Improved measurement of Asteroid (4) Vesta’s rotational axis orientation

We report an improved measurement of the rotational axis orientation of Asteroid (4) Vesta. By analyzing and combining all previous measurements using a limb-fitting technique from ground/HST data collected from 1983 to 2006, we derive a pole solution of (RA = 304.5°, Dec = 41.5°). Images of Vesta acquired with the Wide Field Camera 3 onboard the Hubble Space Telescope (HST) in February 2010 are combined with images from the Wide Field Planetary Camera 2 on HST obtained in 1994, 1996, and 2007 at similar spatial resolution and wavelengths to perform new measurements. Control point stereogrammetry returns a pole solution of (305.1°, 43.4°). An alternate method tracks surface features and fits their projected paths with ellipses to determine a great circle containing the pole for each HST observation. Combined, the four great circles yield a pole solution of (309.3°, 41.9°). These three solutions obtained with almost independent methods are within 3.5° of each other, suggesting a robust solution. Combining the results from all three techniques, we propose an improved value of the rotational axis of Vesta as RA = 305.8° ± 3.1°, Dec = 41.4° ± 1.5° (1-σ error). This new solution changes from (301°, 41°) reported by Thomas et al. (Thomas, P.C., Binzel, R.P., Gaffey, M.J., Zellner, B.H., Storrs, A.D., Wells, E. [1997a]. Icarus 128, 88-94) by 3.6°, and from (306°, 38°) reported by Drummond and Christou (Drummond, J.D., Christou, J. [2008]. Icarus 197, 480-496) by 3.4°. It changes the obliquity of Vesta by up to ∼3°, but increases the Sun-centered RA of Vesta at equinox by ∼8°, and postpones the date of equinox by ∼35 days. The change of the pole position is less than the resolution of all previous images of Vesta, and should not change the main science conclusions of previous research about Vesta.     

Free and forced obliquities of the Galilean satellites of Jupiter

The obliquity, or angular separation between orbit normal and spin pole, is an important parameter for the geodynamics of most Solar System bodies. Tidal dissipation has driven the obliquities of the Galilean satellites of Jupiter to small, but non-zero values. We present estimates of the free and forced obliquities of these satellites using a simple secular variation model for the orbits, and spin pole precession rate estimates based on gravity field parameters derived from Galileo spacecraft encounters. The free obliquity values are not well constrained by observations, but are presumed to be very small. The forced obliquity variations depend only on the orbital variations and the spin pole precession rate parameters, which are quite well known. These variations are large enough to influence spatial and temporal patterns of tidal dissipation and tidal stress.     

Rotational dynamics and internal structure of Titan

Estimates of the moments of inertia of Titan, as separately deduced from its gravitational field and spin pole orientation, are quite different. This discrepancy can be resolved if Titan is either not precessing as a rigid body (e.g. if the shell is decoupled from the interior by an ocean), or if the spin pole is not fully damped (e.g. due to atmospheric excitation). By the end of the Cassini mission, continued monitoring of the changing spin pole orientation, by Cassini radar observations, will determine which effect dominates.     

Mid-infrared lightcurve of Vesta

We present a thermal mid-infrared lightcurve of Asteroid 4 Vesta and use this to infer variations in thermophysical properties over the surface. Vesta was observed over three nights during the May 2007 opposition with the Infrared Telescope Facility on Mauna Kea. Mid-infrared observations are compared to a model based on the Standard Thermal Model which is draped over a Vesta shape model derived from Hubble Space Telescope observations.A visible lightcurve with similar aspect was used to estimate the albedo as Vesta rotates. Shape and albedo can explain some of the features observed in the mid-infrared lightcurve. However, variations in the thermophysical properties, such as the “beaming parameter,” over Vesta’s surface are required to completely explain the observations.In order to match the mid-infrared magnitudes observed of Vesta, a beaming parameter of ∼0.862 is required which is higher than other Main Belt Asteroids such as Ceres and Pallas (0.756), indicating a smoother and/or rockier surface on Vesta. Variations in the beaming parameter with longitude are invoked to reproduce the observed thermal variations. Surface materials with relatively high beaming values, indicating a smoother and/or rockier surface, in the eastern hemisphere of Vesta coincide with locations where impact excavations may have produced surfaces that are younger and brighter relative to the western hemisphere.     

