Collisional history of asteroids: Evidence from Vesta and the Hirayama families

Collisional evolution studies of asteroids indicate that the initial asteroid population at the time mean collisional velocities were pumped up to ～5 km/sec was only modestly larger than it is today; i.e., the asteroid belt was already depleted relative to the mean surface density elsewhere in the planetary region. Numerical simulations of the collisional evolution of hypothetical initial asteroid populations have been run, subject to three constraints: they must (a) evolve to the present observed asteroid size distribution, (b) preserve Vesta's basaltic crust, and (c) produce at least the observed number of major Hirayama families. A “runaway growth” initial asteroid population distribution is found to best satisfy these constraints. A new model is presented for calculating the fragmental size distribution for the disruption of large, gravitationally bound bodies in which the material strength is increased by hydrostatic self-compression. This model predicts that large asteroid behave as intrinsically strong bodies, even if they have had a history of being collisionally fractured. This model, when applied to the breakup of the Themis and Eos family parent bodies, gives size distributions in reasonably good agreement with those observed.     

The Vestan cataclysm: Impact‐melt clasts in howardites and the bombardment history of 4 Vesta

Crystalline impact‐melt samples were created in high‐temperature environments by relatively large craters and, as such, give additional constraints on the nature of the impacts that created them. This article provides new ⁴⁰Ar‐³⁹Ar ages of impact‐melt clasts in howardites and shows that these clasts formed on the HED parent body, 4 Vesta, within the time period 3.3–3.8 Ga. Rather than resulting from an increased number of impacts, however, impact‐melted material in howardites may result from unusually high‐velocity impacts occurring in the asteroid belt during this period. This scenario is similar to the late heavy bombardment of the Moon, pointing to an unusual dynamical event at this time across the inner solar system. Therefore, impact‐melt rocks in howardites uniquely record a Vestan cataclysm.     

The polarization curve and the absolute diameter of Vesta

A new photoelectric polarization curve for Vesta is presented. It is incompatible with Lyot's photographic curve which appears to be inaccurate. The new polarization curve indicates that the reflectivity of Vesta is higher than that of the Moon, and a pre;iminary value of 0.25 ± 0.07 for the reflectivity in the V is suggested. This implies an absolute diameter of about 510 km, a value consistent with the diameter of Vesta calculated from its mass, assuming an achondritic composition.     

The dynamical environment of Dawn at Vesta

Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius. This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km, in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure. Ultimately, the dynamics of Dawn at Vesta identifies issues to be explored in the planning of future EP missions operating in close proximity to larger asteroids.     

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.     

Thermospheric changes shortly after the onset of daytime joule heating

In the first few tens of minutes after the onset of widespread Joule heating, the motion of the ionospheric atmosphere can be approximated by the one-dimensional motion of a gas in a gravity field—a problem that is easily solved because the motion takes place at constant pressure. The solution provides an estimate of time for which the model is applicable to the physical situation. Seasonal variations of the early effects are examined by using ion profiles appropriate to each season. The results show that the atmosphere above 100 km is strongly modified within a few tens of minutes after the onset of widespread heating: the density can double, the temperature can increase several hundred degrees, and the molecular nitrogen concentration can quadruple. Vertical winds exceeding 100 m/sec at 400km altitude are possible for a brief period after the onset of electric fields of 100 mV/m—rare but observed events. In the first few tens of minutes after the onset of a given electric field, the greatest power is deposited in the thermosphere around summer solstice, while the greatest winds occur at 200 km altitude in the summer and at 400km in the winter. These differing seasonal effects show primarily that a given level of change occurs sooner for one season than another, not that long term seasonal differences exist. Once a magnetic storm is in progress, the quiet-day ion profiles change to the non-seasonal storm profile ; for this ion distribution, F-region effects are minimum regardless of season. Joule heating effects in the upper thermosphere are therefore concluded to be self-limiting.     

