Typical Asteroid Research Articles

The surface roughness of (433) Eros as measured by thermal-infrared beaming

In planetary science, surface roughness is regarded to be a measure of surface irregularity at small spatial scales, and causes the thermal-infrared beaming effect (i.e. re-radiation of absorbed sunlight back towards to the Sun). Typically, surface roughness exhibits a degeneracy with thermal inertia when thermophysical models are fitted to disc-integrated thermal-infrared observations of asteroids because of this effect. In this work, it is demonstrated how surface roughness can be constrained for near-Earth asteroid (433) Eros (i.e. the target of NASA's NEAR Shoemaker mission) when using the Advanced Thermophysical Model with thermal-infrared observations taken during an "almost pole-on" illumination and viewing geometry. It is found that the surface roughness of (433) Eros is characterised by an RMS slope of 38 $\pm$ 8{\deg} at the 0.5-cm spatial scale associated with its thermal-infrared beaming effect. This is slightly greater than the RMS slope of 25 $\pm$ 5{\deg} implied by the NEAR Shoemaker laser ranging results when extrapolated to this spatial scale, and indicates that other surface shaping processes might operate, in addition to collisions and gravity, at spatial scales under one metre in order to make asteroid surfaces rougher. For other high obliquity asteroids observed during "pole-on" illumination conditions, the thermal-infrared beaming effect allows surface roughness to be constrained when the sub-solar latitude is greater than 60{\deg}, and if the asteroids are observed at phase angles of less than 40{\deg}. They will likely exhibit NEATM beaming parameters that are lower than expected for a typical asteroid at all phase angles up to 100{\deg}.

On spectral dependence of polarization of asteroids

From the analysis of all of the data available on the spectral dependence of polarization of light reflected by asteroids, it has been shown that the slope of the spectral dependence of polarization of asteroids changes its sign, when moving from the negative branch of the phase curve of polarization to the positive one. This effect also manifests itself in the spectral behavior of polarization of the Moon and, probably, in the polarization of the other atmosphereless bodies. From the analysis of a population of asteroids of different types, a weak correlation between the spectral slopes of the polarization degree and the albedo has been found.

Material composition assessment and discovering sublimation activity on asteroids 145 Adeona, 704 Interamnia, 779 Nina, and 1474 Beira

Spectrophotometric observations of 145 Adeona, 704 Interamnia, 779 Nina, and 1474 Beira—asteroids of close primitive types—allowed us to detect similar mineralogical absorption bands in their reflectance spectra centered in the range 0.35 to 0.92 μm; the bands are at 0.38, 0.44, and 0.67–0.71 μm. On the same asteroids, the spectral signs of simultaneous sublimation activity were found for the first time. Namely, there are maxima at ∼0.35–0.60 μm in the reflectance spectra of Adeona, Interamnia, and Nina and at ∼0.55–075 μm in the spectra of Beira. We connect this activity with small heliocentric distances of the asteroids and, consequently, with a high insolation at their surfaces. Examination of the samples of probable analogues allowed us to identify Fe3+ and Fe2+ in the material of these asteroids through the mentioned absorption bands. For analogues, we took powdered samples of carbonaceous chondrites Orgueil (CI), Mighei (CM2), Murchison (CM2), and Boriskino (CM2), as well as hydrosilicates of the serpentine group. Laboratory spectral reflectance study of the samples of low-iron Mg serpentines (<2 wt % FeO) showed that the equivalent width of the absorption band centered at 0.44–0.46 μm strongly correlates with the content of Fe3+ in octahedral and tetrahedral coordinations. Our conclusion is that this absorption band can be used as a qualitative indicator of Fe3+ in the surface matter of asteroids and other solid celestial bodies. The comparison of the listed analog samples and the asteroids by parameters of the spectral features suggests that the silicate component of the asteroids' surface material is a mixture of hydrated and oxidized compounds, including oxides and hydroxides of bivalent and trivalent iron and carbonaceous-chondritic material. At the same time, the sublimation activity of Adeona, Interamnia, Nina, and Beira at high surface temperatures points to a substantial content of water ice in their material. This contradicts the previously existing notions on the C-type and similar asteroids as bodies containing water only in the bound state. Moreover, since the sublimation process simultaneously occurs in four primitive-type bodies at small heliocentric distances, we may suppose that this phenomenon is common for the main-belt asteroids.

