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The Formation of the Martian Moons
Abstract and Keywords
The origin of the natural satellites or moons of the solar system is as challenging to unravel as the formation of the planets. Before the start of the space probe exploration era, this topic of planetary science was restricted to telescopic observations, which limited the possibility of testing different formation scenarios. This era has considerably boosted this topic of research, particularly after the Apollo missions returned samples from the Moon's surface to Earth. Observations from subsequent deep space missions such as Viking 1 and 2 Orbiters, Voyager 1 and 2, Phobos-2, Galileo, Cassini-Huygens, and the most recent Mars orbiters such as Mars Express, as well as from the Hubble space telescope, have served to intensify research in this area.
Each moon system has its own specificities, with different origins and histories. It is widely accepted that the Earth's Moon formed after a giant collision between the proto-Earth and a body similar in size to Mars. The Galilean moons of Jupiter, on the other hand, appear to have formed by accretion in a circum-Jovian disk, while smaller, irregularly shaped satellites were probably captured by the giant planet. The small and medium-sized Saturnian moons may have formed from the rings encircling the planet. Among the terrestrial planets, Mercury and Venus have no moons, the Earth has a single large moon, and Mars has two very small satellites. This raises some challenging questions: What processes can lead to moon formation around terrestrial planets and what parameters determine the possible outcomes, such as the number and size of moons? The answer to such fundamental questions necessarily entails a thorough understanding of the formation of the Martian system and may have relevance to the possible existence of (exo)moons orbiting exoplanets. The formation of such exomoons is of great importance as they could influence conditions for habitability or for maintaining life over long periods of time on the surface of Earth-like exoplanets, for example by limiting the variations of the orientation of the planet's rotation axis and thus preventing frequent changes of its climate.
Our current knowledge concerning the origin of Phobos and Deimos has been acquired from observational data as well as theoretical work. Early observations led to the idea that the two satellites were captured asteroids but this created difficulties in reconciling the current orbits of Phobos and Deimos with those of captured bodies, hence suggesting the need for an alternative theory. A giant-impact scenario provides a description of how moons similar to Phobos and Deimos can be formed in orbits similar to those observed today. This scenario also restricts the range of possible composition of the two moons, providing a motivation for future missions that aim for the first time to bring material from the Martian system back to Earth.
Keywords: natural satellites, Mars, Martian moons, accretion, giant collision, tides, orbit evolution
Puzzling Origin: Capture Versus In-Situ Formation
The Martian Moon System
The two natural satellites of Mars, Phobos and Deimos, were discovered in August 1877 by the American astronomer Asaph Hall (1878).1 They probably went unnoticed for a long time because of their low albedo and their proximity to Mars, which makes them difficult to observe with Earth-based telescopes (Pascu, Erard, Thuillot, & Lainey, 2014). Subsequent telescopic observations determined that their orbits are near equatorial and near circular, with Phobos orbiting below the synchronous limit and Deimos orbiting above it (see Table 1). Furthermore, the secular acceleration of Phobos' longitude along its orbit, discovered by Sharpless (1945), indicates that its orbit is slowly decaying, with Phobos losing orbital energy and gradually approaching Mars due to tidal dissipation inside the planet (e.g., Burns, 1992). In contrast, Deimos lies above the synchronous limit and thus is receding from the planet, just as the Moon is moving away from the Earth. Deimos' secular acceleration has not yet been observed due to its low mass and greater distance from Mars (see Tables 1 and 2). On the basis of the brightness of the two moons, their sizes were first estimated to be a few tens of kilometers (e.g., Pascu et al., 2014). Phobos and Deimos are thus much smaller than the Earth's Moon, the Galilean satellites of Jupiter, and the main moons of the other giant planets. Earth-based historical observations have thus highlighted the main challenge raised by the Martian system: How to explain the formation of two small moons in near-equatorial and near-circular orbits around their primary planet?
Table 1. Orbital Architecture of the Martian System
Semi-major axis
9375 km (2.77 RM)
23458 km (6.90 RM)
Inclination to the equator
Orbital period
7h 39' 19.47"
30h 18' 1.36"
Secular acceleration along the orbit
1.273 +/− 0.003 mdeg/year2
Source: Jacobson and Lainey (2014).
Note: The synchronous limit is at 20,400 km or around 6 RM, where 1 RM is Mars' mean radius, equal to 3,400 km. This limit is the orbital position where the revolution period around Mars is equal to the spin of the planet (24h39').
Table 2. Bulk Properties of the Martian Moons
Radius (in km)
13.03 x 11.40 x 9.14 (1)
7.5 x 6.1 x 5.2 (2)
Mass (in 1016 kg)
1.066 +/− 0.013 (3)
0.151 +/− 0.003 (4)
Volume (in km3)
5742 +/− 35 (1)
1017 +/− 130 (2)
Density (in g/cm3)
1.856 +/− 0.034 (5)
1.48 +/− 0.22 (6)
Source: (1) Willner et al. (2014); (2) Thomas (1993); (3) Paetzold et al. (2014); (4) Jacobson (2010); (5) using mass from (4) and volume from (1); (6) Rosenblatt (2011).
Note: The radii are from the best-fit ellipsoid to the shape of the body (1).
Are Phobos and Deimos Small Asteroids?
The investigation of the Martian moon system entered a new era with space probe explorations (Duxbury, Zakharov, Hoffmann, & Guinness, 2014). The first missions to make important observations of the two moons were Mariner 9, the Viking 1 and 2 orbiters, and Phobos-2. These provided the first resolved images and spectroscopic observations of the surface of Phobos and Deimos (more recent images are shown in Figures 1 and 2 and more up-to-date spectra in Figure 3), as well as the first determinations of their density (mass and volume, see updated values in Table 2). The data suggested that the two small moons resemble asteroids, with irregular shape, cratered surface, low albedo (Figures 1 and 2), and low density (Table 2). Furthermore, the reflectance spectra of their surfaces in the near-infrared and visible wavelengths, around 0.4 to 4 microns, show an increasing slope toward infra-red wavelengths (reddening slope, Figure 3) that matches those of several primitive low-albedo asteroids (Murchie & Erard, 1996; Murchie et al., 1991; Pang, Pollack, Veverka, Lane, & Ajello, 1978; Pollack et al., 1978). The surface of Phobos shows areas with different spectral slopes defining the so-called red and blue units, while Deimos' surface shows only spectra similar to the Phobos red unit (Figures 2 and 3). The reflectance spectra of Phobos have been confirmed by the recent Mars Reconnaissance Orbiter (Fraeman et al., 2012), Mars Express (Fraeman et al., 2012; Witasse et al., 2014), and Rosetta (Pajola et al., 2012) missions, as well as by observations obtained with the Hubble space telescope (Rivkin, Brown, Trilling, Bell, & Plassman, 2002) and with the ground-based Mayall 4-meter telescope of the Kitt Peak National Observatory (Fraeman et al., 2014). In addition, Mars Express has confirmed the low density of Phobos by improving estimates of its mass (Paetzold, Andert, Jacobson, Rosenblatt, & Dehant, 2014) and volume (Willner, Shi, & Oberst, 2014). The morphological, physical, and spectroscopic similarities between the Martian moons and the primitive asteroids are the main arguments favoring the capture scenario, in which Phobos and Deimos are small low-albedo asteroids captured by the planet (e.g., Burns, 1992; Pajola et al., 2012, 2013; Pang et al., 1978). These asteroids would have formed from the condensation of carbonaceous material in the solar nebula beyond Mars' orbit.
