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We consider initial determination of asteroid orbits in the case of small numbers of observations and short observational arcs. For asteroids having long arcs, we can assess the orbital uncertainties with the help of the covariance matrix that, in the phase space of the orbital elements, defines a set of probability ellipsoids. In initial orbit determination, because of the nonlinear characteristics and multiple solutions of the inversion problem, we cannot readily use the covariance matrix to estimate the orbital uncertainties. However, by computing the eigenvalues and eigenvectors of the formal correlation matrix (that is, by deriving the eigenorbits), we can discern the most indeterminate orbital elements. Here we solve the eigenproblem for 17 single-apparition asteroids.

Results from a series of long-term numerical integrations of orbits centred on that of C/1995 O1 (Hale-Bopp) are presented. Initially, 33 orbits taken from various sources were integrated in realistic models of the Solar system for various time-scales about the present in the range (-3, +2) Myr and analysed to assess the probability of different dynamical outcomes, such as Sun-grazing state or the number of orbits since the comet was captured from a long-period orbit in the Oort cloud. Further integrations were performed using an ensemble of 26 orbits more closely clustered about the present orbit of the comet, based on a more accurate method of orbit determination. We find that the ensemble half-life for the comet tp be captured or ejected is on the order of 0.5 Myr in the backward integrations and 1.2 Myr in the forward integrations, although a few members of our ensemble were captured during strong encounters with Jupiter within 10 revolutions. Comet Hale-Bopp has a probability pb.15 of evolving to a Sun-grazing end-state and, though not a 'new' comet (in the sense of being recently captured from the Oort cloud), it may be considered dynamically young.

We study absorption and scattering by Gaussian random particles in the Rayleigh and Rayleigh-Gans approximations. The random shape is characterized by the autocovariance function, usually parameterized by the standard deviation of radius and the correlation length of angular variations. As for the Rayleigh-Gans approximation, we outline a Monte Carlo algorithm that can be adjusted for almost arbitrary, mathematically star-like particles in random orientation. The algorithm is computationally constrained to particles with size parameters less than about five. We examine how the autocovariance function affects the scattering and absorption properties of Gaussian particles, and compare to the Rayleigh-Gans solution for spheres. By ensemble-averaging the volume of the Gaussian particle, we develop criteria for the validity of the Rayleigh and Rayleigh-Gans approximations. The results help us understand, in part, light scattering by small particles in planetary atmospheres and cometary comae.

We model the shapes of irregular small particles using multivariate lognormal statistics (Gaussian random shape), and compute absorption and scattering cross sections, asymmetry parameters, and scattering phase matrices in the ray optics approximation. The random shape is fully described by the autocovariance function, which can be conveniently modeled by two statistical parameters: the standard deviation of radius and the correlation length of angular variations. We present an efficient spherical harmonics method for generating sample Gaussian random particles, and outline a ray tracing algorithm that can be adapted to almost arbitrary, mathematically star-like particles. We study the scattering and absorption properties of Gaussian random particles much larger than the wavelength by systematically varying their statistical parameters and complex refractive indices. The results help us understand, in part, light scattering by solar system dust particles, and thereby constrain the physical properties of, for example, asteroid regoliths and cometary comae.

The basic physical parameters of asteroids, such as spin parameters, shape and scattering parameters, can provide us with information on the formation and evolution of both the asteroids themselves and the entire solar system. In a majority of asteroids, the disk-integrated photometry measurement constitutes the primary source of the above knowledge. In the present paper, newly observed photometric data and existing data on (585) Bilkis are analyzed based on a Lommel-Seeliger ellipsoid model. With a Markov chain Monte Carlo (MCMC) method, we have determined the spin parameters (period, pole orientation) and shape ( b/a , c/a ) of (585) Bilkis and their uncertainties. As a result, we obtained a rotational period of 8.5738209 h with an uncertainty of 9×10 −7 h, and derived a pole of (136.46 ° , 29.0 ° ) in the ecliptic frame of J2000.0 with uncertainties of 0.67 ° and 1.1 ° in longitude and latitude respectively. We also derived triaxial ratios b/a and c/a of (585) Bilkis as 0.736 and 0.70 with uncertainties of 0.003 and 0.03 respectively.

