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.

Inhomogeneity of asteroid 2008 TC3 (Almahata Sitta meteorites) revealed through magnetic susceptibility measurements

Magnetic susceptibility measurements were performed on freshly fallen Almahata Sitta meteorites. Most recovered samples are polymict ureilites. Those found in the first four months since impact, before the meteorites were exposed to rain, have a magnetic susceptibility in the narrow range of 4.92 ± 0.08 log 10-9 Am2/kg close to the range of other ureilite falls 4.95 ± 0.14 log 10-9 Am2/kg reported by Rochette et al. (2009). The Almahata Sitta samples collected one year after the fall have similar values (4.90 ± 0.06 log 10-9 Am2/kg), revealing that the effect of one-year of terrestrial weathering was not severe yet. However, our reported values are higher than derived from polymict (brecciated) ureilites 4.38 ± 0.47 log 10-9 Am2/kg (Rochette et al. 2009) containing both falls and finds confirming that these are significantly weathered. Additionally other fresh-looking meteorites of non-ureilitic compositions were collected in the Almahata Sitta strewn field. Magnetic susceptibility measurements proved to be a convenient non-destructive method for identifying non-ureilitic meteorites among those collected in the Almahata Sitta strewn field, even among fully crusted. Three such meteorites, no. 16, 25, and 41, were analyzed and their composition determined as EH6, H5 and EL6 respectively (Zolensky et al., 2010). A high scatter of magnetic susceptibility values among small (< 5 g) samples revealed high inhomogeneity within the 2008 TC3 material at scales below 1-2 cm.

Physical properties of meteorites and their role in planetology

Together with cosmic spherules, interplanetary dust particles and lunar samples returned by Apollo and Luna missions, meteorites are the only source of extraterrestrial material on Earth. The physical properties of meteorites, especially their magnetic susceptibility, bulk and grain density, porosity and paleomagnetic information, have wide applications in planetary research and can reveal information about origin and internal structure of asteroids. Thus, an expanded database of meteorite physical properties was compiled with new measurements done in meteorite collections across Europe using a mobile laboratory facility. However, the scale problem may bring discrepancies in the comparison of asteroid and meteorite properties. Due to inhomogenity, the physical properties of meteorites studied on a centimeter or millimeter scale may differ from those of asteroids determined on kilometer scales. Further difference may arise from shock effects, space and terrestrial weathering and from difference in material properties at various temperatures. Close attention was given to the reliability of the paleomagnetic and paleointensity information in meteorites and the methodology to test for magnetic overprints was prepared and verified.