New reflectance spectra of 40 asteroids: A comparison with the previous results and an interpretation

This paper presents and discusses selected reflectance spectra of 40 Main Belt asteroids. The spectra have been obtained by the author in the Crimean Laboratory of the Sternberg Astronomical Institute (2003–2009). The aim is to search for new spectral features that characterize the composition of the asteroids’ material. The results are compared with earlier findings to reveal substantial irregularities in the distribution of the chemical-mineralogical compositions of the surface material of a number of minor planets (10 Hygiea, 13 Egeria, 14 Irene, 21 Lutetia, 45 Eugenia, 51 Nemausa, 55 Pandora, 64 Angelina, 69 Hesperia, 80 Sappho, 83 Beatrix, 92 Undina, 129 Antigone, 135 Hertha, and 785 Zwetana), which are manifest at different rotation phases. The vast majority of the analyzed high-temperature asteroids demonstrate subtle spectral features of an atypical hydrated and/or carbonaceous chondrite material (in the form of impurities or separate units), which are likely associated with the peculiarities of the formation of these bodies and the subsequent dynamic and impact processes, which lead, inter alia, to the delivery of atypical materials. Studies of 4 Vesta aboard NASA’s Dawn spacecraft have found that asteroids of similar types can form their own phyllosilicate generations provided that their surface material contains buried icy or hydrated fragments of impacting bodies. The first evidence has been obtained of a spectral phase effect (SPE) at small phase angles (≤4°) for 10 Hygiea, 21 Lutetia, and, possibly, 4 Vesta. The SPE manifests itself in an increasing spectral coefficient of brightness in the visible range with decreasing wavelength. This effect is present in the reflectance spectrum of CM2 carbonaceous material at a phase angle of 10° and absent at larger angles (Cloutis et al., 2011a). The shape of Hygeia’s reflectance spectra at low phase angles appears to be controlled by the SPE during the most part of its rotation period, which may indicate a predominantly carbonaceous chondrite composition on a part of the asteroid’s surface. For Vesta, the SPE may manifest itself in the flat or slightly concave shape of the asteorid’s reflectance spectra at some of the rotation phases, which is likely caused by the increased number of dark spots on corresponding parts of its surface.

Asteroid observations at low phase angles. IV. Average parameters for the new H, G1, G2 magnitude system

We present new observational data for selected main-belt asteroids of different compositional types. The detailed magnitude–phase dependences including small phase angles (<1°) were obtained for these asteroids, namely: (10) Hygiea (down to the phase angle of 0.3°, C-type), (176) Iduna (0.2°, G-type), (214) Aschera (0.2°, E-type), (218) Bianca (0.3°, S-type), (250) Bettina (0.3°, M-type), (419) Aurelia (0.1°, F-type), (596) Scheila (0.2°, D-type), (635) Vundtia (0.2°, B-type), (671) Carnegia (0.2°, P-type), (717) Wisibada (0.1°, T-type), (1021) Flammario (0.6°, B-type), and (1279) Uganda (0.5°, E-type). For several asteroids, the dependences of brightness on the phase angle were investigated in the BVRI bands. We found a great diversity in the opposition-effect behavior both in the magnitude and the width of the opposition surges, especially for low-albedo asteroids. Some low-albedo asteroids (e.g., (10) Hygiea) display a broad opposition effect with an amplitude of 0.15–0.20mag relative to the extrapolation of the linear part of the phase curve. Other asteroids (e.g., (596) Scheila, (1021) Flammario) show linear magnitude–phase dependences down to small phase angles (0.1–0.2°). Using numerous data sets on the magnitude–phase dependences with extensive phase-angle coverage, we examined in more detail the new three-parameter H, G1, G2 magnitude system. We determined the values of the G1 and G2 parameters for magnitude phase dependences of individual asteroids and obtained the average parameters for main asteroid compositional types. The values obtained can be used for the estimation of the absolute magnitude of an asteroid from a single observed magnitude when the magnitude–phase dependency is unknown and/or to calculate a visible magnitude for the ephemerides.