No satisfactory spectral match between Phobos and Deimos and meteoritic material, recognized as the material of primitive asteroids, has however been found so far (e.g., Murchie & Erard, 1996; Murchie et al., 1991; Vernazza et al., 2010). In addition, the reflectance spectra do not clearly display absorption bands (Figure 3), which provide diagnostics for the composition, in terms of carbonaceous, silicate, or hydrated material. Space weathering (alteration in space environment over time) on airless bodies may nonetheless suppress any such possible bands. It is known that this process is responsible for darkening, reddening, and suppressing absorption bands (as observed for Phobos and Deimos spectra, Figure 3) in reflectance spectra of silicate material, for example on the Moon (Clark, Hapke, Pieters, & Britt, 2002; Pieters, Murchie, Thomas, & Britt, 2014). It may therefore not be possible to determine the true surface composition of the two moons through spectroscopic observations alone (Rosenblatt, 2011). Murchie and Erard (1996) indeed did not rule out that Phobos' spectra could be those of very highly weathered silicate material. It has been proposed more recently that dark silicate (anorthosite) terrains on the Moon can have low albedo similar to those of Phobos and Deimos (Yamamoto, Watanabe, & Matsunaga, 2018). On the other hand, a silicate-rich Phobos would not preclude the possibility of capture, since silicate asteroids can condense from material in the solar nebula closer to Mars' orbit than the region in which carbonaceous asteroids form.
A tentative, very weak absorption band at around 0.65 microns in the spectra of Phobos has recently been detected (Fraeman, et al., 2014; Pajola et al., 2013; see also Figure 3) and could be interpreted as the signature of a carbonaceous composition, although space weathering effects cannot be ruled out (Fraeman et al., 2014). Such effects on carbonaceous material are less well understood than on silicate material, and may give rise to red and even blue spectral slopes observed in reflectance spectra of carbonaceous asteroids (Lantz, Clark, Barucci, & Lauretta, 2013). The effect of space weathering on reflectance spectra was tentatively simulated for carbonaceous meteorite samples, but the result shared little similarity with Phobos and Deimos (Moroz et al., 2004; Vernazza et al., 2010). Emissivity spectra in the thermal infra-red domain (wavelengths from 5 to 50 microns) of the surface of Phobos were also measured for the first time by Mars Odyssey (Roush & Hogan, 2000) and Mars Express (Giuranna et al., 2011; Witasse et al., 2014). In contrast to the reflectance spectra, these emissivity spectra show clear features more typical of silicate rather than carbonaceous meteorite material (Figure 3; see also Giuranna et al., 2011). They have however a coarser spatial resolution than the reflectance spectra and are also more affected by grain-size particles of the surface regolith and, to some extent, by space weathering (Pieters et al., 2014).
The ambiguity in the composition of the Martian moons derived from remote sensing spectral observations raises an intriguing question: Are Phobos and Deimos made of asteroid material (either silicate, carbonaceous, or something else) or do they incorporate some Martian material? The latter would suggest that Phobos and Deimos could have been formed in situ around Mars, thus weakening the asteroid capture scenario. In addition, the current near-equatorial and near-circular orbits of the two moons are unlikely to result from a capture (Burns, 1992; Rosenblatt, 2011).
Is Capture Dynamically Possible?
While specific dynamical conditions are required for capture to occur (Pajola et al., 2012), it is not impossible to trap asteroids in a closed orbit around Mars. It can even be facilitated by a three-body capture mechanism, particularly in the early solar system when there was an abundance of planetesimals and other small debris (Hansen, 2018). The orbit of such a captured body is, however, expected to be significantly elliptical and non-equatorial, as is the case, for example, for the irregular satellites of Jupiter, in contrast to the actual orbits of Phobos and Deimos (see Table 1). The capture scenario thus requires a mechanism to change the post-capture orbit into the current near-equatorial and near-circular orbits observed today.
One possible mechanism is orbital tidal dissipation (Kaula, 1964). The tides raised by the captured satellite inside Mars and the tides raised by Mars inside the satellite contribute to the dissipation of the satellite orbital energy, and hence modify its orbit. Studies have shown, however, that this mechanism is not sufficient to change an elliptical and non-equatorial orbit into the almost circular and equatorial orbit of Deimos within the 5 billion-year lifetime of the solar system (Szeto, 1983). Since Phobos is larger than Deimos (see Table 2), tidal dissipation has a greater effect on its orbit: a very elliptical post-capture orbit can be circularized over 5 billion years (e.g., Burns, 1992; Cazenave, Dobrovolskis, & Lago, 1980; Lambeck, 1979), assuming a bulk rigidity of rocky material with some degree of micro-porosity (for example, a carbonaceous chondrite material; Lambeck, 1979) and a low tidal dissipation factor (Rosenblatt, 2011). Changing the inclination from the ecliptic plane (i.e., the mean orbital plane of the asteroids) to the equatorial plane, however, requires an even more dissipative material (Mignard, 1981), closer to icy rather than rocky material (Rosenblatt, 2011; Rosenblatt & Pinier, 2014).
A number of possible solutions to this problem have been proposed. One suggestion is that the small body was captured in an equatorial orbit; this, however, requires that the orbital distance to Mars decreases rapidly below roughly 13 RM after capture in order to maintain the orbit in the equatorial plane, which seems difficult given how slowly the orbital eccentricity is modified by tidal effects (Burns, 1992). Other authors have proposed that the post-capture orbit was rapidly inclined into the equatorial plane and significantly circularized by drag dissipation in a primitive planetary nebula (Sasaki, 1990). Such a nebula would have been formed around a planet accreting from the solar nebula gas. Drag effect studies (Sasaki, 1990), however, have so far been unable to show whether the density profile and survival time of this nebula are consistent with the requirements of the capture scenario.
Alternative Scenarios: In-Situ Formation
The difficulty of reconciling the outcome of a capture scenario with the current orbital properties of the Martian moons has motivated the search for alternatives. Most of these assume that the moons have accreted in an equatorial disk of debris containing extra-Martian material in order to explain their possible primitive composition (Rosenblatt, 2011).
This idea of a gravitational aggregate of debris as the bulk structure of the Martian moons is based on their low bulk density (see Table 2), suggesting a large amount of porosity in their interior (Andert et al., 2010; Murchie et al., 1991; Rosenblatt, 2011), as well as on plausible explanations for Phobos' main geomorphological surface features such as the large impact crater Stickney (Bruck Syal, Rovny, Owen, & Miller, 2016) and some of its grooves (Hurford et al., 2016). These surface features would indeed require low rigidity that can be accounted for by porosity (Jaeger, Cook, & Zimmerman, 2007; Le Maistre et al., 2013).
Different mechanisms for the formation of the disk have been proposed. One idea is that a body much more massive than Phobos and Deimos might first have been captured by Mars. Its orbit would have rapidly decayed due to tidal forces and the body would have been destroyed when crossing the Roche limit (Singer, 2003). The resulting debris would have formed a ring around Mars below the Roche limit (as modeled later by Black & Mittal, 2015), from which small moons would have emerged. However, this relatively simple scenario leads to another impasse: Mars' Roche limit is about three RM, well inside the synchronous limit, which is about six RM (see Table 1). It is difficult to find a mechanism by which the moons formed at the Roche limit could have migrated far from Mars and then stayed in orbit for a long time, in particular for Deimos, which orbits at a distance of nearly seven RM (see Table 1; see also Rosenblatt & Charnoz, 2012; see also the section "Evolution of the Accretion Disk").