Triaxial ellipsoid dimensions and rotational poles of seven asteroids from Lick Observatory adaptive optics images, and of Ceres

Seven main belt asteroids, 2 Pallas, 3 Juno, 4 Vesta, 16 Psyche, 87 Sylvia, 324 Bamberga, and 707 Interamnia, were imaged with the adaptive optics system on the 3 m Shane telescope at Lick Observatory in the near infrared, and their triaxial ellipsoid dimensions and rotational poles have been determined with parametric blind deconvolution. In addition, the dimensions and pole for 1 Ceres are derived from resolved images at multiple epochs, even though it is an oblate spheroid.     

On the prograde rotation of asteriods

Sets of diameter determinations before and after opposition for the asteriods Ceres, Pallas, Vesta, and Fortuna have been studied statistically for indications of spin direction. All four asteriods are tentatively found to have prograde spin. For Ceres, that conclusion is virtually certain.     

A Mercury orientation model including non-zero obliquity and librations

Planetary orientation models describe the orientation of the spin axis and prime meridian of planets in inertial space as a function of time. The models are required for the planning and execution of Earth-based or space-based observational work, e.g. to compute viewing geometries and to tie observations to planetary coordinate systems. The current orientation model for Mercury is inadequate because it uses an obsolete spin orientation, neglects oscillations in the spin rate called longitude librations, and relies on a prime meridian that no longer reflects its intended dynamical significance. These effects result in positional errors on the surface of ~1.5 km in latitude and up to several km in longitude, about two orders of magnitude larger than the finest image resolution currently attainable. Here we present an updated orientation model which incorporates modern values of the spin orientation, includes a formulation for longitude librations, and restores the dynamical significance to the prime meridian. We also use modern values of the orbit normal, spin axis orientation, and precession rates to quantify an important relationship between the obliquity and moment of inertia differences.     

Spin axis of (2953) Vysheslavia and its implications

Photometric observations made during the years 2000-2005 are used to determine the pole orientation of (2953) Vysheslavia, a ?15-km size member of the Koronis family. We find admissible solutions for ecliptic latitude and longitude of the rotation pole P₃: βp=−64°±10° and λp=11°±8° or P₄: βp=−68°±8° and λp=192°±8°. These imply obliquity values γ=154°±14° and γ=157°±11°, respectively. The sidereal rotation period is Psid=0.2622722±0.0000018 day. This result is interesting for two reasons: (i) the obliquity value between 90° and 180° is consistent with a prediction done by Vokrouhlický et al. [Vokrouhlický, D., Bro?, M., Farinella, P., Kne?evi?, Z., 2001. Icarus 150, 78-93] that Vysheslavia might have been transported to its unstable orbit by the Yarkovsky effect, and (ii) with the obliquity close to 180°, Vysheslavia seems to belong to one of the two distinct groups in the Koronis family found recently by Slivan [Slivan, S.M., 2002. Nature 419, 49-51], further supporting the case of dichotomy in the spin axis distribution in this family. We also argue against the possibility that Vysheslavia reached its current orbit by a recent collisional breakup.     

Obliquity evolution of extrasolar terrestrial planets

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ₀), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ₀∼1) are more likely to be produced than straight ones (sinγ₀∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ₀∼10° or the two-body planar problem in which γ₀=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ₀ (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ₀ space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.     

