Asteroid surface materials: Mineralogical characterizations from reflectance spectra

Mineral assemblages analogous to most meteorite types, with the exception of ordinary chondritic assemblages, have been found as surface materials of Main Belt asteroids. C1- and C2-like assemblages (unleached, oxidized meteoritic clay minerals plus opaques such as carbon) dominate the population throughout the Belt, especially in the outer Belt. A smaller population of asteroids exhibit surface materials similar to C3 (CO, CV) meteoritic assemblages (olivine plus opaque, probably carbon) and are also distributed throughout the Belt. The majority of remaining studied asteroids (20) of 65 asteroids exhibit spectral reflectance curves dominated by the presence of metallic nickel-iron in their surface materials. The C2-like materials which dominate the main asteroid belt population appear to be relatively rare on earth-approaching asteroids

An initial perspective of S-asteroid subtypes within asteroid families

Many main belt asteroids cluster around certain values of semi-major axis (a), inclination (i), and eccentricity (e). Hirayama was the first to notice these concentrations which he interpreted as evidence of disruptions of larger parent bodies. He called these clusters 'asteroid families'. The term 'families' is increasingly reserved for genetic associations to distinguish them from clusters of unknown or purely dynamical origin (e.g. the Phocaea cluster). Members of a genetic asteroid family represent fragments derived from various depths within the original parent planetesimal. Thus, family members offer the potential for direct examination of the interiors of parent bodies which have undergone metamorphism and differentiation similar to that occurring in the inaccessible interiors of terrestrial planets. The differentiation similar to that occurring in the inaccessible interiors of terrestrial planets. The condition that genetic family members represent the fragments of a parent object provides a critical test of whether an association (cluster in proper element space) is a genetic family. Compositions (types and relative abundances of materials) of family members must permit the reconstruction of a compositionally plausible parent body. The compositions of proposed family members can be utilized to test the genetic reality of the family and to determine the type and degree of internal differentiation within the parent planetesimal. The interpretation of the S-class mineralogy provides a preliminary evaluation of family memberships. Detailed mineralogical and petrological analysis was done based on the reflectance spectra of 39 S-type asteroids. The result is a division of the S-asteroid class into seven subtypes based on compositional differences. These subtypes, designated S(I) to S(VII), correspond to surface silicate assemblages ranging from monomineralic olivine (dunites) through olivine-pyroxene mixtures to pure pyroxene or pyroxene-feldspar mixtures (basalts). The most general conclusion is that the S-asteroids cannot be treated as a single group of objects without greatly oversimplifying their properties. Each S-subtype needs to be treated as an independent group with a distinct evolutionary history

Asteroid amphitrite: Surface composition and prospects for the possible Galileo flyby

Studies of the trajectory of the Galileo mission to Jupiter recently revealed that the spacecraft can pass close to one of the largest asteroids (#29 Amphitrite). NASA has therefore altered the mission plan of the Galileo spacecraft to include a possible close flyby of Amphitrite in early December 1986, if the condition of the spacecraft allows. If this option is actually implemented, Amphitrite will become the only asteroid for which any high-spatial resolution images and reflection spectra will be available. To evaluate the value of this data and place Amphitrite in the context of the more than 600 asteroids for which some compositional information exists. Existing data was reexamined, new telescopic spectra of Amphitrite were obtained, and simulated Galileo data sets were constructed

Characterization of Asteroidal Basalts through Reflectance Spectroscopy and Implications for the Dawn Mission

There are currently five known groups of basaltic achondrites that represent material from distinct differentiated parent bodies. These are the howardite-eucrite-diogenite (HED) clan, mesosiderite silicates, angrites, Ibitira, and Northwest Africa (NWA) 011 [1]. Spectroscopically all these basaltic achondrite groups have absorption bands located near 1 and 2 microns due to the presence of pyroxene. Some of these meteorite types have spectra that are quite similar, but nevertheless have characteristics (e.g. spectral slope, band depths, etc.) that may be used to differentiate them from each other

NEOWISE Studies of Spectrophotometrically Classified Asteroids: Preliminary Results

The NEOWISE dataset offers the opportunity to study the variations in albedo for asteroid classification schemes based on visible and near-infrared observations for a large sample of minor planets. We have determined the albedos for nearly 1900 asteroids classified by the Tholen, Bus and Bus-DeMeo taxonomic classification schemes. We find that the S-complex spans a broad range of bright albedos, partially overlapping the low albedo C-complex at small sizes. As expected, the X-complex covers a wide range of albedos. The multi-wavelength infrared coverage provided by NEOWISE allows determination of the reflectivity at 3.4 and 4.6 $\mu$m relative to the visible albedo. The direct computation of the reflectivity at 3.4 and 4.6 $\mu$m enables a new means of comparing the various taxonomic classes. Although C, B, D and T asteroids all have similarly low visible albedos, the D and T types can be distinguished from the C and B types by examining their relative reflectance at 3.4 and 4.6 $\mu$m. All of the albedo distributions are strongly affected by selection biases against small, low albedo objects, as all objects selected for taxonomic classification were chosen according to their visible light brightness. Due to these strong selection biases, we are unable to determine whether or not there are correlations between size, albedo and space weathering. We argue that the current set of classified asteroids makes any such correlations difficult to verify. A sample of taxonomically classified asteroids drawn without significant albedo bias is needed in order to perform such an analysis.Comment: Accepted to Ap