Another possibility is that the disk resulted from a giant impact, similar to that which led to the formation of the Earth's Moon. This was first proposed by Craddock (1994) but was disregarded by the scientific community until new data about Phobos' interior by Mars Express implying a significant amount of porosity and favoring a formation in an accretion disk (e.g., Andert et al., 2010; Rosenblatt, 2011) revived this scenario. A reappraisal of Phobos' origin from the data of the OMEGA spectrometer onboard Mars Express also favored such a scenario (Bibring, 2010). Craddock's (2011) study suggests that a large body (one quarter to one third the size of Mars) collided with the proto-Mars at least 4 billion years ago, blasting debris into space. Phobos and Deimos may be the last surviving moons that emerged from the resulting accretion disk (Figure 4). The problem still remains, however, of reconciling the migration of moons formed at the Roche limit with the current orbits of Phobos and particularly of Deimos today (Rosenblatt & Charnoz, 2012).
A Giant Collision Scenario
The giant impact scenario leading to the formation of moons can be divided into a number of stages (Figure 4), each of which must be carefully examined in order to build a robust model of the formation process, capable of reproducing the observed orbits and of providing information on the composition of the resulting moons.
A Giant Impact Early in Mars' History
The first question to be answered is whether or not there is any evidence for a giant impact; what effect would such an impact have on the planet and what traces would it leave today?
A giant impact (Figure 5) is thought to be responsible for Mars' current spin rate (Craddock, 2011; Dones & Tremaine, 1993); studies suggest that the mass of the impactor was at least 2% that of Mars, of the order of 1022 kg. Such an impact would also leave behind a large crater, which would subsequently have been filled to form a relatively flat basin: the Borealis, Elysium, and Daedalia basins have been identified as possible candidates (Craddock, 2011). An analysis of the elongated crater population on the surface of Mars, supposing that they are all due to impacts of debris from the disk or from the decaying orbit of moons (Schultz & Lutz-Garihan, 1982), suggested that the mass of the disk was of the order of 1019 kg (Craddock, 2011). However, this elongated crater population may also result from grazing asteroid impacts (Bottke, Love, Tytell, & Glotch, 2000), which would allow for less massive disks.
On the other hand, the Borealis basin is the largest potential impact basin, measuring 10,600 km by 8,500 km and covering over 40% of the Martian surface, corresponding to the major hemispheric crustal dichotomy identified on the topography and gravity maps of Mars (Marinova, Aharonson, & Asphaug, 2008). Numerical models based on the smoothed particle hydrodynamics (SPH) approach conclude that a crater of the size of the Borealis basin can be formed by an object of mass 2.6% that of Mars, moving at about 6 km/s and impacting the surface at 45° (Marinova et al., 2008). These parameters are compatible with the kinds of impact thought to have occurred in the early history of the solar system (Wilhelms & Squyres, 1983) and can account for the spin rate of Mars (Dones & Tremaine, 1993). They have been used in subsequent chemistry-focused SPH calculations of the nascent accretion disk just after the giant impact (Citron, Genda, & Ida, 2015; Hyodo, Genda, Charnoz, & Rosenblatt, 2017a; Pignatale et al., 2018). Other authors (Canup & Salmon, 2018), however, argued for an impactor around 10 times less massive, with a similar impact angle and a slightly higher impact velocity (7 km/s instead of 6 km/s), although still within the range of impactor size/energy estimates to form Borealis. However, these impact conditions cannot fully account for the spin of Mars.
Post-Impact Dynamical Evolution of the Debris Cloud Blasted in Mars' Orbit: Formation of an Accretion Disk
Immediately after the giant impact, the ejecta that will eventually form Phobos and Deimos had highly elliptical orbits around Mars, with eccentricities between 0.1 and 0.9, and generally moved at velocities different from those of their neighbors ( Canup & Salmon, 2018; Citron et al., 2015; Hyodo et al., 2017a). At this stage, since the typical temperature is around 2,000 K (Figure 6), the ejecta are mostly in the form of molten droplets whose size is determined by the interplay between their differential or shear velocity and the tension on the surface of the droplet. Assuming a surface tension of 0.3 N/m for a silicate melt yields a typical droplet size just after the giant impact of about 1.5 m (Hyodo et al., 2017a). The droplets will quickly solidify since their cooling time, several tens of minutes, is relatively quick compared to their orbital period. As they orbit, the ejecta may collide with each other and undergo further fragmentation, resulting in grains of the order of 100 micron in size (Hyodo et al., 2017a). The eccentricity of the orbits is damped by such collisions and eventually a thin circular disk of debris is formed (Hyodo, Rosenblatt, Genda, & Charnoz, 2017b). When the midplane of the disk is initially not aligned with the equatorial plane of Mars, the dynamical flattening term J2 of Mars' gravitational potential induces a precession of the disk particles symmetrically around the equatorial plane. Particle–particle inelastic collisions additionally damp their inclination, eventually forming an equatorial circular disk (Hyodo et al., 2017b).
SPH calculations modeling the Borealis-type impact indicate that the resulting disk would have a mass of several 1020 kg (Citron et al., 2015; Hyodo et al., 2017a; Rosenblatt et al., 2016), somewhat larger that the value estimated by Craddock (2011) and by Canup and Salmon (2018), which was about 1018–1019 kg. Crucially for the formation of Phobos and Deimos, the calculations also suggest that while most of the total ejected mass is confined below the Roche limit, roughly 1% lies beyond this, forming a tenuous outer disk of material that can extend past the synchronous limit (Canup & Salmon, 2018; Rosenblatt et al., 2016). The SPH calculations, however, do not have sufficient resolution to provide a precise value for the outer disk mass nor its density profile.
Furthermore, some impact debris could have escaped from Mars' gravity field and started to orbit around the sun. If this ejecta hit a primordial asteroid with a high impact velocity (> 5 km/s), the impact signatures (such as impact melt or/and 40Ar–39Ar resetting age) could be recorded (Hyodo & Genda, 2018). Also, the Borealis-forming impact would excavate Martian mantle material (which is olivine-rich) and potentially implant some of this in the asteroid region as rare A-type asteroids (Hyodo & Genda, 2018; Polishook, Jacobson, Morbidelli, & Aharonson, 2017).
Chemistry of the Debris Cloud
As SPH computations show that the disk material is initially made of a mixture of gas (vapor) and melt (Hyodo et al., 2017a), Phobos and Deimos should be formed from the condensation of these two components (See Figure 7). SPH calculations also suggest that the basic building blocks of the two moons are composed of roughly half-Martian and half-impactor material (Hyodo et al., 2017a), assuming a high-energy Borealis-forming impact (Marinova et al., 2008). A lower-energy impact could result in a higher proportion, up to 80%, of Martian material (Canup & Salmon, 2018).
As the disk cools, the gas condenses into small crystalline dust grains and the melt solidifies (Ronnet et al., 2016). Thermodynamic calculations coupled with dynamical modeling can be used to predict the composition of the building blocks that will accrete into moons (Visscher & Fegley, 2013). In particular, since the impactor may originate far from where Mars itself formed, the question arises as to whether differences in the impactor's chemistry (such as cometary or carbonaceous chondrite) have left a detectable trace in the composition of Phobos and Deimos (Craddock, 2011; Pignatale et al., 2018; Ronnet et al., 2016). This is an important question since, as mentioned in section "Are Phobos and Deimos Small Asteroids?," spectral observations of the surfaces of Phobos and Deimos are unable to clearly determine their composition. Reflectance spectra suggest some carbonaceous material (Fraeman et al., 2014), while emissivity spectra strongly point to the presence of silicates (Giuranna et al., 2011).