Forced obliquity and moments of inertia of Titan

The obliquity of Titan is small, but certainly non-zero, and may be used to place constraints on Titan's internal structure. The measured gravity coefficients of Titan imply that it is non-hydrostatic and thus the normal Darwin-Radau approach to determining internal structure cannot be applied. However, if the obliquity is assumed to be tidally damped (that is, in a Cassini state) then combining the obliquity with the measured gravity coefficients allows Titan's moment of inertia to be determined without invoking hydrostatic equilibrium. For polar moment values in the range (0.3<C/MR²<0.4), tidally-damped obliquity values of (0.115°<|ε|<0.177°) result. If the inferred moment value exceeds 0.4, this strongly suggests the presence of a near-surface ice shell decoupled from the interior, probably by a subsurface ocean.     

Insolation patterns on synchronous exoplanets with obliquity

A previous paper [Dobrovolskis, A.R., 2007. Icarus 192, 1-23] showed that eccentricity can have profound effects on the climate, habitability, and detectability of extrasolar planets. This complementary study shows that obliquity can have comparable effects.The known exoplanets exhibit a wide range of orbital eccentricities, but those within several million kilometers of their suns are generally in near-circular orbits. This fact is widely attributed to the dissipation of tides in the planets. Tides in a planet affect its spin even more than its orbit, and such tidally evolved planets often are assumed to be in synchronous rotation, so that their rotation periods are identical to their orbital periods. The canonical example of synchronous spin is the way that our Moon always keeps nearly the same hemisphere facing the Earth.Tides also tend to reduce the planet’s obliquity (the angle between its spin and orbital angular velocities). However, orbit precession can cause the rotation to become locked in a “Cassini state”, where it retains a nearly constant non-zero obliquity. For example, our Moon maintains an obliquity of about 6.7° with respect to its orbit about the Earth. In comparison, stable Cassini states can exist for practically any obliquity up to ∼90° or more for planets of binary stars, or in multi-planet systems with high mutual inclinations, such as are produced by scattering or by the Kozai mechanism.This work considers planets in synchronous rotation with circular orbits, but arbitrary obliquity β; this affects the distribution of insolation over the planet’s surface, particularly near its poles. For β=0, one hemisphere bakes in perpetual sunshine, while the opposite hemisphere experiences eternal darkness. As β increases, the region of permanent daylight and the antipodal realm of endless night both shrink, while a more temperate area of alternating day and night spreads in longitude, and especially in latitude. The regions of permanent day or night disappear at β=90°. The insolation regime passes through several more transitions as β continues to increase toward 180°, but the surface distribution of insolation remains non-uniform in both latitude and longitude.Thus obliquity, like eccentricity, can protect certain areas of the planet from the worst extremes of temperature and solar radiation, and can improve the planet’s habitability. These results also have implications for the direct detectability of extrasolar planets, and for the interpretation of their thermal emissions.     

Binary asteroid population. 2. Anisotropic distribution of orbit poles of small,inner main-belt binaries

Our photometric observations of 18 main-belt binary systems in more than one apparition revealed a strikingly high number of 15 having positively re-observed mutual events in the return apparitions. Our simulations of the survey showed that it cannot be due to an observational selection effect and that the data strongly suggest that poles of mutual orbits between components of binary asteroids in the primary size range 3–8 km are not distributed randomly: The null hypothesis of an isotropic distribution of the orbit poles is rejected at a confidence level greater than 99.99%. Binary orbit poles concentrate at high ecliptic latitudes, within 30° of the poles of the ecliptic. We propose that the binary orbit poles oriented preferentially up/down-right are due to either of the two processes: (i) the YORP tilt of spin axes of their parent bodies toward the asymptotic states near obliquities 0° and 180° (pre-formation mechanism) or (ii) the YORP tilt of spin axes of the primary components of already formed binary systems toward the asymptotic states near obliquities 0° and 180° (post-formation mechanism). The alternative process of elimination of binaries with poles closer to the ecliptic by dynamical instability, such as the Kozai effect due to gravitational perturbations from the Sun, does not explain the observed orbit pole concentration. This is because for close binary asteroid systems, the gravitational effects of primary’s irregular shape dominate the solar-tide effect.     

