analytic and numerical results show that material of all sizes launched from Deimos forms a ring that is displaced away from the Sun. Grains with radii smaller than ≈270 μm launched from Phobos, however, form a ring that is displaced toward the Sun. This effect, as well as surprisingly large orbital changes for Phobos grains, is due to a near resonance between Mars' orbital motion and the precession of pericenter due to the oblateness force. When viewed from along Mars' vernal equinox (the intersection between Mars' orbital and equatorial planes), the ring formed by Deimos grains smaller than ≈100 μm is tilted out of the equatorial plane. We present a new analytical solution describing this vertical asymmetry and interpret it in terms of the Laplace plane. Finally, we suggest that the martian rings may be sustained through the ejecta produced by energetic collisions between ring particles in the 20–50 μm range and the small moonlets Phobos and Deimos.

The influence of gravitational potential on the disposition of loose material on the surfaces of small satellites is investigated using the martian satellites as examples. "Gravity" on small satellites can depend strongly on tidal and rotational effects, especially for objects of low mean density, such as Phobos. Numerical shape models of Phobos and Deimos allow the mapping of the relative gravitational positions of surface features. Dynamic height, derived from measures of potential energy, is a convenient approximation to heights above a reference equipotential surface for these irregular bodies. Deimos shows a strong correlation of indicators of global downslope movement with dynamic height. For Phobos, the distribution of dynamic heights across its surface has changed substantially over time due to its tidally evolving orbit that has induced changes in the rotational and tidal components of surface accelerations. Areas of minimum and maximum regolith thickness correlate better with high and low regions of dynamic height under conditions of rapid but synchronous rotation than with dynamic heights that occurred at more distant orbits less influenced by tides and rotation. However, some model-dependent measures of regolith depth, such as pit spacing in grooves, show little correlation with dynamic height at any orbit radius. The rougher surface of Phobos does not provide satellitewide pathways for near-surface downslope transport of material as does the surface of Deimos. Although the total amount of regolith on Phobos greatly exceeds that which can be attributed to the visible cratering record, the smoother surface of Deimos probably results from an even greater covering by debris from nearly catastrophic impacts. The Phobos and Deimos examples suggest that asteroids have global redistribution of ejecta only if debris from nearly catastrophic impacts provides smooth surfaces for long-distance downslope motion driven by small impact gardening, seismic effects of larger impacts, and thermal cycling.

Impact-ejecta dynamics around Phobos and Deimos are considered for dust particles of the order of 1 mm and greater. Only the gravitational forces of the planet and the satellite as well as the centrifugal and Coriolis forces are taken into account. In the case of Phobos the ejecta generally either reimpact the surface in tens of minutes after their launch or escape rapidly away from the gravitational attraction of the satellite. Deimos, being subjected to a relatively smaller perturbation force from Mars, can keep its ejecta on reimpacting and temporary satellite orbits for hours. Phobos shows large variability in its escape velocity as a function the launch point and the direction of launch. The statistical properties of large numbers of particles moving around the satellites are determined in a series of Monte Carlo simulations. Two factors, important for the regolith-formation process, are investigated: the escape probability from a given site on the surface and the reimpact probability. Both of these functions vary appreciably over the surfaces of Phobos and Deimos. The differences of the escape probabilities between adjoining regions are greater for Phobos than for Deimos, while the reimpact probability variations are substantial for both satellites. The density patterns for Phobos exhibit an interesting dependence on the particles' launch velocities. For small velocities (4–5 m sec−1) we observe two curved tubes of enhanced density that start from the sub-Mars and anti-Mars points on the surface. The density tends to become isotropic for greater launch velocities. Deimos shows a rather regular, ellipsoidal dust halo. The overall density of dust particles—with the meteoroid flux intensity, cratering laws, and velocity distribution of ejecta taken into account—is estimated to be of about a few hundred particles per kilometer cubed close to the surface of Phobos and drops down to about tens of particles per kilometer cubed at a distance of 40 km from the satellite's center. The density of dust around Deimos is two to three times larger.

Two-color polarimetric observations of C-type asteroid 2100 Ra-Shalom were conducted when its phase angle was 59.7°. No other C-type asteroid has so far been observed at such a large phase angle. We relate the new data point to the available data on C-type asteroids and on Phobos and Deimos and compare the phase curve of these objects with the phase curve of dusty comets. The observed polarization of Ra-Shalom is slightly lower than expected from a common curve of the other C-type asteroids and the martian moons. We conclude that this may be caused by the immature regolith on the surface of this small asteroid.