39Ar‐40Ar ages of eucrites and thermal history of asteroid 4 Vesta

Abstract— Eucrite meteorites are igneous rocks that derived from a large asteroid, probably 4 Vesta. Past studies have shown that after most eucrites formed, they underwent metamorphism in temperatures up to ≥800°C. Much later, many were brecciated and heated by large impacts into the parent body surface. The less common basaltic, unbrecciated eucrites also formed near the surface but, presumably, escaped later brecciation, while the cumulate eucrites formed at depths where metamorphism may have persisted for a considerable period. To further understand the complex HED parent body thermal history, we determined new ³⁹Ar‐⁴⁰Ar ages for 9 eucrites classified as basaltic but unbrecciated, 6 eucrites classified as cumulate, and several basaltic‐brecciated eucrites. Precise Ar‐Ar ages of 2 cumulate eucrites (Moama and EET 87520) and 4 unbrecciated eucrites give a tight cluster at 4.48 ± 0.02 Gyr (not including any uncertainties in the flux monitor age). Ar‐Ar ages of 6 additional unbrecciated eucrites are consistent with this age within their relatively larger age uncertainties. By contrast, available literature data on Pb‐Pb isochron ages of 4 cumulate eucrites and 1 unbrecciated eucrite vary over 4.4–4.515 Gyr, and ¹⁴⁷Sm‐¹⁴³Nd isochron ages of 4 cumulate and 3 unbrecciated eucrites vary over 4.41–4.55 Gyr. Similar Ar‐Ar ages for cumulate and unbrecciated eucrites imply that cumulate eucrites do not have a younger formation age than basaltic eucrites, as was previously proposed. We suggest that these cumulate and unbrecciated eucrites resided at a depth where parent body temperatures were sufficiently high to cause the K‐Ar and some other chronometers to remain as open diffusion systems. From the strong clustering of Ar‐Ar ages at ?4.48 Gyr, we propose that these meteorites were excavated from depth in a single large impact event ?4.48 Gyr ago, which quickly cooled the samples and started the K‐Ar chronometer. A large (?460 km) crater postulated to exist on Vesta may be the source of these eucrites and of many smaller asteroids thought to be spectrally or physically associated with Vesta. Some Pb‐Pb and Sm‐Nd ages of cumulate and unbrecciated eucrites are consistent with the Ar‐Ar age of 4.48 Gyr, and the few older Pb‐Pb and Sm‐Nd ages may reflect an isotopic closure before the large cratering event. One cumulate eucrite gives an Ar‐Ar age of 4.25 Gyr; 3 additional cumulate eucrites give Ar‐Ar ages of 3.4–3.7 Gyr; and 2 unbrecciated eucrites give Ar‐Ar ages of ?3.55 Gyr. We attribute these younger ages to a later impact heating. Furthermore, the Ar‐Ar impact‐reset ages of several brecciated eucrites and eucritic clasts in howardites fall within the range of 3.5–4.1 Gyr. Among these, Piplia Kalan, the first eucrite to show evidence for extinct ²⁶Al, was strongly impact heated ?3.5 Gyr ago. When these data are combined with eucrite Ar‐Ar ages in the literature, they confirm that several large impact heating events occurred on Vesta between ?4.1–3.4 Gyr ago. The onset of major impact heating may have occurred at similar times for both Vesta and the moon, but impact heating appears to have persisted for a somewhat later time on Vesta.     

Impact origin of the Vesta family

Abstract— The compelling petrographic link (Consolmagno and Drake, 1977; Gaffey, 1983) between basaltic achondrite meteorites and the ～530 km diameter asteroid 4 Vesta has been tempered by a perceived difficulty in launching rocks from this asteroid's surface at speeds sufficient to bring them to Earth (Wasson and Wetherill, 1979) without obliterating Vesta's signature crust. I address this impasse in response to recent imaging (Zellner et al, 1996; Dumas and Hainaut, 1996) of a ～450 km impact basin across Vesta's southern hemisphere (Thomas et al., 1997) and model the basin-forming collision using a detailed two-dimensional hydrocode with brittle fracture including self-gravitational compression (cf., Asphaug and Melosh, 1993). A ～42 km diameter asteroid striking Vesta's basaltic crust (atop a denser mantle and iron core) at 5.4 km/s launches multikilometer fragments up to ～600 m/s without inverting distal stratigraphy, according to the code. This modeling, together with collisional, dynamical, rheological and exposure-age timescales (Marzari et al., 1996; Welten et al., 1996), and observations of V-type asteroids (Binzel and Xu, 1993) suggests a recent (<～1 Ga) impact origin for the Vesta family and a possible Vesta origin for Earth-approaching V-type asteroids (Cruik-shank et al., 1991).     