Dawn Mission to Vesta and Ceres

The initial exploration of any planetary object requires a careful mission design guided by our knowledge of that object as gained by terrestrial observers. This process is very evident in the development of the Dawn mission to the minor planets 1 Ceres and 4 Vesta. This mission was designed to verify the basaltic nature of Vesta inferred both from its reflectance spectrum and from the composition of the howardite, eucrite and diogenite meteorites believed to have originated on Vesta. Hubble Space Telescope observations have determined Vesta’s size and shape, which, together with masses inferred from gravitational perturbations, have provided estimates of its density. These investigations have enabled the Dawn team to choose the appropriate instrumentation and to design its orbital operations at Vesta. Until recently Ceres has remained more of an enigma. Adaptive-optics and HST observations now have provided data from which we can begin to confidently plan the mission. These observations reveal a rotationally symmetric body with little surface relief, an ultraviolet bright point that can be used as a control point for determining the pole and anchoring a geographic coordinate system. They also reveal albedo and color variations that provide tantalizing hints of surface processes.     

10 μm polarimetry of ceres

Linear polarimetry of Ceres at 10 μm is presented. These data represent the first published polarization measurements of an asteroid in the thermal infrared. It is found that Ceres is polarized at the 0.2-0.6% level. This data set is compared with theoretical models of the linear polarization of emitted radiation from a spherical plane. These models are used to derive the pole position and thermal inertia of Ceres. Ceres is best fit with a thermal inertia of $\text{0.0010±0.0003}\text{cal}\text{cm}{}^{\mathrm{?2}}\text{°}\text{K}{}^{\mathrm{?1}}\text{sec}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and a pole orientation of β_p = 36° ± 5°, λ_p = 270° ± 3°. It is concluded that 10μm polarimetry is a potentially powerful technique for remotely sensing the pole orientation and thermal inertia of asteroids.     

Orbital change experiments with a Mars general circulation model

We use a Mars general circulation model to examine the effect of orbital changes on the planet’s general circulation and climate system. Experiments are performed for obliquities ranging from 0° to 60° for two different longitudes of perihelion. Each experiment simulates a full Mars year assuming a fixed atmospheric dust distribution and fixed amount of CO₂ in the atmosphere/cap system. We find that global mean surface temperatures and pressures decline with increasing obliquity due to the increasing extent of the winter polar caps. The seasonal CO₂ cycle and intensity of the solstice circulation amplify considerably with increasing obliquity such that global dust storms are likely at both solstices. The most significant feature of the high obliquity solstice circulations is the development of an intense low-level jet associated with the return branch of the Hadley circulation.Model surface stresses are used to map regions of preferred dust lifting, which are defined in terms of an annual deflation potential. For the present obliquity, the model-predicted regions of high deflation potential are in good agreement with Cantor et al.’s (2001, J. Geophys. Res.106, 23653-23688) observations, which gives us some confidence in the model’s ability to predict where lifting might occur when Mars’ orbit parameters are different than they are today. In general we find that the dust lifting potential increases sharply with obliquity and is greatest at times of high obliquity when perihelion coincides with northern summer solstice. Over an obliquity cycle, the model global annual deflation potential ranges from several tenths of a millimeter at 0° obliquity to almost 15 mm at 60° obliquity. Much higher values are possible when the atmosphere is very dusty.We find a strong correlation between the deflation potential and surface thermal inertia: regions of high deflation potential correspond to regions of high thermal inertia (high rock abundance), and regions of low deflation potential correspond to regions of low thermal inertia (high dust/sand abundance). Furthermore, while the regions of preferred lifting (high deflation potential) expand somewhat with increasing obliquity and dust loading, the central parts of Tharsis, Arabia, and Elysium show no tendency for significant lifting at any obliquity or longitude of perihelion. These regions may therefore be very old and represent net long-term sinks for atmospheric dust. It is the topography of the planet, through its influence on surface pressure and wind systems, which ultimately determines where dust accumulates.Finally, as was found by Fenton and Richardson (2001, J. Geophys. Res.106, 32885-32909), we find no tendency for the development of east-southeasterly winds at the Pathfinder site for any of our orbital change experiments. This suggests that the ancient wind regime discussed by Greeley et al. (2000, J. Geophys. Res.105, 1829-1840) was produced by other factors, such as polar wander.     