Context. We study the surface properties of transneptunian populations of Solar-system bodies. Aims. We investigate the surface characteristics of the dwarf planet (136472) Makemake and the resonant object (90482) Orcus. Methods. Using the FORS2 instrument of the ESO-VLT we have carried out linear polarisation measurements of Makemake and Orcus. Results. Polarisation of Orcus is similar to that of smaller size objects. The polarimetric properties of Makemake are very close to those of Eris and Pluto. We have not found any significant differences in the polarisation properties of objects from different dynamical classes. However, there are significant differences in polarisation of large and smaller size objects, and between large TNOs with water-ice and methane-ice dominated surfaces. Conclusions. We confirm the different types of polarisation phase behavior for the largest and smaller size TNOs. To explain subtle surface polarisation of Pluto, Makemake and Eris we assume that their surfaces are covered by a thin layer of hoarfrost masking the surface structure.

[1] A novel automatic classification method is proposed for identifying the habits of large ice-cloud particles and deriving the shape distribution of particle ensembles. This IC-PCA (Ice-crystal Classification with Principal Component Analysis) tool is based on a principal component analysis of selected physical and statistical features of ice-crystal perimeters. The method is developed and tested using image data obtained with a Cloud Particle Imager, but can be applied to other silhouette data as well. For three randomly selected test cases of 222, 200, and 201 crystals from tropical, midlatitude, and arctic ice clouds, the combined classification accuracy of the IC-PCA is 81.1%. Since previous, semiautomatic classification methods are more time-consuming and include a subjective phase, the automatic and objective IC-PCA offers a notable improvement in retrieving the shapes of the individual crystals. As the habit distributions of ice-cloud particles can be applied to computations of radiative impact of cirrus, it is also demonstrated how classification uncertainties propagate into the radiative transfer computations by using the arctic test case as an example. Computations of shortwave radiative fluxes show that the flux differences between clouds of manually and automatically classified crystals can be as large as 10 Wm−2 but also that two manual classifications of the same image data result in even larger differences, implying the need for a systematic and repeatable classification method.

International audience; The low abundance of refractory carbonaceous material in samples collected by Stardust in comet 81P/Wild 2 coma was completely unexpected. If these results are universal to other comets, this necessitates a reformulation of current models of solar system formation. A polarimetric imaging analysis demonstrates that dust is not uniformly distributed within cometary coma, and that the circumnucleus halo region where the dust samples were collected must contain a low population of carbonaceous particles. Such regions are seen in other comets, suggesting that comet 81P/Wild 2 is not unusual and that the anomalous lack of carbon is not necessarily representative of the entire coma.

We study the evolution of the Earth collision probability of asteroid 2008 TC3 using a short observational arc and small numbers of observations. To assess impact probability, we use techniques that rely on the orbital-element probability density function characterized using both Markov-chain Monte-Carlo orbital ranging and Monte-Carlo ranging. First, we evaluate the orbital uncertainties for the object from the night of discovery onwards and examine the collapse of the orbital-element distributions in time. Second, we examine the sensitivity of the results to the assumed astrometric noise. Each of the orbits obtained from the MCMC ranging method is propagated into the future (within chosen time bounds of the expected impact), and the collision probability is calculated as a weighted fraction of the orbits leading to a collision from the Earth. We compare the results obtained with both methods., Comment: Planetary and Space Science