Evidence for a colour dependence in the size distribution of main belt asteroids

We present the results of a project to detect small (~1 km) main-belt asteroids with the 3.6 meter Canada-France-Hawaii Telescope (CFHT). We observed in 2 filters (MegaPrime g' and r') in order to compare the results in each band. Owing to the observational cadence we did not observe the same asteroids through each filter and thus do not have true colour information. However strong differences in the size distributions as seen in the two filters point to a colour-dependence at these sizes, perhaps to be expected in this regime where asteroid cohesiveness begins to be dominated by physical strength and composition rather than by gravity. The best fit slopes of the cumulative size distributions (CSDs) in both filters tend towards lower values for smaller asteroids, consistent with the results of previous studies. In addition to this trend, the size distributions seen in the two filters are distinctly different, with steeper slopes in r' than in g'. Breaking our sample up according to semimajor axis, the difference between the filters in the inner belt is found to be somewhat less pronounced than in the middle and outer belt, but the CSD of those asteroids seen in the r' filter is consistently and significantly steeper than in g' throughout. The CSD slopes also show variations with semimajor axis within a given filter, particularly in r'. We conclude that the size distribution of main belt asteroids is likely to be colour dependent at kilometer sizes and that this dependence may vary across the belt.Comment: 28 pages, 5 figures, submitted to the Astronomical Journa

Loyalty Programs in the Sharing Economy: Optimality and Competition

Loyalty programs are important tools for sharing platforms seeking to grow supply. Online sharing platforms use loyalty programs to heavily subsidize resource providers, encouraging participation and boosting supply. As the sharing economy has evolved and competition has increased, the design of loyalty programs has begun to play a crucial role in the pursuit of maximal revenue. In this paper, we first characterize the optimal loyalty program for a platform with homogeneous users. We then show that optimal revenue in a heterogeneous market can be achieved by a class of multi-threshold loyalty program (MTLP) which admits a simple implementation-friendly structure. We also study the performance of loyalty programs in a setting with two competing sharing platforms, showing that the degree of heterogeneity is a crucial factor for both loyalty programs and pricing strategies. Our results show that sophisticated loyalty programs that reward suppliers via stepwise linear functions outperform simple sign-up bonuses, which give them a one time reward for participating

Loyalty Programs in the Sharing Economy: Optimality and Competition

Loyalty programs are important tools for sharing platforms seeking to grow supply. Online sharing platforms use loyalty programs to heavily subsidize resource providers, encouraging participation and boosting supply. As the sharing economy has evolved and competition has increased, the design of loyalty programs has begun to play a crucial role in the pursuit of maximal revenue. In this paper, we first characterize the optimal loyalty program for a platform with homogeneous users. We then show that optimal revenue in a heterogeneous market can be achieved by a class of multi-threshold loyalty program (MTLP) which admits a simple implementation-friendly structure. We also study the performance of loyalty programs in a setting with two competing sharing platforms, showing that the degree of heterogeneity is a crucial factor for both loyalty programs and pricing strategies. Our results show that sophisticated loyalty programs that reward suppliers via stepwise linear functions outperform simple sign-up bonuses, which give them a one time reward for participating

Ultraviolet and visible photometry of asteroid (21) Lutetia using the Hubble Space Telescope

The asteroid (21) Lutetia is the target of a planned close encounter by the Rosetta spacecraft in July 2010. To prepare for that flyby, Lutetia has been extensively observed by a variety of astronomical facilities. We used the Hubble Space Telescope (HST) to determine the albedo of Lutetia over a wide wavelength range, extending from ~150 nm to ~700 nm. Using data from a variety of HST filters and a ground-based visible light spectrum, we employed synthetic photometry techniques to derive absolute fluxes for Lutetia. New results from ground-based measurements of Lutetia's size and shape were used to convert the absolute fluxes into albedos. We present our best model for the spectral energy distribution of Lutetia over the wavelength range 120-800 nm. There appears to be a steep drop in the albedo (by a factor of ~2) for wavelengths shorter than ~300 nm. Nevertheless, the far ultraviolet albedo of Lutetia (~10%) is considerably larger than that of typical C-chondrite material (~4%). The geometric albedo at 550 nm is 16.5 +/- 1%. Lutetia's reflectivity is not consistent with a metal-dominated surface at infrared or radar wavelengths, and its albedo at all wavelengths (UV-visibile-IR-radar) is larger than observed for typical primitive, chondritic material. We derive a relatively high FUV albedo of ~10%, a result that will be tested by observations with the Alice spectrograph during the Rosetta flyby of Lutetia in July 2010.Comment: 14 pages, 2 tables, 8 figure