Polarimetric properties of asteroids

Quite frequently astronomic polarimetric observations of different celestial bodies do not guarantee a proper phase angle coverage that is required for estimating all of the attributes of their polarization phase curves with a high accuracy. To approximate the phase dependences of polarization observed for particulate surfaces, we use a simple empiric formula recently suggested by Shestopalov (2004). The efficiency of the approximating function in a wide range of phase angles is illustrated with the use of the results of polarimetric measurements of lunar areas, lunar samples, and near-Earth asteroids. For asteroids of various types, we can reproduce their negative polarization branches with adequate accuracy and roughly estimate a probable value of the maximum polarization degree at an appropriate phase angle. From the polarimetric database available at NASA PDS [Asteroid Polarimetric Database V7.0 (2012)] we calculated the main parameters of 153 polarimetric curves of asteroids in various spectral bands with the accuracy comparable to the observation errors. One more purpose of our analysis was to find correlations between the polarimetric and photometric properties of asteroids. For C-, M-, S-, E-type asteroids, the characteristics of the negative branch of polarization curves turned out to correlate closely with the phase coefficient of the photometric function of asteroids and the photometric roughness of asteroid surfaces. This implies that the complex geometry of the surface microrelief affects the polarization properties of asteroids. In particular, the data scattering around regression lines on the plots of the albedo versus the depth of negative polarization branch and the slope of the polarimetric function at inversion angle strongly depends on the differences in the photometric roughness of asteroid surfaces.

Spectrophotometry of (32) Pomona, (145) Adeona, (704) Interamnia, (779) Nina, (330825) 2008 XE3, and 2012 QG42 and laboratory study of possible analog samples

Six asteroids including two NEAs, one of which is PHA, accessible for observation in September 2012 were investigated using a low-resolution (R≈100) spectrophotometry in the range 0.35–0.90μm with the aim to study features of their reflectance spectra. A high-altitude position of our Terskol Observatory (3150m above sea level) favorable for the near-UV and visible-range observations of celestial objects allowed us to probably detect some new spectral features of the asteroids. Two subtle absorption bands centered at 0.53 and 0.74μm were found in the reflectance spectra of S-type (32) Pomona and interpreted as signs of presence of pyroxenes in the asteroid surface matter and its different oxidation. Very similar absorption bands centered at 0.38, 0.44 and 0.67–0.71μm have been registered in the reflectance spectra of (145) Adeona, (704) Interamnia, and (779) Nina of primitive types. We performed laboratory investigations of ground samples of known carbonaceous chondrites, Orguel (CI), Mighei (CM2), Murchison (CM2), Boriskino (CM2), and seven samples of low-iron Mg serpentines as possible analogs of the primitive asteroids. In the course of this work, we discovered an intense absorption band (up to ∼25%) centered at 0.44μm in reflectance spectra of the low-Fe serpentine samples. As it turned out, the equivalent width of the band has a high correlation with content of Fe3+ (octahedral and tetrahedral) in the samples. It may be considered as a confirmation of the previously proposed mechanism of the absorption due to electronic transitions in exchange-coupled pairs (ECP) of Fe3+ neighboring cations. It means that the absorption feature can be used as an indicator of ferric iron in oxidized and hydrated low-Fe compounds on the surface of asteroids and other atmosphereless celestial bodies. Moreover, our measurements showed that the mechanism of light absorption is partially or completely blocked in the case of intermediate to high iron contents. Therefore, the method cannot probably be used for quantitative estimation of Fe3+ content on the bodies. Based on laboratory study of the analog samples, we conclude that spectral characteristics of Adeona, Interamnia, and Nina correspond to a mixture of CI–CM-chondrites and hydrated silicates, oxides and/or hydroxides. Spectral signs of sublimation activity on Adeona, Interamnia, and Nina at minimal heliocentric distances are likely discovered in the short-wavelength range (∼0.4–0.6μm). It is suggested that such cometary-like activity at the highest surface temperatures is a frequent phenomenon for C and close type asteroids including considerable amounts of ices beneath the surface. A usual way of origin of a temporal coma of ice particles around a primitive asteroid is excavated fresh ice at recent impact event(s).The obtained reflectance spectra of two NEAs, (330825) 2008 XE3 and 2012 QG42, are predominantly featureless and could be attributed to S(C) and S(B)-type bodies, respectively. We discuss reasons why weak spectral features seen in reflectance spectra of the main-belt asteroids are not observed in those of NEAs.

