Asteroid identification using statistical orbital inversion methods

An efficient and statistically robust solution for the identification of asteroids among numerous sets of astrometry is presented. In particular, numerical methods have been developed for the short-term identification of asteroids at discovery, and for the long-term identification of scarcely observed asteroids over apparitions, a task which has been lacking a robust method until now. The methods are based on the solid foundation of statistical orbital inversion properly taking into account the observational uncertainties, which allows for the detection of practically all correct identifications. Through the use of dimensionality-reduction techniques and efficient data structures, the exact methods have a loglinear, that is, O(nlog(n)), computational complexity, where n is the number of included observation sets. The methods developed are thus suitable for future large-scale surveys which anticipate a substantial increase in the astrometric data rate. Due to the discontinuous nature of asteroid astrometry, separate sets of astrometry must be linked to a common asteroid from the very first discovery detections onwards. The reason for the discontinuity in the observed positions is the rotation of the observer with the Earth as well as the motion of the asteroid and the observer about the Sun. Therefore, the aim of identification is to find a set of orbital elements that reproduce the observed positions with residuals similar to the inevitable observational uncertainty. Unless the astrometric observation sets are linked, the corresponding asteroid is eventually lost as the uncertainty of the predicted positions grows too large to allow successful follow-up. Whereas the presented identification theory and the numerical comparison algorithm are generally applicable, that is, also in fields other than astronomy (e.g., in the identification of space debris), the numerical methods developed for asteroid identification can immediately be applied to all objects on heliocentric orbits with negligible effects due to non-gravitational forces in the time frame of the analysis. The methods developed have been successfully applied to various identification problems. Simulations have shown that the methods developed are able to find virtually all correct linkages despite challenges such as numerous scarce observation sets, astrometric uncertainty, numerous objects confined to a limited region on the celestial sphere, long linking intervals, and substantial parallaxes. Tens of previously unknown main-belt asteroids have been identified with the short-term method in a preliminary study to locate asteroids among numerous unidentified sets of single-night astrometry of moving objects, and scarce astrometry obtained nearly simultaneously with Earth-based and space-based telescopes has been successfully linked despite a substantial parallax. Using the long-term method, thousands of realistic 3-linkages typically spanning several apparitions have so far been found among designated observation sets each spanning less than 48 hours.

Lightcurve inversion for asteroid spins and shapes

Knowledge of the physical properties of asteroids is crucial in many branches of solar-system research. Knowledge of the spin states and shapes is needed, e.g., for accurate orbit determination and to study the history and evolution of the asteroids. In my thesis, I present new methods for using photometric lightcurves of asteroids in the determination of their spin states and shapes. The convex inversion method makes use of a general polyhedron shape model and provides us at best with an unambiguous spin solution and a convex shape solution that reproduces the main features of the original shape. Deriving information about the non-convex shape features is, in principle, also possible, but usually requires a priori information about the object. Alternatively, a distribution of non-convex solutions, describing the scale of the non-convexities, is also possible to be obtained. Due to insufficient number of absolute observations and inaccurately defined asteroid phase curves, the $c/b$-ratio, i.e., the flatness of the shape model is often somewhat ill-defined. However, especially in the case of elongated objects, the flatness seems to be quite well constrained, even in the case when only relative lightcurves are available. The results prove that it is, contrary to the earlier misbelief, possible to derive shape information from the lightcurve data if a sufficiently wide range of observing geometries is covered by the observations. Along with the more accurate shape models, also the rotational states, i.e., spin vectors and rotation periods, are defined with improved accuracy. The shape solutions obtained so far reveal a population of irregular objects whose most descriptive shape characteristics, however, can be expressed with only a few parameters. Preliminary statistical analyses for the shapes suggests that there are correlations between shape and other physical properties, such as the size, rotation period and taxonomic type of the asteroids. More shape data of, especially, the smallest and largest asteroids, as well as the fast and slow rotators is called for in order to be able to study the statistics more thoroughly.

Cosmic Clowns : Convention, Invention, and Inversion in the Yaqui Easter Ritual

Cosmic Clowns: Convention, Invention, and Inversion in the Yaqui Easter Ritual is an ethnographic study of masked clown figures called Chapayekas. They represent Judas and the Roman soldiers in the Passion play that forms the narrative core of the Easter ritual of the Yaquis, an indigenous group in Sonora, Mexico. The study looks at how the Chapayeka is created as a ritual figure, how their performance is constructed, and what the part of the clown is in the dynamics of the ritual. The material was gathered over three periods of anthropological fieldwork in Cócorit, Sonora during Easter in 2004, 2006 and 2007. The Chapayeka masks portray foreigners, animals, mythological figures, and even figures from television and movies. They combine two kinds of performance: they perform set, conventional actions, and improvise and invent new ones. This creates dialectics of invention and convention that allow the figure to mediate between the ritual and its context and different kinds of beings within the Yaqui cosmology. The conventional side of their performance is a cycle of death and rebirth that is an inversion of the cycle of Jesus. Through invention, they separate themselves from the other performers and make themselves powerful. Alternation between the two modes enhances that power and brings it into the conventions of the ritual; ultimately the Chapayekas revitalize the entire ritual. The study finds that the clowns are extremely important to the continuity of both ritual and culture, as the combination of continuity and change, convention and invention, is what makes it possible to recreate the conventions of Yaqui culture as powerful and compelling in various contexts. Another factor is the prevalence of dialectical mediation, which relates concepts by defining them against each other as opposites, and makes it possible to cross a boundary while keeping it intact. Clowns embody and create dialectics to mediate boundaries while guarding against relativization, the disappearance of distinctions. The Chapayekas create and constitute boundaries between the self and other, microcosm and macrocosm, sacred and profane. The study argues that all clown and trickster figures are characterized by constantly alternating between invention and convention; this is what connects them to the collective and moral aspect of culture and, at the same time, makes them unpredictable and powerful. It is possible to do justice to the opposed aspects of these ambiguous and paradoxical figures by taking into account the different foundations and contextual effects of the different modes of symbolization.