The thermodynamic calculations, using different types of impactor, predict a great diversity of final compositions for impactors carrying different amounts of C, H, O, Fe, Si; changing the proportion of these elements can significantly modify the resulting chemistry of the dust and melt (Pignatale et al., 2018). For example, a CV-chondrite type (anhydrous carbonaceous) impactor would bring metallic iron, silica, iron sulfides, and carbon; a cometary object would bring the largest carbon and water ice content; an enstatite chondrite would bring the largest quantities of sulfides.
The presence or absence of compounds such as metallic iron, iron oxides and iron-rich silicates, sulfides, carbon, and water ice can therefore hint at the nature of the impactor.
Most of the impactors (carbonaceous-, enstatite-, and mars-type) produce iron-rich dust and some (carbonaceous-, cometary-type) also produce substantial quantities of carbon-rich dust, an opaque material, which thus lowers the albedo of the surface of the accreted bodies. Furthermore, as the grain size does not exceed 0.1~10 microns (Hyodo et al., 2017a), the reflectance of the surface is reduced (Ronnet et al., 2016). The solidified material also tends to lack a perfect crystalline structure, reducing the reflectance further. The small amount of dust (at most 5%) in the final material may nonetheless explain the low reflectance spectra of the surface of Phobos and Deimos (see the section "Are Phobos and Deimos Small Asteroids?" and Figure 3).
The possible imperfect crystallization of melt could result in compositional variability for the building blocks of Phobos (Pignatale et al., 2018), which may reflect the so-called blue and red spectral units observed on the surface of Phobos (Murchie et al., 1991; see also Figure 2). Indeed, such chemical variability seems necessary in order to explain the puzzling stratigraphic relationship between the blue and red units observed throughout the area of the large impact crater Stickney (Basilevsky et al., 2014).
Moreover, all types of impactor composition considered in Pignatale et al. (2018), except the CI-chondrite type (water-rich carbonaceous), produce a low amount of iron-rich silicates in the dust, which could explain the emissivity signature of Phobos' surface (Giuranna et al., 2011). In addition, the melt concentrates minerals of silicate-rich minerals that may explain the good match between Phobos' emissivity spectra and those of silicate material (Giuranna et al., 2011).
The material condensed in Mars' orbit after a giant impact hence may not be incompatible with the spectral observations of the surface of the Martian moons, thus would not require any asteroidal material formed beyond Mars' orbit to account for these spectral observations. However, more detailed simulations of reflectance and emissivity spectra for the predicted condensed material are needed to assess the matching with Phobos' and Deimos' spectra. These studies are challenging since the additional space weathering effect is only well known for silicate material. The matching of simulated and observed spectra can therefore yield ambiguous results (Gaffey, 2010).
In their giant collision model, Canup and Salmon (2018) predict a disk debris temperature similar to the one in Hyodo et al. (2017a) but a different Mars-to-impactor ratio of the debris composition (80% Mars–20% impactor). The final composition, however, should be quite similar to that predicted by Pignatale et al. (2018) for a Mars-like impactor (which results in a full Mars composition). Nevertheless, a smaller amount of iron-rich silicate dust should be present, which would render the reflectance spectra less dark than what is actually observed.
If the giant impact hypothesis is correct, depletion of volatiles such as water vapor may occur since the impact is generally energetic (Hyodo et al., 2017a; Hyodo, Genda, Charnoz, Pignatale, & Rosenblatt, 2018; Nakajima & Canup, 2017). Hyodo et al. (2018) consider two possible mechanisms for volatile depletion: hydrodynamic escape of vapor and blow-off of the volatile-rich condensates from the vapor by radiation pressure.
The vapor temperature just after the impact is TVAP~2000 K and the orbits of the debris are highly eccentric (Hyodo et al., 2017a), increasing their chance of escaping the system as the distance to Mars becomes greater. SPH calculations indicate that 10–40% of the vapor satisfy the escape conditions during the first orbit from the impact point, depending on the impactor composition and vapor temperature between 1,000–2,000 K. Since the vapor contains more volatile elements than the melt, some fraction of the volatile may be lost from the original abundance by hydrodynamic escape (Hyodo et al., 2018).
Along the trajectory of the debris from impact point to apocenter (at the farthest distance from Mars), some fraction of the vapor may also condense and form small volatile-rich dust particles. The heat on Mars' surface generated by the impact (2,000–6,000 K) is strong enough to blow-off these small dust particles; "moderately" volatile elements, whose the condensation temperature is 700–2,000 K and whose ratio of radiation pressure to gravitational forces is larger than 0.1, are most likely to be removed by radiation pressure (Hyodo et al., 2018). This loss of volatile elements has to be taken into account in any prediction of the final composition of the material condensed in Mars' orbit from a giant collision.
Evolution of the Accretion Disk
SPH calculations of the initial impact and the nascent accretion disk are computationally very demanding, and 3D hydrodynamic simulations are therefore limited to 10–20 hours after the impact. This is, however, sufficient to study the orbital distribution of the blasted material around Mars that will then form the accretion disk (see the section "Post-Impact Dynamical Evolution of the Debris Cloud Blasted in Mars' Orbit" and Figure 6). Describing the long-term evolution of this multi-fluid disk (vapor mixed with solids) with a hydrodynamics code is, however, not feasible with the computing resources available today.
SPH calculations nonetheless provide material radial distributions whose density decreases with distance from Mars. The calculations do not have enough resolution to provide fine details of the disk structure. Nevertheless, most of the mass is clearly concentrated below the Roche limit and can form a dense inner disk, while the rest of the material, which extends slightly beyond the synchronous limit, forms a low-density outer disk (Canup & Salmon, 2018; Hyodo et al., 2017a; Rosenblatt et al., 2016).
The physics of the dense inner disk is similar to that of a viscous fluid (Salmon, Charnoz, Crida, & Brahic, 2010). The strong effective viscosity results from the formation of spiral self-gravitating wakes, owing to the large surface density of the inner disk. As a result, the inner disk spreads outwards from the planet. When material crosses the Roche limit, it can accrete into individual moons (low mass satellites; see Charnoz, Salmon, & Crida, 2010). The orbital evolution of these moons is then driven by two opposite forces due to their gravitational interaction with the inner disk material (which transfers angular momentum to the moons' orbits, thus repelling them) and with the planet (through tidal dissipation which reduces the angular momentum of the moon's orbit, see section "Orbital Evolution of the Martian Satellites after the Accretion Period"). The former interaction pushes the orbit of each moonlet outwards while the second pulls it back toward the planet when the orbit is below the synchronous limit. Beyond this limit, the two forces act in the same direction and the moonlet migrates outwards definitively, but very slowly. This mechanism has successfully explained the formation of the small moons of Saturn from the planet's ring system, where the synchronous limit is in fact slightly below the Roche limit (Charnoz et al., 2010).
In the case of Mars, the synchronous limit (6 RM) is far beyond the Roche limit (about 2.45 RM). After the giant impact, the inner disk is massive and disk–satellite interactions dominate planet–satellite tidal interactions. Thus, any moonlet forming at the Roche limit is initially pushed outward. However, as the disk's edge is located at the Roche limit, disk–satellite interactions cannot push a satellite beyond the synchronous limit; the maximal outward migration distance is defined by the 2:1 Lindblad resonance with the outer edge of the inner disk (i.e., the Roche limit), which is about 4.5 RM (Charnoz et al., 2010; Rosenblatt & Charnoz, 2012).