Fragments of Late Eocene Earth-impacting asteroids linked to disturbance of asteroid belt

The onset of Earth's present icehouse climate in the Late Eocene coincides with astronomical events of enigmatic causation. At ∼36 Ma ago the 90–100 km large Popigai and Chesapeake Bay impact structures formed within ∼10–20 ka. Enrichments of 3He in coeval sediments also indicate high fluxes of interplanetary dust to Earth for ∼2 Ma. Additionally, several medium-sized impact structures are known from the Late Eocene. Here we report from sediments in Italy the presence of abundant ordinary chondritic chromite grains (63–250 μm) associated with the ejecta from the Popigai impactor. The grains occur in the ∼40 cm interval immediately above the ejecta layer. Element analyses show that grains in the lower half of this interval have an apparent H-chondritic composition, whereas grains in the upper half are of L-chondritic origin. The grains most likely originate from the regoliths of the Popigai and the Chesapeake Bay impactors, respectively. These asteroids may have approached Earth at comparatively low speeds, and regolith was shed off from their surfaces after they passed the Roche limit. The regolith grains then settled on Earth some 100 to 1000 yrs after the respective impacts. Further neon and oxygen isotopic analyses of the grains can be used to test this hypothesis.If the Popigai and Chesapeake Bay impactors represent two different types of asteroids one can rule out previous explanations of the Late Eocene extraterrestrial signatures invoking an asteroid shower from a single parent-body breakup. Instead a multi-type asteroid shower may have been triggered by changes of planetary orbital elements. This could have happened due to chaos-related transitions in motions of the inner planets or through the interplay of chaos between the outer and inner planets. Asteroids in a region of the asteroid belt where many ordinary chondritic bodies reside, were rapidly perturbed into orbital resonances. This led to an increase in small to medium-sized collisional breakup events over a 2–5 Ma period. This would explain the simultaneous delivery of excess dust and asteroids to the inner solar system. Independent evidence for our scenario are the common cosmic-ray exposure ages in the range of ca. 33–40 Ma for recently fallen H and L chondrites.The temporal coincidence of gravity disturbances in the asteroid belt with the termination of ice-free conditions on Earth after 250 Ma is compelling. We speculate that this coincidence and a general correlation during the past 2 Ga between K–Ar breakup ages of parent bodies of the ordinary chondrites and ice ages on Earth suggest that there may exist an astronomical process that disturbs both regions of the inner asteroid belt and Earth's orbit with a potential impact on Earth's climate.

Modeling Momentum Transfer from Kinetic Impacts: Implications for Redirecting Asteroids

Kinetic impactors are one way to deflect a potentially hazardous object headed for Earth. The Asteroid Impact and Deflection Assessment (AIDA) mission is designed to test the effectiveness of this approach and is a joint effort between NASA and ESA. The NASA-led portion is the Double Asteroid Redirect Test (DART) and is composed of a ∼300-kg spacecraft designed to impact the moon of the binary system 65803 Didymos. The deflection of the moon will be measured by the ESA-led Asteroid Impact Mission (AIM) (which will characterize the moon) and from ground-based observations. Because the material properties and internal structure of the target are poorly constrained, however, analytical models and numerical simulations must be used to understand the range of potential outcomes. Here, we describe a modeling effort combining analytical models and CTH simulations to determine possible outcomes of the DART impact. We examine a wide parameter space and provide predictions for crater size, ejecta mass, and momentum transfer following the impact into the moon of the Didymos system. For impacts into “realistic” asteroid types, these models produce craters with diameters on the order of 10 m, an imparted Δv of 0.5–2mm/s and a momentum enhancement of 1.07 to 5 for a highly porous aggregate to a fully dense rock.

