• Asteroid orbital ranging using Markov-Chain Monte Carlo

      Oszkiewicz, D.; Muinonen, K.; Virtanen, J.; Granvik, M. (The Meteoritical Society, 2009-01-01)
      We present a novel Markov-Chain Monte-Carlo orbital ranging method (MCMC) for poorly observed single-apparition asteroids with two or more observations. We examine the Bayesian a posteriori probability density of the orbital elements using methods that map a volume of orbits in the orbital-element phase space. In particular, we use the MCMC method to sample the phase space in an unbiased way. We study the speed of convergence and also the efficiency of the new method for the initial orbit computation problem. We present the results of the MCMC ranging method applied to three objects from different dynamical groups. We conclude that the method is applicable to initial orbit computation for near-Earth, main-belt, and transneptunian objects.
    • Asteroid photometric and polarimetric phase curves: Joint linear-exponential modeling

      Muinonen, K.; Penttilä, A.; Cellino, A.; Belskaya, I. N.; Delbò, M.; Levasseur-Regourd, A. C.; Tedesco, E. F. (The Meteoritical Society, 2009-01-01)
      We present Markov-Chain Monte-Carlo methods (MCMC) for the derivation of empirical model parameters for photometric and polarimetric phase curves of asteroids. Here we model the two phase curves jointly at phase angles approximately <25 degrees using a linear-exponential model, accounting for the opposition effect in disk-integrated brightness and the negative branch in the degree of linear polarization. We apply the MCMC methods to V-band phase curves of asteroids 419 Aurelia (taxonomic class F), 24 Themis (C), 1 Ceres (G), 20 Massalia (S), 55 Pandora (M), and 64 Angelina (E). We show that the photometric and polarimetric phase curves can be described using a common nonlinear parameter for the angular widths of the opposition effect and negative-polarization branch, thus supporting the hypothesis of common physical mechanisms being responsible for the phenomena. Furthermore, incorporating polarimetric observations removes the indeterminacy of the opposition effect for 1 Ceres. We unveil a trend in the interrelation between the enhancement factor of the opposition effect and the angular width: the enhancement factor decreases with decreasing angular width. The minimum polarization and the polarimetric slope at the inversion angle show systematic trends when plotted against the angular width and the normalized photometric slope parameter. Our new approach allows improved analyses of possible similarities and differences among asteroidal surfaces.
    • OpenOrb: Open-source asteroid orbit computation software including statistical ranging

      Granvik, M.; Virtanen, J.; Oszkiewicz, D.; Muinonen, K. (The Meteoritical Society, 2009-01-01)
      We are making an open-source asteroid orbit computation software package called OpenOrb publicly available. OpenOrb is built on a well-established Bayesian inversion theory, which means that it is to a large part complementary to orbit-computation packages currently available. In particular, OpenOrb is the first package that contains tools for rigorously estimating the uncertainties resulting from the inverse problem of computing orbital elements using scarce astrometry. In addition to the well-known least-squares method, OpenOrb also contains both Monte-Carlo (MC) and Markov-Chain MC (MCMC; Oszkiewicz et al. [2009]) versions of the statistical ranging method. Ranging allows the user to obtain sampled, non-Gaussian orbital-element probability-density functions and is therefore optimized for cases where the amount of astrometry is scarce or spans a relatively short time interval. Ranging-based methods have successfully been applied to a variety of different problems such as rigorous ephemeris prediction, orbital element distribution studies for transneptunian objects, the computation of invariant collision probabilities between near-Earth objects and the Earth, detection of linkages between astrometric asteroid observations within an apparition as well as between apparitions, and in the rigorous analysis of the impact of orbital arc length and/or astrometric uncertainty on the uncertainty of the resulting orbits. Tools for making ephemeris predictions and for classifying objects based on their orbits are also available in OpenOrb. As an example, we use OpenOrb in the search for candidate retrograde and/or high-inclination objects similar to 2008 KV42 in the known population of transneptunian objects that have an observational time span shorter than 30 days.