Modeling the early evolution of Vesta

The early evolution of the asteroid Vesta has been extensively studied because of the availability of relevant data, especially important new studies of HED meteorites which originated from Vesta and the Dawn mission to Vesta in 2011–2012. These studies have concluded that an early melting episode led to the differentiation of Vesta into crust, mantle, and core. This melting episode is attributed to the decay of ²⁶Al, which has a half‐life of 7.17 × 10⁵ yr. This heating produced a global magma ocean. Surface cooling of this magma ocean will produce a solid crust. In this paper, we propose a convective heat‐transfer mechanism that effectively cools the asteroid when the degree of melting reaches about 50%. We propose that a cool solid surface crust, which is gravitationally unstable, will founder into the solid–liquid mix beneath and will very effectively transfer heat that prevents further melting of the interior. In this paper, we quantify this process. If Vesta had a very early formation, melting would commence at an age of about 1,30,000 yr, and solidification would occur at an age of about 10 Myr. If Vesta formed with a time delay greater than about 2 Myr, no melting would have occurred. An important result of our model is that the early melting episode is restricted to the first 10 Myr. This result is in good agreement with the radiometric ages of the HED meteorites.     

UBV photometry of Vesta

A lightcurve of Vesta, obtained on four nights between June 23 and 30 June 1978 during the coordinated campaign for the determination of the rotation period, is presented. The observations were performed at the 91-cm telescope of the Catania Observatory employing UBV filters and a photon counting photometer. The V lightcurve apparently shows a single maximum, suggesting that the 5^h20^m29^s.2 period is the correct one. Features are evident near the maximum and the minimum closely resembling those of Johnson's lightcurve of 22 December 1950 and Taylor's of January 21, 1973. The amplitude in V light is 0^m.105 and small variations are also found in the color indices. The largest color variation is for the U-V with Δm = 0.^m.05, which is slightly larger than the value 0^m.02 found by T. Gehrels [Astron. J.72, 929 (1967)]. The maximum and minimum values occur at the same phase with respect to the maximum V light as found by Gehrels, i.e., Vesta appears bluer near 0^p.25 and redder near 0^p.7. Corrections with the solar phase angle were made using the coefficients given by Gehrels for the B-V and U-V while a new value of 0.036 mag/deg was assumed for the V observations. The available amplitudes of Vesta's lightcurve were analyzed with respect to the longitude position and the solar phase angle.     

Radar detection of Vesta

Asteroid 4 Vesta was detected on 1979 November 6 with the Arecibo Observatory's S-band (12.6-cm-wavelength) radar. The echo power spectrum, received in the circular polarization opposite to that transmmited,, yields a radar cross section of (0.2 ± 0.1)πa², for a = 272 km. The data are too noisy to permit derivation of Vesta's rotation period.     

The rotation period and pole orientation of asteroid 4 Vesta

In 1971 asteroid Vesta was observed in a region of the sky in which it had never been observed before. Its photometric lightcurve had two distinct maxima. Those observations have been the only strong evidence to support a rotation period of about 10 hr 41 min. Lightcurves made in 1982, when Vesta was at the same aspect as 1971, do not show two different maxima. It is concluded that there was a systematic error in the 1971 observations. At this time a definitive statement cannot be made about the true period of Vesta, although the 5 hr 20 min period does appear more plausible. Radar echoes in 1988 and 1992 should resolve the problem. The shorter rotation period was assumed and the photometric astrometry method applied. The sidereal period is 5 hr 20 min 31.68 sec 0.2225889 ± 0.0000002 days, the rotation is prograde, and the coordinates of the north pole are 103° longitude and +43° latitude with an uncertainty of abour 6°.     