Asteroid Diversion Considerations and Comparisons of Diversion Techniques

The threat of asteroid impacts on Earth poses a low-probability but high consequence risk, with possible outcomes ranging from regional to global catastrophe. However, unique amongst such global threats we have the capability of averting such disasters. Diversion approaches by either kinetic impactor or nuclear energy deposition are the two most practical technologies for mitigating hazardous near Earth asteroids. One of the greatest challenges in understanding our options is the uncertain response of asteroids to such impulsive techniques, due both to our lack of knowledge of the composition and structure of these objects as well as their highly varied nature. Predicting whether we will simply divert or break up a given object is a crucial: the weak self-gravity and inferred weak structure of typical asteroids present the strong possibility the body will fragment for modest impulses. Predictive modeling of failure and fragmentation is one important tool for such studies. In this paper we apply advances in modeling failure and fracture using Adaptive Smoothed Particle Hydrodynamics (ASPH) to understand mega-cratering on asteroids as a validation exercise, and show examples of diverting the near Earth asteroid Bennu using both a kinetic impactor and ablative blow-off due to nuclear energy deposition.

PCR-RFLP Methodology to Identify &amp;lt;i&amp;gt;Nocardia&amp;lt;/i&amp;gt; Isolates in Cuba

Nocardiosis diagnosis is a major challenge. The clinical features and radiological findings are nonspecific. Traditionally, Nocardia identification is based on colonial and microscopical morphology and biochemical tests. However, molecular biology techniques allow a better characterization of species and biotypes. PCR-RFLP of the 65-kDa heat shock protein (HSP) gene provides a rapid, sensitive, and time and labor-efficient method for this proposal. Using this technique, six of eight isolates tested were identified as Nocardia asteroides type VI. PCR-RFLP of the 65-kDa HSP gene could be very useful for determining the incidence of this pathogen in different population groups and its association with susceptibility/resistance profiles to the drugs of choice for treatment. This work is the first molecular detection of Nocardia species in Cuba.

THE 3 μm SPECTRUM OF JUPITER's IRREGULAR SATELLITE HIMALIA

We present a medium resolution spectrum of Jupiter's irregular satellite Himalia covering the critical 3 $\mu$m spectral region. The spectrum shows no evidence for aqueously altered phyllosilicates, as had been suggested from the tentative detection of a 0.7 $\mu$m absorption, but instead shows a spectrum strikingly similar to the C/CF type asteroid 52 Europa. 52 Europa is the prototype of a class of asteroids generally situated in the outer asteroid belt between less distant asteroids which show evidence for aqueous alteration and more distant asteroids which show evidence for water ice. The spectral match between Himalia and this group of asteroids is surprising and difficult to reconcile with models of the origin of the irregular satellites.

Polarimetric survey of main-belt asteroids

Aims. We present the results of a polarimetric survey of main-belt asteroids at Complejo Astronomico El Leoncito (CASLEO), San Juan, Argentina. The aims of this survey are to increase the database of asteroid polarimetry and to estimate the diversity in the polarimetric properties of asteroids that belong to different taxonomic classes. Methods. The data were obtained using the CASPOL polarimeter at the 2.15 m telescope. CASPOL is a polarimeter based on a CCD detector and a Savart plate. The survey began in 1995 and data on a large sample of asteroids were obtained until 2012. A second period began in 2013 using a polarimeter with a more sensitive detector in order to study small asteroids, families, and special taxonomic groups. Results. We present and analyze the unpublished results for 128 asteroids of different taxonomic types, 55 of them observed for the first time. The observational data allowed us to find probable new cases of Barbarian objects but also two D -type objects, (565) Marbachia and (1481) Tubingia, that seem to have phase-polarization curves with a large inversion angle. The data obtained combined with data from the literature enabled us to find phase-polarization curves for 121 objects of different taxonomic types and to study the relations between several polarimetric and physical parameters. Using an approximation for the phase-polarization curve we found the index of refraction of the surface material and the scatter separation distance for all the objects with known polarimetric parameters. We also found that the inversion angle is a function of the index of refraction of the surface, while the phase angle where the minimum of polarization is produced provides information about the distance between scatter particles or, to some extent, the porosity of the surface.

