Pre-encounter observations of 951 Gaspra

Photometry and colorimetry of 951 Gaspra were obtained on nine nights during the 1990 opposition. A composite lightcurve constructed using data from eight of those nights yielded a synodic rotational period of 7.04346 +/- 0.00006 hours, a mean absolute V magnitude of 11.8026 +/- 0.0025, and a slope parameter of 0.285 +/- 0.005. The apparent discrepancy can be easily resolved by realizing that their determination is based primarily on data obtained after opposition. Different phase functions pre- and post-opposition are a natural consequence of a changing aspect during an opposition. If the sub-Earth latitude on Gaspra is at a less equatorial aspect after opposition than it was before opposition, then we would expect to see a shallower phase function (corresponding to a larger numerical value of the slope parameter). Adding weight to this hypothesis is the last observation of the opposition, made in May after Gaspra had passed post opposition quadrature, which is displaced toward brighter absolute magnitudes relative to the rest of our data, indicating an even more poleward sub-Earth latitude than earlier in the opposition. Because the orbits of Earth and Gaspra are nearly coplanar, a substantial change in sub-Earth latitude during the opposition would not have been possible unless the obliquity of the asteroid's rotational axis is not small

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

A revised asteroid polarization-albedo relationship using WISE/NEOWISE data

We present a reanalysis of the relationship between asteroid albedo and polarization properties using the albedos derived from the Wide-field Infrared Survey Explorer. We find that the function that best describes this relation is a three-dimensional linear fit in the space of log(albedo)-log(polarization slope)-log(minimum polarization). When projected to two dimensions the parameters of the fit are consistent with those found in previous work. We also define p* as the quantity of maximal polarization variation when compared with albedo and present the best fitting albedo-p* relation. Some asteroid taxonomic types stand out in this three-dimensional space, notably the E, B, and M Tholen types, while others cluster in clumps coincident with the S- and C-complex bodies. We note that both low albedo and small (D<30 km) asteroids are under-represented in the polarimetric sample, and we encourage future polarimetric surveys to focus on these bodies.Comment: 16 pages, Accepted to Ap

Cosmological perturbations on local systems

We study the effect of cosmological expansion on orbits--galactic, planetary, or atomic--subject to an inverse-square force law. We obtain the laws of motion for gravitational or electrical interactions from general relativity--in particular, we find the gravitational field of a mass distribution in an expanding universe by applying perturbation theory to the Robertson-Walker metric. Cosmological expansion induces an ($\ddot a/a) \vec r$ force where $a(t)$ is the cosmological scale factor. In a locally Newtonian framework, we show that the $(\ddot a/a) \vec r$ term represents the effect of a continuous distribution of cosmological material in Hubble flow, and that the total force on an object, due to the cosmological material plus the matter perturbation, can be represented as the negative gradient of a gravitational potential whose source is the material actually present. We also consider the effect on local dynamics of the cosmological constant. We calculate the perihelion precession of elliptical orbits due to the cosmological constant induced force, and work out a generalized virial relation applicable to gravitationally bound clusters.Comment: 10 page

NEOWISE Studies of Asteroids with Sloan Photometry: Preliminary Results

We have combined the NEOWISE and Sloan Digital Sky Survey data to study the albedos of 24,353 asteroids with candidate taxonomic classifications derived using Sloan photometry. We find a wide range of moderate to high albedos for candidate S-type asteroids that are analogous to the S-complex defined by previous spectrophotometrically-based taxonomic systems. The candidate C-type asteroids, while generally very dark, have a tail of higher albedos that overlaps the S types. The albedo distribution for asteroids with a photometrically derived Q classification is extremely similar to those of the S types. Asteroids with similar colors to (4) Vesta have higher albedos than the S types, and most have orbital elements similar to known Vesta family members. Finally, we show that the relative reflectance at 3.4 and 4.6 $\mu$m is higher for D-type asteroids and suggest that their red visible and near-infrared spectral slope extends out to these wavelengths. Understanding the relationship between size, albedo, and taxonomic classification is complicated by the fact that the objects with classifications were selected from the visible/near-infrared Sloan Moving Object Catalog, which is biased against fainter asteroids, including those with lower albedos.Comment: ApJ accepte

The Pan-STARRS Moving Object Processing System

We describe the Pan-STARRS Moving Object Processing System (MOPS), a modern software package that produces automatic asteroid discoveries and identifications from catalogs of transient detections from next-generation astronomical survey telescopes. MOPS achieves > 99.5% efficiency in producing orbits from a synthetic but realistic population of asteroids whose measurements were simulated for a Pan-STARRS4-class telescope. Additionally, using a non-physical grid population, we demonstrate that MOPS can detect populations of currently unknown objects such as interstellar asteroids. MOPS has been adapted successfully to the prototype Pan-STARRS1 telescope despite differences in expected false detection rates, fill-factor loss and relatively sparse observing cadence compared to a hypothetical Pan-STARRS4 telescope and survey. MOPS remains >99.5% efficient at detecting objects on a single night but drops to 80% efficiency at producing orbits for objects detected on multiple nights. This loss is primarily due to configurable MOPS processing limits that are not yet tuned for the Pan-STARRS1 mission. The core MOPS software package is the product of more than 15 person-years of software development and incorporates countless additional years of effort in third-party software to perform lower-level functions such as spatial searching or orbit determination. We describe the high-level design of MOPS and essential subcomponents, the suitability of MOPS for other survey programs, and suggest a road map for future MOPS development.Comment: 57 Pages, 26 Figures, 13 Table

Dualities for modal algebras from the point of view of triples

In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by Cartesian product on the relational side and show that in some cases the corresponding operation on the algebraic side represents bimorphisms

NEOWISE Observations of Near-Earth Objects: Preliminary Results

With the NEOWISE portion of the \emph{Wide-field Infrared Survey Explorer} (WISE) project, we have carried out a highly uniform survey of the near-Earth object (NEO) population at thermal infrared wavelengths ranging from 3 to 22 $\mu$m, allowing us to refine estimates of their numbers, sizes, and albedos. The NEOWISE survey detected NEOs the same way whether they were previously known or not, subject to the availability of ground-based follow-up observations, resulting in the discovery of more than 130 new NEOs. The survey's uniformity in sensitivity, observing cadence, and image quality have permitted extrapolation of the 428 near-Earth asteroids (NEAs) detected by NEOWISE during the fully cryogenic portion of the WISE mission to the larger population. We find that there are 981$\pm$19 NEAs larger than 1 km and 20,500$\pm$3000 NEAs larger than 100 m. We show that the Spaceguard goal of detecting 90% of all 1 km NEAs has been met, and that the cumulative size distribution is best represented by a broken power law with a slope of 1.32$\pm$0.14 below 1.5 km. This power law slope produces $\sim13,200\pm$1,900 NEAs with $D>$140 m. Although previous studies predict another break in the cumulative size distribution below $D\sim$50-100 m, resulting in an increase in the number of NEOs in this size range and smaller, we did not detect enough objects to comment on this increase. The overall number for the NEA population between 100-1000 m are lower than previous estimates. The numbers of near-Earth comets will be the subject of future work.Comment: Accepted to Ap