Orbital history of the Martian satellites with inferences on their origin

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.     

Exchange of ejecta between Telesto and Calypso: Tadpoles, horseshoes, and passing orbits

We have numerically integrated the orbits of ejecta from Telesto and Calypso, the two small Trojan companions of Saturn’s major satellite Tethys. Ejecta were launched with speeds comparable to or exceeding their parent’s escape velocity, consistent with impacts into regolith surfaces. We find that the fates of ejecta fall into several distinct categories, depending on both the speed and direction of launch.The slowest ejecta follow suborbital trajectories and re-impact their source moon in less than one day. Slightly faster debris barely escape their parent’s Hill sphere and are confined to tadpole orbits, librating about Tethys’ triangular Lagrange points L₄ (leading, near Telesto) or L₅ (trailing, near Calypso) with nearly the same orbital semi-major axis as Tethys, Telesto, and Calypso. These ejecta too eventually re-impact their source moon, but with a median lifetime of a few dozen years. Those which re-impact within the first 10 years or so have lifetimes near integer multiples of 348.6 days (half the tadpole period).Still faster debris with azimuthal velocity components ?10 m/s enter horseshoe orbits which enclose both L₄ and L₅ as well as L₃, but which avoid Tethys and its Hill sphere. These ejecta impact either Telesto or Calypso at comparable rates, with median lifetimes of several thousand years. However, they cannot reach Tethys itself; only the fastest ejecta, with azimuthal velocities ?40 m/s, achieve “passing orbits” which are able to encounter Tethys. Tethys accretes most of these ejecta within several years, but some 1% of them are scattered either inward to hit Enceladus or outward to strike Dione, over timescales on the order of a few hundred years.     

Blowing in the wind. II. Creation and redistribution of refractory inclusions in a turbulent protoplanetary nebula

Ca-Al rich refractory mineral inclusions (CAIs) found at 1-6% mass fraction in primitive chondrites appear to be 1-3 million years older than the dominant (chondrule) components which were accreted into the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the Sun. We reassess the situation in terms of a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can overcome inward drift, and prevent significant numbers of CAI-size particles from being lost into the Sun for times on the order of 10⁶ years. CAIs can form early, when the inner nebula was hot, and persist in sufficient abundance to be incorporated into primitive planetesimals at a much later time. Small (?0.1 mm diameter) CAIs persist for longer times than large (?5 mm diameter) ones. To obtain a quantitative match to the observed volume fractions of CAIs in chondrites, another process must be allowed for: a substantial enhancement of the inner hot nebula in silicate-forming material, which we suggest was caused by rapid inward drift of meter-sized objects. This early in nebula history, the drifting rubble would have a carbon content probably an order of magnitude larger than even the most primitive (CI) carbonaceous chondrites. Abundant carbon in the evaporating material would help keep the nebula oxygen fugacity low, plausibly solar, as inferred for the formation environment of CAIs. The associated production of a larger than canonical amount of CO₂ might also play a role in mass-independent fractionation of oxygen isotopes, leaving the gas rich in ¹⁶O as inferred from CAIs and other high temperature condensates.     

The Distribution of Craters Within Craters

Photometric correction is a necessary step in planetary image pre-processing since the images of planetary surfaces are acquired by orbiting spacecraft at various observational geometries. In this study, visible (748 nm) and near-infrared (948 nm) bands of Hyper Spectral Imager (HySI) onboard Chandrayaan-1 have been used to derive a preliminary photometric correction for lunar data. The purpose of the proposed photometric correction for HySI is to convert observations taken at solar incidence (i), sensor emission (e), and the solar phase angles (α) to a fixed geometry by applying i?=?α?=?30° and e?=?0° to each image. The Lommel–Seeliger function was used to model the lunar limb darkening effect, while topography data from the merged Digital Elevation Model of Lunar Reconnaissance Orbiter—Lunar Orbiter Laser Altimeter (LRO-LOLA) and SELENE Terrain Camera (TC) was used to correct local topographic effects. Data from Moon Mineralogy Mapper (M³), SELENE Multiband Imager (MI) and Clementine Ultraviolet and Visible Camera (UV/VIS) were also used to compare radiance, reflectance and phase functions derived from HySI. Our analysis reveals that HySI is darker than M³ primarily due to low surface radiance conditions observed by HySI. The derived phase functions for the two HySI bands indicate a good correlation between the derived reflectance and phase angle as well as with the phase functions derived for the empirically corrected M³ data. This approach led to the derivation of a photometric correction for maria regions. Finally, it is expected that the proposed correction would be applicable to all HySI images covering the lunar mare region.