We have carried out a two-body orbital uncertainty analysis for more than 10,000 asteroids observed at single apparitions. Our working database included the epoch, number of observations, observational arc, orbital elements and their 1−σ uncertainties, several orbital quality metrics (which we term the mean motion, leak and sleak metrics), the correlations among the orbital elements, and the 1−σ skyplane uncertainties one month after the last observation. The orbital quality metrics correlated clearly with the observational arc. We found semi-empirical power laws of the form θ ≈ 10 T −2 arc / N − 3 and σ ψ ≈ 6 × 10 4 T −2 arc / N − 3 (leakmetric θ in radians, sky-plane uncertainty σψ in arcsec, observational arc Tarc in days, and number of observations N). The power laws are valid for single-apparition main-belt asteroids to within a factor of five. The sleak and leak metrics were often dominated by the uncertainty in the eccentricity or the uncertainty in the mean longitude. We outline two principal applications of the orbital quality estimates: assessment of whether an orbit is accurate enough for proper element calculation, and the establishment of simple criteria for judging how an asteroid's orbit and ephemeris prediction are likely to improve with further observation.

I review progress in interpreting the opposition effect and negative linear polarization observed for solar system dust particles. The so–called coherent backscattering mechanism has recently been introduced to explain the observations. However, fundamental difficulties in theoretical modeling still prevent quantitative interpretation. I also review some of the key observations that questioned the hitherto widely accepted mutual–shadowing explanation for the opposition effect. I summarize previous theoretical and experimental work on the opposition effect and negative polarization.

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.

We are constructing a database of J2000.0 osculating elements for all asteroids that have reasonably calculable orbits, and to make it publicly accessible via anonymous ftp. The database will be a very dynamic one; it will change on a quasi-daily basis as new observations and orbits become available. At present, an incomplete version of the database is online. In this paper, we present and discuss sample records of asteroid orbital data as they might appear in more mature form.

About a dozen physical mechanisms and models aspire to explain the negative polarization of light scattered by atmosphereless celestial bodies. This is too large a number for the reliable interpretation of observational data. Through a comparative analysis of the models, our main goal is to answer the question: Does any one model have an advantage over the others? Our analysis is based on new laboratory polarimetric and photometric data as well as on theoretical results. We show that the widely used models due to Hopfield and Wolff cannot realistically explain the phase-angle dependence of the degree of polarization observed at small phase angles. The so-called interference or coherent backscattering mechanism is the most promising model. Models based on that mechanism use well-defined physical parameters to explain both negative polarization and the opposition effect. They are supported by laboratory experiments, particularly those showing enhancement of negative polarization with decreasing particle size down to the wavelength of light. According to the interference mechanism, pronounced negative branches of polarization, like those of C-class asteroids, may indicate a high degree of optical inhomogeneity of light-scattering surfaces at small scales. The mechanism also seems appropriate for treating the negative polarization and opposition effects of cometary dust comae, planetary rings, and the zodiacal light.

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.

MarcoPolo-R is a sample return mission to a primitive Near-Earth Asteroid (NEA) proposed in collaboration with NASA. It will rendezvous with a primitive NEA, scientifically characterize it at multiple scales, and return a unique sample to Earth unaltered by the atmospheric entry process or terrestrial weathering. MarcoPolo-R will return bulk samples (up to 2 kg) from an organic-rich binary asteroid to Earth for laboratory analyses, allowing us to: explore the origin of planetary materials and initial stages of habitable planet formation; identify and characterize the organics and volatiles in a primitive asteroid; understand the unique geomorphology, dynamics and evolution of a binary NEA. This project is based on the previous Marco Polo mission study, which was selected for the Assessment Phase of the first round of Cosmic Vision. Its scientific rationale was highly ranked by ESA committees and it was not selected only because the estimated cost was higher than the allotted amount for an M class mission. The cost of MarcoPolo-R will be reduced to within the ESA medium mission budget by collaboration with APL (John Hopkins University) and JPL in the NASA program for coordination with ESA’s Cosmic Vision Call. The baseline target is a binary asteroid (175706) 1996 FG3, which offers a very efficient operational and technical mission profile. A binary target also provides enhanced science return. The choice of this target will allow new investigations to be performed more easily than at a single object, and also enables investigations of the fascinating geology and geophysics of asteroids that are impossible at a single object. Several launch windows have been identified in the time-span 2020–2024. A number of other possible primitive single targets of high scientific interest have been identified covering a wide range of possible launch dates. The baseline mission scenario of MarcoPolo-R to 1996 FG3 is as follows: a single primary spacecraft provided by ESA, carrying the Earth Re-entry Capsule, sample acquisition and transfer system provided by NASA, will be launched by a Soyuz-Fregat rocket from Kourou into GTO and using two space segment stages. Two similar missions with two launch windows, in 2021 and 2022 and for both sample return in 2029 (with mission duration of 7 and 8 years), have been defined. Earlier or later launches, in 2020 or 2024, also offer good opportunities. All manoeuvres are carried out by a chemical propulsion system. MarcoPolo-R takes advantage of three industrial studies completed as part of the previous Marco Polo mission (see ESA/SRE (2009)3, Marco Polo Yellow Book) and of the expertise of the consortium led by Dr. A.F. Cheng (PI of the NASA NEAR Shoemaker mission) of the JHU-APL, including JPL, NASA ARC, NASA LaRC, and MIT.