Fugitives from the Vesta family

Spectroscopic observations of Asteroid (4) Vesta and numerous members of the Vesta family located in the inner asteroid belt have determined that these objects have reflectance properties of basaltic material. A plausible hypothesis is that the surface of Vesta was punctured by large impacts in the past which dispersed fragments of its basaltic crust into space and produced one of the most prominent asteroid families ever created in the belt. Until recently, Vesta was the only known object in the asteroid belt which underwent differentiation and survived to the present epoch. Since 2000, many new small basaltic asteroids have been discovered in the inner and outer parts of the asteroid belt, possibly representing fragments from distinct differentiated bodies. These discoveries may help us to better understand the number and nature of objects in the inner Solar System that underwent geological differentiation. To investigate these issues we performed extensive numerical simulations whose aim was to reproduce, as precisely as possible, the dynamical evolution of Vesta's ejected fragments over timescales comparable to the family's age. Specifically, we numerically integrated the orbital evolution of 6600 test bodies with orbits that started within the Vesta family and dynamically evolved over 2 Gy. Our model included gravitational perturbation of all planets (except Mercury) and the Yarkovsky effect. The results show that a relatively large fraction of the original Vesta family members may have evolved out of the family borders defined by clustering algorithms and are now dispersed over the inner asteroid belt. We compared the orbital distribution of our model fragments with the orbital locations of known basaltic asteroids in various parts of the inner main belt to find that: (i) Most basaltic asteroids with semimajor axis located outside the Vesta family's borders in the inner main belt, including (809) Lundia and (956) Elisa, are most likely fugitives from the Vesta family that have evolved to their current orbits via various identified dynamical pathways. Our results also suggest that the Vesta family is at least ∼1 Gy old. (ii) Interestingly, orbits of many basaltic asteroids with , like those of (4796) Lewis and (5379) Abehiroshi, are displaced from the Vesta family to low inclinations and are not obtained in our simulations with sufficient efficiency. We propose that: (i) these small basaltic asteroids may be fragments of differentiated bodies other than (4) Vesta; or (ii) they were liberated from the Vesta's surface before (or during) the Late Heavy Bombardment epoch ∼3.8 Gy ago and their orbital inclinations separated from that of Vesta when secular resonances swept through the region.     

The spin state of 433 Eros and its possible implications

In this paper, we show that Asteroid (433) Eros is currently residing in a spin-orbit resonance, with its spin axis undergoing a small-amplitude libration about the Cassini state 2 of the proper mode in the nonsingular orbital element sinI/2exp(?Ω), where I the orbital inclination and Ω the longitude of the node. The period of this libration is ?53.4 kyr. By excluding these libration wiggles, we find that Eros' pole precesses with the proper orbital plane in inertial space with a period of ?61.4 kyr. Eros' resonant state forces its obliquity to oscillate with a period of ?53.4 kyr between ?76° and ?89.5°. The observed value of ?89° places it near the latter extreme of this cycle. We have used these results to probe Eros' past orbit and spin evolution. Our computations suggest that Eros is unlikely to have achieved its current spin state by solar and planetary gravitational perturbations alone. We hypothesize that some dissipative process such as thermal torques (e.g., the so-called YORP effect) may be needed in our model to obtain a more satisfactory match with data. A detailed study of this problem is left for future work.     