     

The fate of ejecta from Hyperion

Ejecta from Saturn's moon Hyperion are subject to powerful perturbations from nearby Titan, which control their ultimate fate. We have performed numerical integrations to simulate a simplified system consisting of Saturn (including optical flattening as well as dynamical oblateness), its main ring system (treated as a massless flat annulus), the moons Tethys, Dione, Titan, Hyperion, and Iapetus, and the Sun (treated simply as a massive satellite). At several different points in Hyperion's orbit, 1050 massless particles, more or less evenly distributed over latitude and longitude, were ejected radially outward from 1 km above Hyperion's mean radius at speeds 10% faster than escape speed from Hyperion. Most of these particles were removed within the first few thousand years, but ∼3% of them survived the entire 100,000-year duration of the simulations. Ejecta from Hyperion are much more widely scattered than previously thought, and can cross the orbits of all of Saturn's satellites. About 9% of all the particles escaped from the saturnian system, but Titan accreted ∼78% of the total, while Hyperion reaccreted only ∼5%. This low efficiency of reaccretion may help to account for Hyperion's small size and rugged shape. Only ∼1% of all the particles hit other satellites, and another ∼1% impacted Saturn itself, while ∼3% of them struck its main rings. The high proportion of impacts into Saturn's rings is surprising; these collisions show a broad decline in impact speed with time, suggesting that Hyperion ejecta gradually spread inwards. Additional simulations were used to investigate the dependence of ejecta evolution on launch speed, the mass of Hyperion, and the presence of the Sun. In general, the wide distribution of ejecta from Hyperion suggests that it does contribute to “Population II” craters on the inner satellites of Saturn. Ejecta which escape from a satellite into temporary orbit about its planet, but later reimpact into the same moon or another one produce “poltorary” impacts, intermediate in character between primary and secondary impacts. It may be possible to distinguish poltorary craters from primary and secondary craters on the basis of morphology.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

Carbon dioxide-water clathrate as a reservoir of CO2 on Mars

It has been suggested that the residual polar caps of Mars contain a reservoir of permanently frozen carbon dioxide which is controlling the atmospheric pressure. However, observational data and models of the polar heat balance suggest that the temperatures of the Martian poles are too high for solid CO₂ to survive permanently. On the other hand, the icelike compound carbon dioxide-water clathrate (CO₂ · 6H₂O) could function as a CO₂ reservoir instead of solid CO₂, because it is stable at higher temperatures. This paper shows that the permanent polar caps may contain several millibars of CO₂ in the form of clathrate, and discusses the implications of this permanent clathrate reservoir for the present and past atmospheric pressure on Mars.     

Lifetimes of small bodies in planetocentric (or heliocentric) orbits

Stray bodies orbiting a planet or the Sun are removed by collisions with larger objects or by expulsion from the system. However, their rate of removal generally cannot be described by the simple exponential law used to describe radioactive decay, because their effective half-life lengthens with time. Previous studies of planetesimals, comets, asteroids, meteorites, and impact ejecta from planets or satellites have fit the number of survivors S vs elapsed time t using exponential, logarithmic, and power laws, but no entirely satisfactory functional form has been found yet. Herein we model the removal rates of impact ejecta from various moons of Jupiter, Saturn, and Neptune. We find that most situations are fit best by stretched exponential decay, of the form S(t)=S(0)exp(−β[t/t₀]). Here t₀ is the time when the initial population has declined by a factor of e≈2.72, while the dimensionless exponent β lies between 0 and 1 (often near 1/3). The e-folding time S⁻¹[dS/dt] itself grows as the [1−β] power of t. This behavior is suggestive of a diffusion-like process.     

Internal stresses in phobos and other triaxial bodies

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.     

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

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