We review and evaluate the contributions of Mariner 9 in improving our knowledge of the dynamical characteristics of Mars and its two satellites, Phobos and Deimos. Primary results include the discovery of the large gravitational and topographical bulge in the Tharsis region, the development of a detailed gravity model representable as coefficients in a spherical harmonic expansion, the development of a topographic model exhibiting a three kilometer displacement of the center of figure from the center of mass, and the determination of the size, shape and motion of Phobos and Deimos.

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.

Viking Orbiter images of Phobos and Deimos have been measured to establish global control networks for 98 surface features of the former and 53 of the latter; photogrammetric triangulation has yielded body-fixed coordinates of these control-points, as well as mean triaxial radii of 13.3 x 11.1 x 9.3 km for Phobos and 7.5 x 6.2 x 5.4 for Deimos. Expressions are also obtained for the inertial orientations of these bodies' spin axes and prime meridians. While these expressions should be accurate to a few tenths of a deg for the 1971-1980 period, their accuracy will degrade with time as the orbit accuracy degrades.

A thermal model of the Martian satellites is developed that takes into account their ellipsoidal shape, eclipse effects, the temperature dependence of the heat conduction coefficient, and the reflected and thermal radiation of Mars. Results for the diurnal temperature behavior of Phobos and Deimos for different latitudes, longitudes, and seasons are presented.

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.

During its active lifetime Mariner 9 obtained 32 high-resolution pictures of Phobos, and 9 of Deimos. The spacecraft orbit was adequate for about 80% complete coverage of Phobos. However, the coverage of the outer satellite was restricted to the Mars-facing side. The approaches used in processing the pictures are discussed. For each satellite picture a coordinate grid of the satellite was obtained with the aid of a computer.

The limb darkening at small phase angles of several materials believed to be analogs of those found on the surfaces of asteroids and other related objects such as Phobos and Deimos is investigated. The materials include three carbonaceous chondrites, one ordinary chondrite, and a steel powder. The wavelength dependence of the limb darkening at visible and near-IR wavelengths is examined. The effects of surface roughness on limb-darkening parameters, and hence on measured geometric albedos, are estimated, and the implications for spherical and ellipsoidal asteroids are discussed.

We have used the integrated brightnesses from Mariner 9 high-resolution images to determine the large phase angle (20° to 80°) phase curves of Phobos and Deimos. The derived phase coefficients are β = 0.032 ± 0.001 mag/deg for Phobos and β = 0.030 ± 0.001 mag/deg for Deimos, while the corresponding phase integrals are q Phobos = 0.52 and q Deimos = 0.57. The predicted intrinsic phase coefficients of the surface material are β i = 0.019 mag/deg and β i = 0.017 mag/deg for Phobos and Deimos, respectively. The phase curves, phase coefficients and phase integrals are typical of objects whose surface layers are dark and intricate in texture, and are consistent with the presence of a regolith on both satellites. The relative reflectance of Deimos to Phobos is 1.15±0.10. The presence of several bright patches on Deimos could account for this slight difference in average reflectance.

The role of tidal dissipation within the Martian satellite system is examined through orbital evolution integrations and assessed in the context of its origin scenario through calculations of collision probabilities between Phobos and Deimos in the distant past. A wide range of assumptions concerning models of dissipation by anelastic tidal deformation within Mars and its satellites has been considered in investigating the possibility of a capture origin using generalized Q laws and the Darwin-Kaula formulation of the secular evolution equations. The integration of the equations of evolution confirms a previous finding (P. Goldreich, Mon. Not. Roy. Astron. Soc. 126, 257–268, 1963; S. F. Singer, Trans. Amer. Geophys. Union 51, 637–641, 1970; K. Lambeck, J. Geophys. Res. 84, 5651–5658, 1979) that Deimos in its present form could not have been captured. Calculations of collision probabilities provide further evidence against a capture origin, for if Phobos and Deimos were captured, they would most probably have collided at some stage. It seems reasonable to assume that a collision event would not have resulted in a highly regular Deimos orbit, even though Phobos could have been tidally evolved to its present orbit after a collision. An accretion origin is therefore preferred over capture, although an accretion model that is consistent with the likely carbonaceous chondritic composition of the Martian satellites has yet to be established. Constraints on the Q laws of Phobos can then be established on the assumption that a collision between Phobos and Deimos has not occurred in the past 1.5 billion years or longer, as indicated by their exposure ages (J. Veverka, Vistas Astron. 22, 163–192, 1978).

Known properties of the current solar system and Bodenheimer's (1977) model of early Jovian evolution are employed to develop a mechanism for satellite capture based on gas drag in primordial circumplanetary envelopes. In particular, the deceleration and fragmentation of two parent bodies passing through an extended primordial Jovian nebula may account for the clusters of prograde and retrograde satellites of Jupiter. Subsequently, the fragments probably underwent limited orbital evolution, and were dispersed by collision with a stray body. The heavy element cores of the outer planets may also be due to primordial gas drag capture. Nebular drag capture of the Martian satellites Phobos and Deimos, Neptune's Nereid and Triton, and Saturn's Phoebe and Iapetus is also conceivable.