Bayesian a priori and a posteriori probability densities are employed to determine asteroid orbital elements from optical astrometric observations. For near-earth asteroids and Jupiter Trojans, the two-body approximation can yield grossly erroneous uncertainty estimates because of the scattering effect of close planetary encounters or prolonged weak planetary perturbations. For main-belt asteroids, the two-body approximation works efficiently, from which it is inferred that, although the ephemeris must be computed from an integrated orbit, only approximate partial derivatives are needed to attain sufficient accuracy in predicting ephemeris uncertainties. The semimajor and semiminor axes of the 2D 1-sigma sky-plane uncertainty ellipse during the years 1993 to 2005 in the many-body and two-body linear approximations are shown.

We study the interrelation of the internal field of irregular particles to the far-field scattering characteristics by modifying the internal field of dipole groups. In this paper, we concentrate on the longitudinal component, i.e., the internal-field component parallel to the incident wave vector. We use the discrete-dipole approximation to determine the internal field and switch off the longitudinal component from the dipoles that have the highest energy density above a preset cutoff value. We conclude that only a relatively small number of core dipoles, about 5% of all dipoles, contribute to the negative linear polarization at intermediate scattering angles. These core dipole groups are located at the forward part of the particles. The number of core dipoles in the group becomes greater as particle asphericity increases. We find that the interference between the scattered waves from the core dipole groups, which was studied previously for spherical particles, is preserved to a large extent for nonspherical particles.

International audience; 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.

International audience; Results of the first polarimetric observations of Centaurs (5145) Pholus and (10199) Chariklo, and new observations of (2060) Chiron are presented together with the estimates of their absolute magnitudes. Observations were carried out at the 8 m ESO Very Large Telescope in 2007-2008. They revealed noticeable negative polarization in the phase-angle range 0.5-4.4° with a minimum varying from -1% to -2.1% in the R band. All three objects show diverse polarization phase-angle behaviour, each distinctly different from that of transneptunian objects. We found evidence of surface heterogeneity for Chariklo while Chiron and Pholus appear to have rather homogeneous surfaces. Polarization phase behaviours of Chiron and Pholus are significantly different from any other Solar System bodies studied so far. A shift of negative polarization minima toward small phase angles seems to be a characteristic feature of polarization properties of Centaurs. Presence of a small amount of water frost on a dark surface is considered as one of the possible ways to explain these properties.

