Isotopic algebras with non-isomorphic congruence lattices

We give examples of pairs of isotopic algebras with non-isomorphic congruence lattices. This answers the question of whether all isotopic algebras have isomorphic congruence lattices.Comment: 3 pages; comments welcom

The taxonomic distribution of asteroids from multi-filter all-sky photometric surveys

The distribution of asteroids across the Main Belt has been studied for decades to understand the compositional distribution and what that tells us about the formation and evolution of our solar system. All-sky surveys now provide orders of magnitude more data than targeted surveys. We present a method to bias-correct the asteroid population observed in the Sloan Digital Sky Survey (SDSS) according to size, distance, and albedo. We taxonomically classify this dataset consistent with the Bus and Bus-DeMeo systems and present the resulting taxonomic distribution. The dataset includes asteroids as small as 5 km, a factor of three in diameter smaller than in previous works. Because of the wide range of sizes in our sample, we present the distribution by number, surface area, volume, and mass whereas previous work was exclusively by number. While the distribution by number is a useful quantity and has been used for decades, these additional quantities provide new insights into the distribution of total material. We find evidence for D-types in the inner main belt where they are unexpected according to dynamical models of implantation of bodies from the outer solar system into the inner solar system during planetary migration (Levison et al. 2009). We find no evidence of S-types or other unexpected classes among Trojans and Hildas, albeit a bias favoring such a detection. Finally, we estimate for the first time the total amount of material of each class in the inner solar system. The main belt's most massive classes are C, B, P, V and S in decreasing order. Excluding the four most massive asteroids, Ceres, Pallas, Vesta and Hygiea that heavily skew the values, primitive material (C-, P-types) account for more than half main-belt and Trojan asteroids by mass, most of the remaining mass being in the S-types. All the other classes are minor contributors to the material between Mars and Jupiter.Comment: Accepted for publication in Icarus -- 43 pages, 15 figures, 7 table

Spectral properties of near-Earth and Mars-crossing asteroids using Sloan photometry

The nature and origin of the asteroids orbiting in near-Earth space, including those on a potentially hazardous trajectory, is of both scientific interest and practical importance. We aim here at determining the taxonomy of a large sample of near-Earth (NEA) and Mars-crosser (MC) asteroids and analyze the distribution of these classes with orbit. We use this distribution to identify their source regions and to study the strength of planetary encounters to refresh asteroid surfaces. We measure the photometry of these asteroids over four filters at visible wavelengths on images taken by the SDSS. These colors are used to classify the asteroids into a taxonomy consistent with the widely used Bus-DeMeo taxonomy based on spectroscopy. We report here on the taxonomic classification of 206 NEAs and 776 MCs determined from SDSS photometry, representing an increase of 40% and 663% of known taxonomy classifications in these populations. Using the source region mapper by Greenstreet et al. (2012), we compare the taxonomic distribution among NEAs and main-belt asteroids of similar diameters. Both distributions agree at the few percent level for the inner part of the Main Belt and we confirm this region as a main source of near-Earth objects. The effect of planetary encounters on asteroid surfaces are also studied by developing a simple model of forces acting on a surface grain during planetary encounter, which provides the minimum distance at which a close approach should occur to trigger resurfacing events. By integrating numerically the orbit of the 519 S-type and 46 Q-type asteroids back in time and monitoring their encounter distance with planets, we seek to understand the conditions for resurfacing events. The population of Q-type is found to present statistically more encounters with Venus and the Earth than S-types, although both types present the same amount of encounters with Mars.Comment: Accepted for publication in Icarus. 45 pages, 11 figures, 4 tables, 2 tables in appendix (supplementary material

Making the Magic: How Public Relations is Handled at the Disney Parks

The Walt Disney Company has always been an organization that has prided itself on its corporate image. One of their biggest successes has been their 11 theme parks across the globe. Ever since its creation in 1955, Disneyland has been known as the happiest place on earth. However, many wonder how this reputation came to be and how it is being maintained today. To find this answer, one must look to the creative minds behind Disney\u27s public relations. By examining the Disney parks and their public relations history, tactics, crisis management and current and future campaigns, companies can find out the secret behind the success of the Disney parks and find out what works and what does not. By doing so, companies can take a page out of Disney\u27s PR playbook and learn some lessons from the House of Mouse that will help them develop public relations strategies for their own organization

Rotationally Resolved Spectroscopy of Asteroid Pairs: No Spectral Variation Suggests Fission is followed by Settling of Dust