Visible-wavelength spectroscopy of subkilometer-sized near-Earth asteroids with a low delta-v

Abstract This paper provides a unique data set representing the taxonomic type of near-Earth asteroids (NEAs) accessible by available spacecraft. The research on NEAs has entered upon a new phase, thanks to sample-return space explorations together with state-of-the-art large ground-based telescopes. We made observations of 13 asteroids with the Subaru, GEMINI-North, GEMINI-South, and Okayama 188 cm telescopes. Twelve of them have low delta-v orbits with the potential to be investigated by manned/unmanned spacecraft. Also, ten subkilometer-sized bodies are included among them, and are one of remarkable characteristics in terms of their evolutionary scenario. We have found that eleven asteroids are classified as S-complex, and one asteroid as the V-type. Most S-complex asteroids (eight out of eleven, ∼ 70%) have spectra similar to subgroups of Q- or Sq-type, suggesting that these objects are less matured by space weathering. We discuss the dominance of S-complex asteroids based on previous research.

On protecting the planet against cosmic attack: Ultrafast real-time estimate of the asteroid׳s radial velocity

A new method for the line-of-sight velocity estimation of a high-speed near-Earth object (asteroid, meteorite) is suggested. The method is based on the use of fractional, one-half order derivative of a Doppler signal. The algorithm suggested is much simpler and more economical than the classical one, and it appears preferable for use in orbital weapon systems of threat response. Application of fractional differentiation to quick evaluation of mean frequency location of the reflected Doppler signal is justified. The method allows an assessment of the mean frequency in the time domain without spectral analysis. An algorithm structure for the real-time estimation is presented. The velocity resolution estimates are made for typical asteroids in the X-band. It is shown that the wait time can be shortened by orders of magnitude compared with similar value in the case of a standard spectral processing.

Precovery of near‐Earth asteroids by a citizen‐science project of the Spanish Virtual Observatory

AbstractThis article describes a citizen‐science project conducted by the Spanish Virtual Observatory (SVO) to improve the orbits of near‐Earth asteroids (NEAs) using data from astronomical archives. The list of NEAs maintained at the Minor Planet Center (MPC) is checked daily to identify new objects or changes in the orbital parameters of already catalogued objects. Using NEODyS we compute the position and magnitude of these objects at the observing epochs of the 938 046 images comprising the Eigth Data Release of the Sloan Digitised Sky Survey (SDSS). If the object lies within the image bound‐aries and the magnitude is brighter than the limiting magnitude, then the associated image is visually inspected by the project's collaborators (the citizens) to confirm or discard the presence of the NEA. If confirmed, accurate coordinates and, sometimes, magnitudes are submitted to the MPC. Using this methodology, 3226 registered users have made during the first fifteen months of the project more than 167 000 measurements which have improved the orbital elements of 551 NEAs (6% of the total number of this type of asteroids). Even more remarkable is the fact that these results have been obtained at zero cost to telescope time as NEAs were serendipitously observed while the survey was being carried out. This demonstrates the enormous scientific potential hidden in astronomical archives. The great reception of the project as well as the results obtained makes it a valuable and reliable tool for improving the orbital parameters of near‐Earth asteroids. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Near-infrared spectroscopy of 3:1 Kirkwood Gap asteroids II: Probable and plausible parent bodies; primitive and differentiated

The 3:1 Kirkwood Gap asteroids are a mineralogically diverse set of asteroids located in a region that delivers meteoroids into Earth-crossing orbits. Mineralogical characterizations of asteroids in/near the 3:1 Kirkwood Gap can be used as a tool to “map” conditions and processes in the early Solar System. The chronological studies of the meteorite types provide a “clock” for the relative timing of those events and processes. By identifying the source asteroids of particular meteorite types, the “map” and “clock” can be combined to provide a much more sophisticated understanding of the history and evolution of the late solar nebula and the early Solar System.A mineralogical assessment of twelve 3:1 Kirkwood Gap asteroids has been carried out using near-infrared spectral data obtained from 2010 to 2011 combined with visible spectral data (when available) to cover the spectral interval of 0.4–2.5μm. Eight of these asteroids have surfaces with basaltic-type silicate assemblages, indicating at least partial melting within their parent bodies. Although HED-like mineralogies are present these objects exhibit subdued features indicating the presence of an additional phase (e.g., NiFe metal) or process (e.g., space weathering). Four of these asteroids appear to be ordinary chondrite assemblages. Three of these are plausibly linked to the probable H-chondrite parent body, (6) Hebe.