The Mercury Imaging X-ray Spectrometer (MIXS) on the BepiColombo Mercury Planetary Orbiter (MPO), will measure fluorescent X-ray emission from the surface of Mercury in the energy range 0.5 – 7.5 keV, which is induced by incident solar X-rays and solar wind electrons and protons. These X-rays will reveal the elemental composition of the surface of Mercury and aid the determination of the planet's evolution.\ud \ud MIXS is a two component instrument. A collimated channel (MIXS-C) provides measurements on scales of 70-270 km, sufficient to separate the major Mercurian terrains. A second channel (MIXS-T) is the first imaging X-ray telescope for planetary remote sensing and will make measurements on spatial scales of less than 10 km for major elements during solar flares, sufficient to isolate surface landforms, such as craters and their internal structures. The spatial resolution achieved by MIXS-T is made possible by novel, low mass microchannel plate X-ray optics, in a Wolter type I optical geometry.\ud \ud MIXS measurements of surface elemental composition will help determine rock types, the evolution of the surface and ultimately a probable formation process for the planet. In this paper we present MIXS and its predicted performance at Mercury as well as discussing the role that MIXS measurements will play in answering the major questions about Mercury.

We report, for the f irst time to our knowledge, comparisons of light-scattering computations for large, randomly oriented, moderately absorbing spheroids based on the geometric-optics approximation and the exact T-matrix method. We show that in most cases the geometric-optics approximation is (much) more accurate for spheroids than for surface-equivalent spheres and can be used in phase function computations (but not in polarization computations) for nonspherical particles with size parameters as small as 60. Differences in the single-scattering albedo between geometric-optics and T-matrix results are surprisingly small, even for small size parameters.

We report progress in the design of the BepiColombo Mercury Imaging X-ray Spectrometer (MIXS). This instrument consists of two modules; a Wolter I soft X-ray telescope based on radially packed microchannel plate optics (MIXS-T) and a profiled collimator which uses a square pore square packed microchannel plate array to restrict its field of view (MIXS-C). Both instrument modules have identical focal planes (DEPFET macropixel array) providing an energy resolution of better than 200 eV FWHM throughout the mission. The primary science goal of MIXS is to perform X-ray fluorescence spectroscopy of the Hermean surface with unprecedented spatial and energy resolution. This allows discrimination between different regolith types, and by combining with data from other instruments, between competing models of crustal evolution and planetary formation. MIXS will also probe the complex coupling between the planet's surface, exosphere and magnetosphere by observing Particle Induced X-ray Emission (PIXE).

We report progress in the design, theoretical modeling and experimental characterisation of microchannel plate (MCP) X-ray optics for the BepiColombo Mercury Imaging X-ray Spectrometer (MIXS). We show that MCP optics technology allows the design of a highly capable imaging telescope with 1 m focal length, a 1° field of view and approximately 50 cm2 of on-axis effective area at 1 keV. Of a total instrument mass budget 7.3 kg, less than 2.3 kg is allocated to the optics assemblies, telescope tubes, support structures and the electron diverters (used to deflect electrons from the focal plane). The instrument science goals require an imaging resolution of 9 arcminutes, with a design goal of 2 arcminutes. Recent experimental data, taken from individual optic elements is presented to show that MCP quality is in good agreement with the error budgets assumed in theoretical calculations of performance.

The macroscopic shapes, rotational states, and scattering parameters of atmosphereless bodies can be deduced from photometric measurements of total brightnesses in different viewing/illumination geometries. The problem is solved with nonlinear optimization techniques; the use of positive definite quantities effectively removes the apparent ill-posedness of the problem. Since the parameters of scattering laws such as the Hapke model cannot be unambiguously determined from photometric data only, we propose a simple empirical scattering model for the purpose. Our methods can obtain convex hull-like shapes even for strongly nonconvex objects; a conception of the major concavities can also be formed.