Submillimeter lightcurves of Vesta

Thermal lightcurves of Asteroid Vesta with significant amplitude have been observed at 870 μm (345 GHz) using the MPIfR 19-channel bolometer of the Heinrich–Hertz Submillimeter Telescope. Shape and albedo are not sufficient to explain the magnitude of this variation, which we relate to global variations in thermal inertia and/or other thermophysical parameters. Vesta's lightcurve has been observed over several epochs with the same general shape. However, there are some changes in morphology that may in part be related to viewing geometry and/or asteroid season. Inconsistent night-to-night variations exhibit the inherent difficulties in photometry at this wavelength. We are able to match the observed brightness temperatures with a relatively simple thermal model that integrates beneath the surface and assumes reasonable values of thermal inertia, loss tangent and refractive index, and without having to assume low values of emissivity in the submillimeter. High flux portions of the submillimeter lightcurve are found to correspond to regions with weak mafic bands observed in Hubble Space Telescope images.     

Vesta as the howardite,eucrite and diogenite parent body: Implications for the size of a core and for large-scale differentiation

Abstract— If Vesta is the parent body of the howardite, eucrite, and diogenite (HED) meteorites, then geo-chemical and petrologic constraints for the meteorites may be used in conjunction with astronomical constraints for the size and mass of Vesta to (1) determine the size of a possible metal core in Vesta and (2) model the igneous differentiation and internal structure of Vesta. The density of Vesta and petrologic models for HED meteorites together suggest that the amount of metal in the parent body is <25 mass%, with a best estimate of ～5%, assuming no porosity. For a porosity of up to 5% in the silicate fraction of the asteroid, the permissible metal content is <30%. These results suggest that any metal core in the HED parent body and Vesta is not unusually large. A variety of geochemical and other data for HED meteorites are consistent with the idea that they originated in a magma ocean. It appears that diogenites formed by crystal accumulation in a magma ocean cumulate pile and that most noncumulate eucrites (excepting such eucrites as Bouvante and Statinem) formed by subsequent crystallization of the residual melts. Modelling results suggest that the HED parent body is enriched in rare earth elements by a factor of ～2.5–3.5 relative to CI-chondrites and that it has approximately chondritic Mg/Si and Al/Sc ratios. Stokes settling calculations for a Vesta-wide, nonturbulent magma ocean suggest that early-crystallizing magnesian olivine, orthopyroxene, and pigeonite would have settled relatively quickly, permitting fractional crystallization to occur, but that later-crystallizing phases would have settled (or floated) an order of magnitude more slowly, allowing, instead, a closer approach to equilibrium crystallization for the more evolved (eucritic) melts. This would have inhibited the formation of a plagioclase-flotation crust on Vesta. Plausible models for the interior of Vesta, which are consistent with the data for HED meteorites and Vesta, include a metal core (<130 km radius), an olivine-rich mantle (～65–220 km thick), a lower crustal unit (～12–43 km thick) composed of pyroxenite, from which diogenites were derived, and an upper crustal unit (～23–42 km thick), from which eucrites originated. The present shape of Vesta (with ～60 km difference in the maximum and minimum radius) suggests that all of the crustal materials, and possibly some of the underlying olivine from the mantle, could have been locally excavated or exposed by impact cratering.     

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.     

Distribution of iron on Vesta

We have completed a mapping study of 7.6 MeV gamma rays produced by neutron capture by Fe at the surface of the main belt asteroid 4 Vesta as measured by the bismuth germanate scintillator of the Gamma Ray and Neutron Detector (GRaND) on the Dawn spacecraft. The procedures used to determine Fe counting rates are presented, along with a global map, constituting the necessary initial step to quantify Fe abundances. While the final calibration of orbital data to absolute concentrations has not been determined, the range of fully corrected Fe counting rates is compared with that of Fe in howardites. We find that the global distribution of corrected Fe counting rates is generally consistent with mineralogy and composition determined independently by other instruments on the Dawn spacecraft, including measurements of pyroxene absorption bands by the Visible and Infrared Spectrometer and Framing Camera, and an index of diogenitic materials provided by neutron absorption measurements by GRaND. In addition, there is a distinctive low Fe region in the western hemisphere that was not reported by reflectance or optical observations, possibly indicating the presence of a cumulate eucrite component in Vesta's regolith.     