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.

The unusual dynamical behavior of Phobos, its strange appearance, and its mysterious network of grooves all make it an intriguing object. Geophysical studies, though, have been hampered by the lack of suitable theories applicable to nonspherical bodies. In this paper the Martian satellites are modeled as homogeneous, elastic triaxial ellipsoids subject to tidal, rotational, and self-gravitational stresses. A novel semianalytical treatment then gives the stress and strain fields throughout their interiors. Yield phenomena and their possible surface expressions are also investigated. The results indicate that Phobos and Deimos have always been stable with respect to tidal fracture or disruption, but that Phobos will probably break up before colliding with Mars. Applications of the new formulation to other nonspherical bodies in the solar system are also discussed.

Mariner 9 television pictures of Phobos are used to study the uniformity of a certain photometric scattering parameter over the surface of the satellite, assuming that the scattering law for Phobos can be represented by the Hapke-Irvine equation. Ways of avoiding topographically irregular areas are discussed, phase functions for Phobos are obtained from scans along the photometric equator, and the photometric behavior of selected areas not along this equator is examined. Searches are conducted for anomalously bright areas and evidence of solid rock on the surface. The results indicate that: (1) at least three large regions on the surface of Phobos are covered by a dark material of complex texture which scatters light according to the Hapke-Irvine law; (2) the average intrinsic phase coefficient of this material is 0.020 mag/deg over the phase-angle range from 20 to 80 deg; (3) even the topographically irregular areas have photometric properties similar to those of the three smooth regions; (4) the surface of Phobos is rougher than that of Deimos on the largest scale; and (5) apparent bright patches are most likely caused by local tilts of the surface.

A three-dimensional numerical model is used to study the dynamical environment of Phobos and Deimos. Surface gravity, escape speeds, and ejecta impact contours are calculated both for the satellites at their present orbit distances, and for orbit distances they may have had in the past. Impact loci for Stickney ejecta are also calculated and compared with the observed groove locations in order to evaluate a possible secondary-impact origin for the grooves on Phobos. Attention is also given to the possible influence of the dynamical environment on shaping the satellites' surfaces.

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.

Mariner 9 photographs of Phobos and Deimos have yielded new information about the orbits, rotation periods, sizes, shapes, and surface characteristics of the satellites. Both satellites appear to be in synchronous rotation. They are irregular, heavily cratered bodies whose shapes appear to have been determined largely by impact fragmentation and spalling. The surfaces of both satellites have crater densities close to saturation and nearly identical, very low albedos. Lower limits on the tensile and yield strengths are estimated, and it is concluded that both satellites may consist of well-consolidated, though possibly highly fractured material.

Polarization measurements were carried out in orange light for Phobos and Deimos on the Mariner 9 A-camera system at large phase angles. The presence of regoliths on the satellites is indicated by a comparison of the measurement data with the results of laboratory measurements on powdered rock samples. Four different sets of assumptions concerning the filter factors were taken into account in the data reduction process.

Revised crater counts for Phobos are presented which are based on uniform Mariner 9 imagery and Duxbury's (1974) map of the satellite. The contiguous portion of the satellite's surface on which all craters down to the limiting resolution of 0.2 to 0.3 km in diameter would be expected to be identified is delineated and found to contain 87 identifiable craters larger than 0.2 km in diameter. Analysis of the crater size distribution shows that the surface appears to be saturated for craters exceeding 1 km in diameter but the crater counts definitely fall below the saturation curve for smaller craters. Reasons for this fall-off are considered, and it is noted that too few craters are visible in Mariner 9 images of Deimos to permit meaningful crater counts on that satellite's surface. It is concluded that, contrary to a previous assertion, the surfaces of Phobos and Deimos are not known to be saturated with craters larger than 0.2 km in diameter.

Using Mariner 9 results on the shapes, rotation periods, and photometric functions of Phobos and Deimos, approximate orbital light curves are calculated 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.

Reductions of Mariner 9 TV data of Phobos and Deimos tend to corroborate the existence of a secular acceleration of Phobos commensurate with two recently reported values based on a reprocessing of earth-based data. These values of secular acceleration have been used together with Mariner 9 data on the physical size of Phobos and earth-based photoelectric observations which infer a carbonaceous composition for Phobos to place upper and lower bounds of 50 and 150, respectively, on the tidal dissipation function of Mars. The corresponding upper and lower bounds on the tidal lag angle are 0.19 and 0.57 deg.