Over time, the dense inner disk empties, losing material either inwards to the surface of Mars or outwards across the Roche limit. As the disk density decreases, the Lindblad resonances become weaker (i.e., disk–satellite interactions decrease) and tidal dissipation eventually dominates, causing the orbits of any moonlet below the synchronous limit to decay. Eventually all these moonlets disappear below the Roche limit. The lifetime of the moonlet system depends on the mass of the inner disk; for a disk of mass 1019 kg, moonlets with the mass of Phobos or Deimos can form, but they completely disappear after 200 million years (Rosenblatt & Charnoz, 2012), which is much lower than the presumed age of Phobos' surface, which is estimated to be as old as 4 billion years (Schmedemann, Michael, Ivanov, Murray, & Neukum, 2014). A more massive disk would evolve even faster and would produce more massive moonlets, while a lighter disk would evolve more slowly but would produce moonlets less massive than Phobos and Deimos.
As the moons cross back below the Roche limit, they do not necessarily crash onto the surface of Mars. They can be disrupted by the tidal forces of Mars, breaking apart to form a new inner disk less massive than the initial disk (Black & Mittal, 2015). The whole process of moon formation can then restart from this new less massive disk. It has been suggested that Phobos today is the result of the latest iteration, 2.5 billion years ago, of such a cycle of disk formation and dispersal processes, initially triggered by a giant impact (Hesselbrock & Minton, 2017). However, a caveat of this scenario is the absence of a faint remnant ring around Mars.
These studies, however, do not take into account the low-density outer disk whose existence is suggested by SPH simulations. The question then is, could Phobos and Deimos have formed from the material in this outer disk?
How to Form Two Small Outer Satellites From a Circum-Martian Accretion Disk: A Dynamical Solution
Since the density of the outer disk is low, it can be represented by a set of small bodies or satellite embryos, rather than as a viscous fluid, as was done for the dense inner disk. The evolution of these satellite embryos can be followed by numerically integrating the N-body equations of motion. A collision is commonly deemed to have occurred if two bodies approach each other to within their mutual Hill radius. The collision is treated as inelastic, resulting in accretion if the relative rebound velocity is smaller than the mutual escape velocity. One caveat is that disruption (i.e., the break-up of one or both colliding bodies) is neglected, based on the assumption that the resulting fragments remain close to each other and thus quickly recombine.
N-body simulations of the evolution of such an outer disk usually result in a stable configuration involving typically a dozen or so small moons whose orbits change little so that there are no more collisions (a dynamically "frozen" system). The masses and orbits of these moons reflect the initial density profile of the disk due to the conservation of the center of mass (Rosenblatt et al., 2016). For instance, the moons tend to be homogeneously distributed if the accretion disk is uniform. In order to enhance accretion efficiency, and hence the possibility of forming Phobos and Deimos with their actual masses at the expected distances from Mars, it is necessary to somehow dynamically excite the outer disk.
Such an excitation is provided by the outward migration of the more massive transient inner moons that form at the Roche limit. The satellite embryos in the outer disk can be trapped in mean-motion resonances with the inner moons (when the ratio of their orbital period is a ratio of two integers), and follow concurrently their outward migration. The accumulation of embryos in a resonance favors accretion through collisions, while collisions also provide a mechanism of escaping the resonance. In approximately one third of the results reported by Rosenblatt et al. (2016), two moons were formed by this mechanism, the more massive lying below the synchronous orbit and the less massive lying above it, as for the Martian system (see Tables 1 and 2).
Since more massive inner moons migrate more quickly, the rate of collisions and hence the possibility of accretion can increase, which can lead to cases where all the debris in the outer disk has been accreted onto one or more of the inner moons. This in turn suggests a limit for the mass of the inner disk and hence of the initial impactor. Canup and Salmon (2018) place this limit at around 2x1021 kg (impactor) and 2x1019 kg (disk) compared to the values of 2x1022 kg (impactor) and 5x1020 kg (disk) in Rosenblatt et al. (2016). Although the initial mass of the disk, and thus the energy of the impact, in both studies differ significantly, the basic process of forming moons from re-accretion of debris after a giant collision with Mars is similar (Figure 8).
As well as increasing the semi-major axis of a trapped satellite embryo, mean-motion resonances can also increase its eccentricity. More massive inner moons migrate more quickly, leading to larger eccentricities for the satellite embryos. These can be reduced through collisions and accretion processes, but in numerical simulations (Rosenblatt et al., 2016) the final two outer moons often have eccentricities somewhat larger than those of Phobos and Deimos today. Tidal forces acting over billions of years can help damp these eccentricities, as discussed in the section "Orbital Evolution of the Martian Satellites after the Accretion Period." Alternatively, if the mass of the initial impactor is smaller, the inner disk and hence the moons formed from it will be less massive. The outward migration would then be less rapid, the mean-motion resonances would have less effect, which could result in more numerous small moons in the outer disk with less eccentric orbits (Canup & Salmon, 2018).
Orbital Evolution of the Martian Satellites After the Accretion Period
If tidal evolution cannot allow capture scenarios, it also sets stringent constraints on accretion scenarios. Compared to other planets with moons in our solar system, for Mars the ratio of the centrifugal acceleration to gravitational acceleration is quite small, resulting in a relatively distant synchronous limit at about 6 RM. In contrast to the Earth, this ratio may have barely changed throughout Mars' history (Dones & Tremaine, 1993). The Martian system therefore best illustrates the following rule (Murray & Dermott, 1999): moons above the synchronous limit move away and siphon off angular momentum from the planet (Deimos behaves like most moons in the solar system, including Earth's Moon), while moons below the synchronous limit fall back and restore angular momentum to the planet (Phobos is the most notorious example, but Mars likely had many more moons in the past, see section "A Giant Collision Scenario").
The precise orbital tidal evolution is controlled by gravitational torques from the tidal bulges raised on Mars by the moons and from the tidal bulges raised on the moons by Mars. The evolution equations (Kaula, 1964) depend on a set of parameters k2/Q(~χ) describing tidal dissipation: k2 is the degree-2 potential Love number and Q(~χ) is the tidal quality factor at the principal tidal frequency ~χ (Efroimsky & Lainey, 2007). The Love number k2 depends weakly on frequency; for Mars it can be estimated from tidal perturbations on the orbital motion of Martian spacecraft, which gives a k2 value equal to 0.169 with an error of about 2% (Genova et al., 2016; Konopliv, Park, & Folkner, 2016); for the moons, it has not been measured but models predict k2 ∼10-4 for monoliths with a silicate composition (Lambeck, 1979) and k2 ∼10-3 for rubble piles also with a silicate composition; the porosity indeed decreases rigidity (Jaeger et al., 2007) and in turn increases k2 (Le Maistre et al., 2013; Rosenblatt, 2011), which would be consistent with the high porosity inferred from the mass and volume of Phobos (Andert et al., 2010; Rosenblatt, 2011). The quality factors Q(~χ) depend strongly on the principal tidal frequency ~χ; for Mars it can be estimated at the current semi-diurnal frequency from the secular acceleration of the mean anomaly of Phobos' current orbit, which yields Q = 82.8 ± 0.2 (Jacobson, 2010). The quality factors for Phobos and Deimos have not been measured but rubble piles are expected to be more dissipative than non-porous rocks, with Q < 100 (Goldreich & Sari, 2009).