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.     

The sizes of color patches on the surface of the asteroid 4 Vesta

The sizes of color patches on the surface of the asteroid 4 Vesta were estimated with the spectral-frequency method. We used the digital records of the asteroid spectra obtained on February 2, 3, 4, and 7, 2002, with the TV system and the slitless afocal spectrograph of the MTM-500 telescope at the Research Institute of the Crimean Astrophysical Observatory. The spectral resolution caused by the image quantity was about 40 Å and the exposure duration was 30 s. The energy calibration was performed both with the artificial light-emitting diode standard and three standard stars. The synthetic color indices B-V and V-R were calculated from the asteroid spectra taken out of the atmosphere. From these data, the changes with an asteroid rotation phase were eliminated. After that, the periods that were significantly smaller than the asteroid rotation period were searched for, and each time the data were whitened for the obtained period. Assuming that the patch sizes are determined by the half-obtained period and that the patches are located in the equatorial region of the asteroid, we estimated the sizes of 20 and 19 patches in the long-and short-wavelength ranges, respectively. The smallest found patch was about 9 km across. The statistical estimates of the reddish patches and the comparison with the statistics of old craters allowed us to suggest that the reddish patches on the asteroid Vesta surface are old formations.     

Near-IR imaging of Asteroid 4 Vesta

The Keck Observatory's adaptive optics (AO) system has been used to observe Asteroid 4 Vesta during its 2003 closest approach to Earth. Broadband K^′- and L^′-band images, centered at 2.1 and 3.6 μm, respectively, are presented here. The sharpness of the images was improved by applying a deconvolution algorithm, MISTRAL, to the images. The K^′- and L^′-band images at spatial resolutions of 53 km (^0.055″) and 88 km (^0.085″), respectively, display albedo features on the surface of the asteroid that can also be seen in the HST images (673 nm) presented by Thomas et al. [1997. Impact excavation on Asteroid 4 Vesta: Hubble Space Telescope results. Science 277, 1492-1495] and Binzel et al. [1997. Geologic mapping of Vesta from 1994 Hubble Space Telescope images. Icarus 128, 95-103] at the same latitudes and longitudes. While we cannot determine the morphology of these features, we can speculate that some of the albedo features may be impact craters filled with dark material. Spectra, centered at 1.65 and 2.1 μm, were also obtained. Spectra were corrected for the solar flux and are similar to those published by Gaffey [1997. Surface lithologic heterogeneity of Asteroid 4 Vesta. Icarus 127, 130-157], along the same wavelength range.     

Vesta: The first pyroxene band from new spectroscopic measurements

New spectral reflectance measurements of asteroid 4 Vesta were obtained using a silicon vidicon spectrometer with a resolution of 0.002–0.004 μm. The major absorption band in the near infrared has a minimum at 0.924 ± 0.004 μm with a bandwidth of 0.18 μm full width at half power (fwhp). The band represents a 30% absorption relative to peak reflectance at 0.75 μm. The absorption band has been interpreted to be due to electronic absorptions in ferrous iron in sixfold coordination in the pyroxene, pigeonite. The increased spectral resolution of these observations compared to earlier spectrophotometry enables us to refine the pyroxene composition, from the position of the Fe²⁺ absorption band, and arrive at a relative calcium content [Ca/(Mg + Fe + Ca)] of 10–12%. The absorption band is symmetric about its center, implying the presence of little or no olivine. The existence of the 2.0-μm pyroxene band which was verified by Larson and Fink (1975) confirms the interpretation based on the 1.0-μm band.