Photometric mapping of Asteroid (4) Vesta’s southern hemisphere with Hubble Space Telescope

We present the surface mapping of the southern hemisphere of Asteroid (4) Vesta obtained from Hubble Space Telescope (HST). From 105 images of Vesta through four filters in the wavelengths best to characterize the 1-μm pyroxene band, we constructed albedo and color-ratio maps of Vesta. These new maps cover latitudes −50° to +20°. The southern hemisphere of Vesta displays more diverse albedo and color features than the northern hemisphere, with about 15 new albedo and color features identified. The overall longitudinal albedo and color variations in the southern hemisphere are comparable with that of the northern hemisphere, with a range of about ±20% and ±10%, respectively. The eastern hemisphere is brighter and displays more diogenitic minerals than the western hemisphere. Correlations between 1-μm band depth and band width, as well as between 1-μm band depth and albedo, are present on a global scale, attributed to pyroxene composition variations. The lack of correlations between albedo and the spectral slope indicates the absence of globalized space weathering. The lack of a global correlation between 1-μm band depth and topography suggests that the surface composition of Vesta is not completely controlled by a single impact. The distribution of compositional variation on Vesta suggests a possible large impact basin. Evidence of space weathering is found in regions, including the bright rim of the south-pole crater where the steepest gravitational slope on Vesta is, and a dark area near a gravitationally flat area. We propose to divide the surface of Vesta into six geological units different from the background according to their 1-μm absorption features and spectral slopes, including two eucrite-rich units, a low-Ca eucrite unit, a diogenite-rich unit, a space weathered unit, and a freshly exposed unit. No evidence of olivine-rich area is present in these data.     

The distribution of basaltic asteroids in the Main Belt

We present the observational results of a survey designed to target and detect asteroids whose photometric colors are similar to those of Vesta family members and thus may be considered as candidates for having a basaltic composition. Fifty basaltic candidates were selected with orbital elements that lie outside of the Vesta dynamical family. Optical and near-infrared spectra were used to assign a taxonomic type to 11 of the 50 candidates. Ten of these were spectroscopically confirmed as V-type asteroids, suggesting that most of the candidates are basaltic and can be used to constrain the distribution of basaltic material in the Main Belt. Using our catalog of V-type candidates and the success rate of the survey, we calculate unbiased size-frequency and semi-major axis distributions of V-type asteroids. These distributions, in addition to an estimate for the total mass of basaltic material, suggest that Vesta was the predominant contributor to the basaltic asteroid inventory of the Main Belt, however scattered planetesimals from the inner Solar System (a<2.0 AU) and other partially/fully differentiated bodies likely contributed to this inventory. In particular, we infer the presence of basaltic fragments in the vicinity of Asteroid 15 Eunomia, which may be derived from a differentiated parent body in the middle Main Belt (2.5<a<2.8). We find no asteroidal evidence for a large number of previously undiscovered basaltic asteroids, which agrees with previous theories suggesting that basaltic fragments from the ∼100 differentiated parent bodies represented in meteorite collections have been “battered to bits” [Burbine, T.H., Meibom, A., Binzel, R.P., 1996. Meteorit. Planet. Sci. 31, 607-620].     

Primordial metamorphism of asteroids via electrical induction in A T Tauri-like solar wind

Simple evolutionary models of asteroids of various sizes and solar distances have been constructed assuming unipolar electrical induction heating due to passage of the Sun through a T Tauri phase with an increased magnetic field. Typical T Tauri conditions and an elementary solar wind model were used to calculate induced currents in modlels assuming electrical conductivities appropriate for carbonaceous material. Two restrictions with opposite dependence upon radius dominate the results. The electrical insulating tendency of a cold surface favors heating of larger bodies. The current-limiting backpressure of the induced magnetic field favors heating of smaller bodies. Thus it is found that maximum heating, in some cases sufficient for melting, occurs for model asteroids at the inner edge of the belt and with (model-dependent) radii from 25 to 250 km. This effect, if operant, would have produced a primordial distribution of metamorphosed asteroids primarily occurring at small solar distance and intermediate size. The observational evidence for such a distribution is unclear because the primordial distribution has likely been considerably modified by collisions, particularly at smaller sizes. There does seem to be some consistency with the model in the distribution of the largest asteroids, though data are sparse. In particular, this model seems relevant to the well-known dichotomy between Ceres and Vesta.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978Also Dept of Planetary Sciences