In the course of tidal evolution, the orbit of the Martian moons shrinks or expands, according to whether it is within or beyond the synchronous limit, mainly due to dissipation within the planet, and circularizes mainly due to dissipation within the moon (Goldreich, 1963); the inclination is barely affected (Mignard, 1981). As the orbit tidally evolves, it passes through several resonances, mainly between the mean motion and Mars's spin at 3.8 RM (a 2:1 resonance) and 2.9 RM (a 3:1 resonance), which will generally re-excite the eccentricity (Yoder, 1982). Other resonances, for example between the pericenter and Mars' mean motion, are harder to model (Yokoyama, 2002), given the chaotic variations of Mars' obliquity (Laskar & Robutel, 1993; Touma & Wisdom, 1993).
If Phobos and Deimos formed from a massive initial disc of debris, with a mass ∼ 10−3 MM (where MM is the mass of Mars), corresponding to an impactor of mass ∼ 10−1.5 MM (Citron et al., 2015), mean-motion resonances with large transient moons (see section "How to Form Two Small Outer Satellites from a Circum-Martian Accretion Disk") could facilitate the formation of exactly two moons with the correct semi-major axes, but with an eccentricity of around 10−2 for Deimos (Rosenblatt et al., 2016). Damping this eccentricity by tidal forces to that observed today would require k2/Q to be of the order of 10−4 for Deimos, at the upper limit of the expected range for rubble piles, and of the order of 10−6 for Phobos, at the lower limit of the expected range for monolithic rocks, thus implying a different structure or composition for the two moons. If Phobos and Deimos were formed from a less massive initial disk of debris, with a mass or around 10−5 MM, corresponding to an impactor of mass about 10−3 MM, mean-motion resonances would be largely ineffective, preventing undesirable excitation of eccentricities, but with the result that several moons could be left orbiting Mars (Canup & Salmon, 2018). For these to disappear, the value of k2/Q for Mars would have to be an order of magnitude larger than that presently observed, which makes the current orbital configuration with exactly two moons much less likely. The current resolution of SPH simulations is, however, too coarse to model the distribution of mass in the outer region of the initial disc of debris.
The formation of moons in the solar system is a long-standing topic of research (Peale & Canup, 2015). Each moon system has unique characteristics, making it difficult to envisage a common mechanism of formation. Recent spacecraft exploration of giant planets, in particular the Cassini mission around Saturn, have brought to light the role played by rings of debris and tidal forces on the formation and orbital evolution of small moons (Crida & Charnoz, 2012). Similar processes can explain the formation of Phobos and Deimos in a disk following a giant impact on Mars. A robust scenario must, however, be able to explain the formation of two small moons rather than a single massive one. The spin imparted to the planet by the impactor plays a major role, as this determines where the synchronous limit is, in particular if it is within or beyond the planet's Roche limit. A post-impact fast rotator will have a synchronous limit close to the planet, which favors the accretion of debris into a single body, as in the case of Earth's moon. A post-impact slow rotator such as Mars, with a spin of about 24 hours, corresponds to a relatively far synchronous limit; moons that form close to the Roche limit, by viscous spreading of the disk, migrate outwards through the interaction with the remnant disk, but under tidal forces they will eventually fall back toward Mars. Only small moons formed close to or beyond the synchronous limit are expected to remain in orbit for a long time. The current spin of Mars is an argument in favor of a relatively massive impactor, which could also be responsible for the formation of the Borealis basin (Hyodo et al., 2017b).
Numerical simulations for the complete scenario, from the initial impact to accretion and the long-term evolution of the two moons, yield better agreement with the present orbits than the previous widely accepted capture hypothesis and are still compatible with the observations concerning their composition. The amount of material blasted into orbit primarily depends on the mass of the impactor and on the angle of impact. This is crucial as it drives the evolution of the debris cloud into an accretion disk, as well as determining its eventual chemical composition. The various collision parameters are, however, difficult to constrain as they depend on the detailed dynamics of the early solar system (Hansen, 2018).
JAXA (Japan Aerospace Exploration Agency) plans a sample return mission from Phobos in the 2020s. The Martian Moons Exploration (MMX) probe will collect about 10 grams of material from Phobos' regolith. If the giant impact hypothesis is correct, MMX would collect not only material from the impactor but also from Mars, including ancient mantle material (Hyodo et al., 2017a). The detailed composition of these samples would help constrain the thermodynamical environment in which they formed and hence the parameters of the giant impact.
Further observations and analysis are thus required to test the giant impact hypothesis and future sample return missions such as MMX will give critical information about the composition (Murchie, Britt, & Pieters, 2014) and hence the origin of the Martian moons, Phobos and Deimos.
Further Reading
Scientific Papers
Geology and surface characteristics of Phobos and Deimos:
Basilevsky, A. T., Lorenz, C. A., Shingareva, T. V., Head, J. W., Ramsley, K. R., & Zubarev, A. E. (2014). The surface geology and geomorphology of Phobos. Planetary and Space Science, 102, 95–118.Find this resource:
Busch, M. W., Ostrob, S. J., Bennerb, L. A. M., Giorginib, J. D., Magric, C., Howell, E. S., . . . Chandler, J. F. (2007). Arecibo radar observations of Phobos and Deimos. Icarus, 186, 581–584.Find this resource:
Cipriani, F., Witasse, O., Leblanc, F., Modolo, R., & Johnson, R. E. (2011). A model of interaction of Phobos' surface with the Martian environment. Icarus, 212, 643–648.Find this resource:
Hurford, T. A., Asphaug, E., Spitale, J. N., Hemingway, D., Rhoden, A. R., Henning, W. G., . . . Walker, M. (2016). Tidal disruption of Phobos as the cause of surface features. Journal of Geophysical Research Planets, 121, 1054–1065.Find this resource:
Murchie, S. L., Britt, D. T., Head, J. W., Pratt, S. F., Fisher, P. C., Zhukov, B. S., . . . Robinson, M. S. (1991). Color heterogeneity of the surface of Phobos: Relationships of geological features and comparison to meteorite analogs. Journal of Geophysical Research, 96, 5925–5945.Find this resource:
Murray, J. B., & Heggie, D. C. (2014). Character and origin of Phobos' grooves. Planetary and Planetary and Space Science, 102, 119–143.Find this resource:
Pieters, C. M., Murchie, S., Thomas, N., & Britt, D. (2014). Composition of surface materials on the moons of Mars. Planetary and Space Science, 102, 144–151.Find this resource:
Ramsley, K. R., & Head, J. W. (2017). The Stickney crater ejecta secondary impact crater spike on Phobos: Implications for the age of Stickney and the surface of Phobos. Planetary and Space Science, 138, 7–24.Find this resource:
Phobos' interior shape, rotation, and interior structure:
Fanale, F. P., & Salvail, J. R. (1990). Evolution of the water regime of Phobos. Icarus, 88, 380–395.Find this resource:
Le Maistre, S., Rivoldini, A., & Rosenblatt, P. (2019). Signature of Phobos' interior structure in its gravity field and libration. Icarus, 321, 272–290.Find this resource:
Oberst, J., Zubarev, A., Nadezhdina, I., Shishkina, L., & Rambaux N. (2014). The Phobos geodetic control point network and rotation model. Planetary and Space Science, 102, 45–50.Find this resource:
Rambaux, N., Castillo-Rogez, J. C., Le Maistre S., & Rosenblatt, P. (2012). Rotational motion of Phobos. Astronomy & Astrophysics, 548, 11.Find this resource:
Willner, K., Shi, X., & Oberst, J. (2014). Phobos' shape and topography models. Planetary and Space Science, 102, 51–59.Find this resource:
SPH simulations:
Canup, R. M. (2004). Simulations of a late lunar-forming impact. Icarus, 168, 433–456.Find this resource:
Accretion process:
Chambers, J. E., & Wetherill, G. W. (1998). Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions. Icarus, 136, 304–327.Find this resource:
Charnoz, S., Salmon, J., & Crida, A. (2010). The recent formation of Saturn's moonlets from viscous spreading of the main rings. Nature, 465, 752–754.Find this resource:
Ida, S., Kokubo, E., & Takeda, T. (2001). N-body simulations of moon accretion. In M. Y. Marov & H. Rickman (Eds.), Collisional processes in the solar system, Vol. 261. Astrophysics and Space Science Library (pp. 203–222). Dordrecht, Netherlands: Springer.Find this resource:
Tidal dissipation, secular acceleration, and orbital evolution:
Jacobson, R. A., & Lainey, V. (2014). Martian satellite orbits and ephemerides. Planetary and Space Science, 102, 35–44.Find this resource:
Kaula, W. M. (1964). Tidal dissipation by solid friction and the resulting orbital evolution. Reviews of Geophysics, 2, 661–685.Find this resource:
Yoder, C. F. (1982). Tidal rigidity of Phobos. Icarus, 49, 327–346.Find this resource:
Formation of natural satellites:
Peale, S. J., & Canup, R. M. (2015). The origin of the natural satellites. In G. Schubert & T. Spohn (Eds.), Treatise on geophysics (Vol. 10, 2nd ed., pp. 559–604). Amsterdam, The Netherlands: Elsevier B.V.Find this resource:
Books on the Solar System
Armitage, P. J. (2010). Astrophysics of planet formation. New York: Cambridge University Press.Find this resource:
Melosh, H. J. (1989). Impact cratering: A geologic process. New York: Oxford University Press.Find this resource:
Murray, C. D., & Dermott, S. F. (1999). Solar system dynamics. Cambridge, U.K.: Cambridge University Press.Find this resource:
Spohn, T., Breuer, D., & Johnson, T. V. (2014). Encyclopedia of the solar system (3rd ed.). Amsterdam, Netherlands: Elsevier.Find this resource:
Digital Resources on Topics
The Lindblad resonance:
• http://jeheo.weebly.com/uploads/5/3/8/0/53803559/lindblad_resonance_doyle_151119.pdf
• https://www.oxfordreference.com/view/10.1093/oi/authority.20110803100106597
Movie and images:
• A reappraisal of the origin of Mars' moons: https://www.astro.oma.be/en/a-reappraisal-of-the-origin-of-mars-moons/
• Mars Express flyby as seen from Phobos (animation): https://www.youtube.com/watch?v=6Kn3wOWZg78
• Mars Express heading towards daring flyby of Phobos: https://www.esa.int/Our_Activities/Space_Science/Mars_Express/Mars_Express_heading_towards_daring_flyby_of_Phobos
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Basilevsky, A. T., Lorenz, C. A., Shingareva, T. V., Head, J. W., Ramsley, K. R., & Zubarev, A. E. (2014). The surface geology and geomorphology of Phobos. Planetary and Space Science, 102, 95–118.Find this resource:
Bibring, J. P. (2010). Phobos' origin: A reappraisal. In EPSC, Vol. 5, EPSC2010-554 (abstract).Find this resource:
Black, B. A., & Mittal, T. (2015). The demise of Phobos and development of a Martian ring system. Nature Geoscience, 8(12), 913–917.Find this resource:
Bottke, W. F., Love S. G., Tytell, D., & Glotch, T. (2000). Interpreting the elliptical crater populations on Mars, Venus, and the Moon. Icarus, 145(1), 108–121.Find this resource:
Bruck Syal, M., Rovny, J., Owen, J. M., & Miller, P. L. (2016). Excavating Stickney crater at Phobos. Geophysical Research Letters, 43, 10,595–10,601.Find this resource:
Burns, J. A. (1992). Contradictory clues as to the origin of the Martian moons. In H. H. Kieffer, B. M. Jakosky, C. W. Snyder, & M. S. Matthews (Eds.), Mars (pp. 1283–1301). Tucson: University of Arizona Press.Find this resource:
Canup, R., & Salmon, J. (2018). Origin of Phobos and Deimos by the impact of a Vesta-to-Ceres sized body with Mars. Science Advances, 4(4).Find this resource:
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Charnoz, S., Salmon, J., & Crida, A. (2010). The recent formation of Saturn's moonlets from viscous spreading of the main rings. Nature, 465, 752–754.Find this resource:
Citron, R. I., Genda, S., & Ida, S. (2015). Formation of Phobos and Deimos via a giant impact. Icarus, 252, 334–338.Find this resource:
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Craddock, R. A. (2011). Are Phobos and Deimos the result of a giant impact? Icarus, 211(2), 1150–1161.Find this resource:
Crida, A., & Charnoz, S. (2012). Formation of regular satellites from ancient massive rings in the solar system. Science, 338(6111), 1196–1199.Find this resource:
Dones, L., & Tremaine, S. (1993). On the origin of planetary spins. Icarus, 103(1), 67–92.Find this resource:
Duxbury, T. C., Zakharov, A. V., Hoffmann, H., & Guinness, E. A. (2014). Spacecraft exploration of Phobos and Deimos. Planetary and Space Science, 102, 9–17.Find this resource:
Efroimsky, M., & Lainey, V. (2007). Physics of bodily tides in terrestrial planets and the appropriate scales of dynamical evolution. Journal of Geophysical Research, 112(E12).Find this resource:
Fraeman, A. A., Arvidson, R. E., Murchie, S. L., Rivkin, A., Bibring, J. P., Choo, T. H., . . . Zabalueva, E. V. (2012). Analysis of disk-resolved OMEGA and CRISM spectral observations of Phobos and Deimos. Journal of Geophysical Research, 117.Find this resource:
Fraeman, A. A, Murchie, S. L., Arvidson, R. E., Clark, R. N., Morris, R. V., Rivkin, A. S., & Vilas, F. (2014). Spectral absorptions on Phobos and Deimos in the visible/near infrared wavelengths and their compositional constraints. Icarus, 229, 196–205.Find this resource:
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Hesselbrock, A. J., & Minton, D. A. (2017). An ongoing satellite-ring cycle of Mars and the origins of Phobos and Deimos. Nature Geoscience, 10(4), 266–269.Find this resource:
Hurford, T. A., Asphaug, E., Spitale, J. N., Hemingway, D., Rhoden, A. R., Henning, W. G., . . .Walker, M. (2016). Tidal disruption of Phobos as the cause of surface features. Journal of Geophysical Research Planets, 121, 1054–1065.Find this resource:
Hyodo, R., & Genda, H. (2018). Implantation of Martian materials in the inner solar system by a mega impact on Mars. Astrophysical Journal Letters, 856(2).Find this resource:
Hyodo, R., Genda, H., Charnoz, S., Pignatale, F. C. F., & Rosenblatt, P. (2018). On the impact origin of Phobos and Deimos. IV: Volatile depletion. Astrophysical Journal, 860(2).Find this resource:
Hyodo, R., Genda, H., Charnoz, S., & Rosenblatt, P. (2017a). On the impact origin of Phobos and Deimos. I: Thermodynamic and physical aspects. Astrophysical Journal, 845(2).Find this resource:
Hyodo, R., Rosenblatt, P., Genda, H., & Charnoz, S. (2017b). On the impact origin of Phobos and Deimos. II: True polar wander and disk evolution. Astrophysical Journal, 851(2).Find this resource:
Jacobson, R. A. (2010). The orbits and masses of the Martian satellites and the libration of Phobos. Astronomical Journal, 139(2), 668–679.Find this resource:
Jacobson, R. A., & Lainey, V. (2014). Martian satellite orbits and ephemerides. Planetary and Space Science, 102, 35–44.Find this resource:
Jaeger, J. C., Cook, N. G. W., & Zimmerman, R. W. (2007). Micromechanical models. In J. C. Jaeger, N. G. W. Cook, & R. W. Zimmerman (Eds.), Fundamentals of rock mechanics (4th ed., pp. 281–320). Oxford, U.K.: Blackwell.Find this resource:
Kaula, W. M. (1964). Tidal dissipation by solid friction and the resulting orbital evolution. Reviews of Geophysics, 2, 661–685.Find this resource:
Konopliv, A. S., Park, R. S., & Folkner, W. M. (2016). An improved JPL Mars gravity field and orientation from Mars orbiter and lander tracking data. Icarus, 274, 253–260.Find this resource:
Lambeck, K. (1979). On the orbital evolution of the Martian satellites. Journal of Geophysical Research, 84, 5651–5658.Find this resource:
Lantz, C., Clark, B. E., Barucci, M. A., & Lauretta, D. S. (2013). Evidence for the effects of space weathering spectral signatures on low albedo asteroids. Astronomy & Astrophysics, 554.Find this resource:
Laskar, J., & Robutel, P. (1993). The chaotic obliquity of the planets. Nature, 361(6413), 608–612.Find this resource:
Le Maistre, S., Rosenblatt, P., Rambaux, N., Castillo-Rogez, J. C., Dehant, V., & Marty, J. C. (2013). Phobos interior from librations determination using Doppler and star tracker measurements. Planetary and Space Science, 85, 106–122.Find this resource:
Marinova, M. M., Aharonson, O., & Asphaug, E. (2008). Mega-impact formation of the Mars hemispheric dichotomy. Nature, 453(7199), 1216–1219.Find this resource:
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Murchie, S. L., Britt, D. T., Head, J. W., Pratt, S. F., Fisher, P. C., Zhukov, B. S., . . . Robinson, M. S. (1991). Color heterogeneity of the surface of Phobos: Relationships of geological features and comparison to meteorite analogs. Journal of Geophysical Research, 96, 5925–5945.Find this resource:
Murchie, S. L., Britt, D. T., & Pieters, C. M. (2014). The value of Phobos sample return. Planetary and Space Science, 102, 176–182.Find this resource:
Murchie, S., & Erard, S. (1996). Spectral properties and heterogeneity of Phobos from measurements by Phobos 2. Icarus, 123(1), 63–86.Find this resource:
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Nakajima, M., & Canup, R. M. (2017). Origin of the Martian moons and their volatile abundances. Paper presented at American Geophysical Union Fall Meeting, abstract #P54B-05.Find this resource:
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(1.) Asaph Hall was greatly supported by his wife Angeline Stickney in his quest of Martian satellites.


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Guide to Hiring a Traffic Ticket Attorney
When a motorist or a road user violates traffic laws, it is the role of a law enforcement officer to issue a traffic ticket. The tickets offered to the motorist can either be a moving or a non-moving ticket. Example of a moving ticket include speed limit violation while a non-moving ticket consists of a parking violation.
When the traffic police officer assess the vehicle of a motorist and find out that it is not in roadworthy, say it wheel are worn out, the driver will be required to pay a fine or his or her points are deducted, however, the penalty varies depending on a country. When a motorist fails to pay for the fine that is stated by the law enforcement officer, will have to come to a court of law to face trial or they can be prosecuted.
When a motorist is required to appear in court for violating a traffic rule; they need to look for a good traffic ticket attorney who will represent them fully in court proceedings. The following are the advantages of hiring a traffic ticket attorney. Motorist need to have an attorney since the lawyers save s them time, the lawyers will represent them in court when they are asked to come hence enabling the motorist to go on with their engagements while the lawyer is in court proceedings. Furthermore, the penalties, and fees that a traffic police orders a motorist to pay when found violating the traffic rules are normally not friendly, they are at times costly, therefore when you have an attorney, he or she will try their best to ensure that the penalties are withdrawn or reduced. In most cases, the penalties and fines are not easy to comprehend since they come with additional financial blows including increase in auto insurance rates, as well as increase in points added to the motorist's driving record. Road users who have traffic ticket attorney are free from the risk of their driving license being revoked or suspended by a traffic officer when their records of violation of the traffic rules reach unsustainable level.
As much as traffic ticket attorneys are useful, most motorist find it difficult in choosing the best lawyer to represent them in court. When looking for a lawyer, choose the one who has vast knowledge and experience in handling such cases. It is vital for motorist to consider hiring lawyers who are insured with a recognized insurance company in the area.
Also when looking for a traffic ticket lawyer, motorists need to ask for referrals about the attorney from friends and relatives. In addition, ensure that the attorney you hire has good number of staff since the attorney will need his team to assist him in preparing the court files, therefore consider the one with a sufficient staff.
A 10-Point Plan for Services (Without Being Overwhelmed)

subset: commoncrawl


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About Us
The Faculty of Commerce, Law and Management (CLM) was constituted as part of the University of the Witwatersrand's re-organisation process in 2001. Based in the Commerce, Law and Management Building on Braamfontein Campus West, the Faculty is the second largest in the University of the Witwatersrand. It consists of six Schools, four of which offer undergraduate and postgraduate programmes while two offer postgraduate programmes exclusively.
The former are based on Braamfontein Campus West
The Postgraduate Schools are based on the Parktown Management Campus
There are three discipline-based libraries managed by the Faculty:
- Commerce Library
- Law Library
- Management Library (on the Parktown Management Campus)
CLM offers professional development in the business and legal areas of expertise as well as educational programmes that compare with the very best globally. We are persistent on increasing our intake of postgraduate students and post-doctoral fellows to produce groundbreaking research output. Our programmes prepare our graduates to:
- join a group of distinctive public and private sector leaders in the fast-growing world of financial service industries
- become men and women with entrepreneurial spirit who are able to think analytically, make decisions and solve problems
- follow various exciting careers in the legal profession, in industry and commerce, or in government and the diplomatic corps
- participate significantly in the global economy.


text: Data Binding in Sparkline for WPF and Silverlight In this video we examine how to bind the data from a class to the sparkline. Specifically, we'll create a Plain Old CLR Object (POCO) and bind it to various Sparkline types to see the data displayed using this lightweight graphic. Download the project December 4, 2013


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Challenging China: Wealthy Entrepreneurs Take on Beijing
Three business people, made rich in China's boom of the past two decades, are now pushing for social and political reform, testing the limits of the Communist Party's tolerance for criticism. The Wall Street Journal profiles them in three videos: wsj.com/challengingchina
This transcript has been automatically generated and may not be 100% accurate.
I ... is this is just the last economic success has created a cost of a wealthy entrepreneur is ... they can walk in and critique from communist pots he insisted ... the ... but somehow become outspoken critics of the system and free social media but on Thursday and the promotion of what's going on there ... the wealth and influence is a potentially powerful threat to the communist coffee ... especially when economic growth is slowing ... and more Chinese unquestioning awe Steve Earle ... our ... President Xi Singh ... says he wants the bees knees cost to feel free to share their opinions while still abiding by the middle ... it's a complicated relationship ... this China's government comes down on free speech some business people still channeling the coffee on and ... pushing the boundaries between Caulfield parties' will call rates