On the accuracy of indirect methods for estimating the sizes of asteroids

We have shown that the least reliable data source for estimating the albedo of asteroids is the maximal value of the degree of negative polarization. To increase the accuracy of the method that uses the data on the slope of the positive branch of polarization, the values of the approximating coefficient should be selected in accordance with a specified type of asteroids. The similar situation is in the shadow method, where the value of the phase integral q should be selected in accordance with each of the types. Moreover, the estimates obtained by both methods will be more reliable if the phase dependences of brightness that are characteristic of a specified type of asteroids, including the range of the opposition effect, are used in transforming from A(0) to A(α). The modeling performed with the Irvine-Yanovitskii modification of the shadow model of Hapke showed that the values of the phase coefficient β (10° ≤ α ≤ 20°) and q are, respectively, in the ranges of 0.016–0.030 and 0.6–1.0 for the E-type asteroids, 0.026–0.033 and 0.42–0.52 for the M-type asteroids, and 0.031–0.039 and 0.42–0.52 for the C-type asteroids.

Shadow mechanism and the opposition effect of brightness of atmosphereless celestial bodies

We consider the Irvine-Yanovistkii modification of the shadow model developed by Hapke for the opposition effect of brightness. The relation between the single scattering albedo ω and the transparency coefficient of particles κ is suggested to be used in the form κ = (1 − ω)n, which allows the number of unknowns in the model to be reduced to two parameters (the packing density of particles g and ω) and the single-scattering phase function χ(α). The analysis of spectrophotometric measurements of the moon and Mars showed that the data on the observed opposition effect and the changes in the color index with the phase angle α well agree if the values of n = 0.25 and g = 0.4 (the moon) and 0.6 (Mars) are assumed in calculations. When being applied to asteroids of several types, this method also yielded a satisfactory agreement. For the E-type asteroids, the sets of parameters are [g = 0.6, ω = 0.6, Ag = 0.21, and q = 0.83] or [g = 0.3, ω = 0.4, Ag = 0.15, and q = 0.71] under the Martian single-scattering phase function; for the M-type asteroids, it is [g = 0.4, ω ≤ 0.1, Ag ≤ 0.075, and q ≤ 0.42] under the lunar single-scattering phase function; for the S-type asteroids, it is [g = 0.4, ω = 0.4, Ag = 0.28, and q = 0.49] under the lunar single-scattering phase function; and for the C-type asteroids, it is [g = 0.6, ω ≤ 0.1, Ag ≤ 0.075, and q = 0.43] under the modified lunar single-scattering phase function. The polarization measurements fulfilled by Gehrels et al. (1964) for the bright feature on the lunar surface, Copernicus (L = -20°08′, φ = +10°11′), at a phase angle α = 1.6° revealed the deviations in the position of the polarization plane from that typical for the negative branch. They were 22° and 12° in the G and I filters, respectively. At the same time, the deviation was within the error (±3°) in the U filter and for the dark feature Plato (L = -10°32′, φ = +51°25′), which can be caused by the coherent mechanism of the formation of the polarization peak.

Dawn′s exploration of Vesta

On 16 July 2011, after completing nearly four years of interplanetary flight, Dawn entered orbit around (4) Vesta, the second most massive body in the main asteroid belt. Dawn used solar electric propulsion to spiral to six different orbits to accomplish its science campaign. Although the transfers to progressively lower orbits presented significant challenges, all were executed smoothly. During its nearly 14 months in orbit, Dawn spiraled down to 210km above the surface and back up before initiating the gradual departure to travel to dwarf planet (1) Ceres for a 2015 rendezvous. Dawn′s exploration of Vesta has shown it to be geologically complex and fascinating, resembling terrestrial planets more than typical asteroids. Among the principal features is a 500-km-diameter impact basin within which is the second tallest mountain known in the solar system. This paper presents Dawn′s operations at Vesta and summarizes the principal findings.