We examine the spectral properties of asteroid pairs that were disrupted in the last 2 Myrs to examine whether the site of the fission can be revealed. We studied the possibility that the sub-surface material, perhaps on one hemisphere, has spectral characteristics differing from the original weathered surface, by performing rotationally-resolved spectroscopic observations to look for local variations as the asteroid rotates. We observed 11 asteroids in pairs in the near-IR and visible range. Photometry was also conducted to determine the rotational phases of a spectrum on the asteroid lightcurves. We do not detect any rotational spectral variations within the signal-to-noise, which allow us to constrain the extent of any existing surface heterogeneity. For each observed spectrum of a longitudinal segment of an asteroid, we estimate the maximal size of an un-detected "spot" with a spectral signature different than the average. For 5 asteroids the maximal diameter of such a spot is smaller by a factor of two than the diameter of the secondary member. Therefore, the site of the fission is larger than any area with a unique spectral parameters and the site of the fission does not have a unique spectrum. In the case of an S-complex asteroid, where the site of fission is expected to present non-weathered spectra, a lack of a fission spot can be explained if the rotational-fission process is followed by the spread of dust that re-accumulates on the primary asteroid and covers it homogeneously. This is demonstrated for the young asteroid 6070 that presents an Sq-type spectrum while its inner material, that is presumably revealed on the surface of its secondary member, 54827, has a fresher, Q-type spectrum. The spread of dust observed in the disruption event of asteroid P/2013 R3, might be an example of such a process and an indication that it was indeed formed in a rotational-fission event.Comment: 16 pages, 15 figures, 6 Tables. Accepted for publication in Icaru

Active vibration damping of the Space Shuttle remote manipulator system

The feasibility of providing active damping augmentation of the Space Shuttle Remote Manipulator System (RMS) following normal payload handling operations is investigated. The approach used in the analysis is described, and the results for both linear and nonlinear performance analysis of candidate laws are presented, demonstrating that significant improvement in the RMS dynamic response can be achieved through active control using measured RMS tip acceleration data for feedback

Unexpected D-type Interlopers in the Inner Main Belt

Very red featureless asteroids (spectroscopic D-types) are expected to have formed in the outer solar system far from the sun. They comprise the majority of asteroids in the Jupiter Trojan population, and are also commonly found in the outer main belt and among Hildas. The first evidence for D-types in the inner and middle parts of the main belt was seen in the Sloan Digital Sky Survey (SDSS). Here we report follow-up observations of SDSS D-type candidates in the near-infrared. Based on follow up observations of 13 SDSS D-type candidates, we find a ~20% positive confirmation rate. Known inner belt D-types range in diameter from roughly 7 to 30 kilometers. Based on these detections we estimate there are ~100 inner belt D-types with diameters between 2.5 and 20km. The lower and upper limits for total mass of inner belt D-types is 2x$10^{16}$ kg to 2x$10^{17}$ kg which represents 0.01% to 0.1% of the mass of the inner belt. The inner belt D-types have albedos at or above the upper end typical for D-types which raises the question as to whether these inner belt bodies represent only a subset of D-types, they have been altered by external factors such as weathering processes, or if they are compositionally distinct from other D-types. All D-types and candidates have diameters less than 30km, yet there is no obvious parent body in the inner belt. Dynamical models have yet to show how D-types originating from the outer solar system could penetrate into the inner reaches of the Main Belt under current scenarios of planet formation and subsequent Yarkovsky drift.Comment: 16 pages, 3 figures, 4 tables -- accepted for publication in Icaru

Mars Encounters cause fresh surfaces on some near-Earth asteroids

All airless bodies are subject to the space environment, and spectral differences between asteroids and meteorites suggest many asteroids become weathered on very short (<1My) timescales. The spectra of some asteroids, particularly Q-types, indicate surfaces that appear young and fresh, implying they have been recently been exposed. Previous work found that Earth encounters were the dominant freshening mechanism and could be responsible for all near-Earth object (NEO) Q-types. In this work we increase the known NEO Q-type sample of by a factor of three. We present the orbital distributions of 64 Q-type near-Earth asteroids, and seek to determine the dominant mechanisms for refreshing their surfaces. Our sample reveals two important results: i) the relatively steady fraction of Q-types with increasing semi-major axis and ii) the existence of Q-type near-Earth asteroids with Minimum Orbit Intersection Distances (MOID) that do not have orbit solutions that cross Earth. Both of these are evidence that Earth-crossing is not the only scenario by which NEO Q-types are freshened. The high Earth-MOID asteroids represent 10% of the Q-type population and all are in Amor orbits. While surface refreshing could also be caused by Main Belt collisions or mass shedding from YORP spinup, all high Earth-MOID Q-types have the possibility of encounters with Mars indicating Mars could be responsible for a significant fraction of NEOs with fresh surfaces.Comment: Accepted for publication in Icarus -- 14 pages, 8 figures, 1 table, 2 appendice