Light scattering by Gaussian random particles

We introduce multivariate lognormal statistics to describe the shapes of small particles, and compute scattering phase matrices in the ray optics approximation. The results help us understand light scattering by solar system dust particles, and thereby constrain the physical properties of, for example, asteroid regoliths and cometary comae. The present stochastic geometry could turn useful in modeling the shapes of asteroids.     

The SMART-1 AMIE experiment: implication to the lunar opposition effect

The lunar surface reveals a sharp opposition effect, which is to be explained by the shadowing and coherent backscattering mechanisms. Generalizing the radiative transfer theory via Monte Carlo methods, we are carrying out studies of backscattering in regolith-like scattering media. We have also started systematic laboratory measurements of structural simulators of lunar regolith. The SMART-1 AMIE and D-CIXS/XSM experiments provide us a unique opportunity for a simultaneous multiwavelength study of the lunar regolith close to opposition, since the SMART-1 spacecraft will pass over several different types of lunar surface at zero phase angles. Results of our theoretical and laboratory investigations can be used as a basis to interpret the SMART-1 AMIE and D-CIXS/XSM experiments. In particular, it seems to be possible to estimate regional variations of regolith particle volume fraction and their size. A short review of observational, experimental and theoretical works is also presented here.     

OpenOrb: Open‐source asteroid orbit computation software including statistical ranging

Abstract— 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.     

A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka

Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the perturbations due to other planets.     

Asteroid identification over apparitions

We present a new method for the linking of scarce asteroid astrometry over apparitions, and apply it both to simulated and real data to prove its feasibility. Up to date, there has not been a robust method available to search for linkages between the approximately 50,000 provisionally designated sets of asteroid astrometry spanning less than two days. Unless such a scarce set of astrometry is linked to another set of astrometry, the underlying object can be considered lost as the ephemeris uncertainties are substantial. The new method, which can tackle the challenges, is based on Ranging, which is a fully nonlinear, statistical orbital inversion method. Ranging properly treats astrometric uncertainties and propagates the uncertainty to the resulting orbital-element probability density, which is sampled by a set of orbits. The new orbital-element-space multiple-address-comparison (oMAC) method uses dimensionality-reduction techniques and tree structures to efficiently search for overlapping probability densities in the orbital-element phase space. Overlapping probability densities indicate a candidate linkage between astrometric observation sets. To accept a candidate linkage, we have to find a many-body orbital solution which reproduces the observed positions within the observational uncertainties. To find the linking orbit, we use a multi-step approach starting from a Monte-Carlo generation of possible orbits in a reduced volume of the orbital-element phase space and ending with a least-squares orbital solution, which, in addition to the Sun's gravitation, also takes into account the gravitational influence of the relevant planets. The new multiple-address-comparison method has a loglinear computational complexity, that is, it scales as O(nlogn), where n is the number of included observation sets. It has recently also been implemented for the ephemeris-space multiple-address-comparison (eMAC) method, which is optimized for the short-term linking of scarce astrometry.     

The Umov effect for single irregularly shaped particles with sizes comparable with wavelength

The Umov effect manifests itself as an inverse correlation between the linear polarization maximum of an object’s scattered light P_max and its geometric albedo A. This effect is observed for the Moon, Mercury and Mars, and there are data suggesting this effect is valid for asteroids. The Umov effect is due to the contribution of interparticle multiple scattering that increases albedo and decreases polarization. We here study if the Umov effect can be extended to the case of single irregularly shaped particles with sizes comparable with the wavelength. This, in particular, is important for cometary dust polarimetry. We show the Umov effect being valid for weakly absorbing irregular particles (Im(m) ? 0.02) almost through the entire range of size parameters x considered. Highly absorbing particles (Im(m) > 0.02) follow the Umov effect only if x exceeds 14. In the case of weakly absorbing particles, the inverse correlation is essentially non-linear, which is caused by the contribution of particles with small x. However, averaging over many different types of irregularly shaped particles could make it significantly more linear. The size averaging does not change qualitatively the diagram log(P_max)-log(A) for weakly absorbing particles. For single irregular particles whose sizes are comparable with wavelength, there is no reliable correlation between the slope of the polarization curve h near the inversion phase angle and geometric albedo A. Using the extended Umov Law, we estimate the geometric albedo of dust particles forming cometary circumnuclear haloes A = 0.1 − 0.2, which is a few times larger than the average geometric albedo over the entire comae. Note that, using the obtained values for A of cometary particles, one can derive their number density in circumnuclear haloes from photometric observations.     

A three-parameter magnitude phase function for asteroids

We develop a three-parameter H, G₁, G₂ magnitude phase function for asteroids starting from the current two-parameter H, G phase function. We describe stochastic optimization of the basis functions of the magnitude phase function based on a carefully chosen set of asteroid photometric observations covering the principal types of phase dependencies. We then illustrate the magnitude phase function with a chosen set of observations. It is shown that the H, G₁, G₂ phase function systematically improves fits to the existing data and considerably so, warranting the utilization of three parameters instead of two. With the help of the linear three-parameter phase function, we derive a nonlinear two-parameter H, G₁₂ phase function, and demonstrate its applicability in predicting phase dependencies based on small numbers of observations.     

The strange polarimetric behavior of Asteroid (234) Barbara

We have discovered that the Asteroid (234) Barbara exhibits very anomalous polarimetric properties. The phase-polarization curve of this asteroid is unique and is not matched by any other known atmosphereless body of our Solar System. Although a few preliminary conjectures can be made, for the moment the reasons of the peculiar polarimetric properties of this asteroid remain essentially unknown.     

Asteroid spin‐axis longitudes from the Lowell Observatory database

By analyzing brightness variation with ecliptic longitude and using the Lowell Observatory photometric database, we estimate spin‐axis longitudes for more than 350,000 asteroids. Hitherto, spin‐axis longitude estimates have been made for fewer than 200 asteroids. We investigate longitude distributions in different dynamical groups and asteroid families. We show that asteroid spin‐axis longitudes are not isotropically distributed as previously considered. We find that the spin‐axis longitude distribution for Main Belt asteroids is clearly nonrandom, with an excess of longitudes from the interval 30°–110° and a paucity between 120° and 180°. The explanation of the nonisotropic distribution is unknown at this point. Further studies have to be conducted to determine if the shape of the distribution can be explained by observational bias, selection effects, a real physical process, or other mechanism.