[1] The morphology and composition of mineral-dust particles in two surface samples collected in the Sahara desert are investigated by electron microscope imaging, X-ray diffractography, and energy-dispersive spectroscopy. Most submicron particles in the samples are found to be flake-like and thin, and appear to be composed of either calcite or dolomite. The single-scattering properties of these flake-like particles are modeled using the discrete-dipole approximation for size parameters from 1 to 10. For simplicity, the particles are assumed to be composed of calcite, as the properties of dolomite are very similar. The birefringence of calcite is fully accounted for in the simulations, but to assess the importance of birefringence on scattering, two equivalent, isotropic cases analogous to internal and external mixing also are considered. The results show that both isotropic analogs scatter similarly, whereas birefringence affects the light scattering considerably. In particular, the asymmetry parameter is systematically smaller for birefringent than for isotropic flakes. The birefringence also weakens the negative-polarization branch (NPB) near the backscattering direction. Flakes are found to scatter light very differently from volume-equivalent spheroids, spheres, or roundish irregularly shaped particles: their asymmetry parameters tend to be much higher, and their backscattering enhancement and their NPBs are much weaker. The results demonstrate that the single-scattering properties of different mineral-dust types can be remarkably different. Whether the findings have a significant impact on the assessment of the radiative impact of atmospheric dust depends on the abundance of flake-like particles in the atmosphere, which is not known.

International audience; 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 25° 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.

We introduce techniques for characterizing convex shape models of asteroids with a small number of parameters, and apply these techniques to a set of 87 models from convex inversion. We present three different approaches for determining the overall dimensions of an asteroid. With the first technique, we measured the dimensions of the shapes in the direction of the rotation axis and in the equatorial plane and with the two other techniques, we derived the best-fit ellipsoid. We also computed the inertia matrix of the model shape to test how well it represents the target asteroid, i.e., to find indications of possible non-convex features or albedo variegation, which the convex shape model cannot reproduce. We used shape models for 87 asteroids to perform statistical analyses and to study dependencies between shape and rotation period, size, and taxonomic type. We detected correlations, but more data are required, especially on small and large objects, as well as slow and fast rotators, to reach a more thorough understanding about the dependencies. Results show, e.g., that convex models of asteroids are not that far from ellipsoids in root-mean-square sense, even though clearly irregular features are present. We also present new spin and shape solutions for Asteroids (31) Euphrosyne, (54) Alexandra, (79) Eurynome, (93) Minerva, (130) Elektra, (376) Geometria, (471) Papagena, and (776) Berbericia. We used a so-called semi-statistical approach to obtain a set of possible spin state solutions. The number of solutions depends on the abundancy of the data, which for Eurynome, Elektra, and Geometria was extensive enough for determining an unambiguous spin and shape solution. Data of Euphrosyne, on the other hand, provided a wide distribution of possible spin solutions, whereas the rest of the targets have two or three possible solutions.

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 ( n log n ) , 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.

International audience

We consider the scattering of light by single wood fibers both theoretically and experimentally. We describe the size and the shape distributions and the internal structure and chemical composition of the wood fibers. We have modeled the random shape of the hollow, cylindrical wood fiber by using multivariate lognormal statistics. We have computed wood-fiber absorption and scattering cross sections, asymmetry parameters, and scattering phase matrices in the ray-optics approximation. Finally, we have provided experimental results from angular scattering measurements for wood fibers and present what we believe is the first comparison between these measurements and ray-optics computations for Gaussian random wood-fiber models. In spite of the complicated internal structure of the wood fiber, our model together with the ray-optics treatment explains the scattering measurements surprisingly well.

The single particle phase function and the degree of linear polarization for small crystals randomly oriented in space have been computed using the geometric ray tracing theory and assuming that the crystals are optically homogeneous and isotropic. Results for a monoclinic augite crystal and for tetrahedral, octahedral and cubic ammonia crystals are presented and shortly commented on. The newly discovered opposition spikes of some bright atmosphereless satellites could be explained by a small amount of retroreflecting crystals in the regolith. Further, the enhanced backward scattering of red sunlight by particles in Jupiter's atmosphere reduced from measurements on the Pioneer 10 and 11 missions could be related to the existence of orthorhombic ammonia crystals in the atmosphere.

We investigate the surface characteristics of the large dwarf planet (136199) Eris. With the FORS1 instrument of the ESO VLT, we have obtained Bessell broadband R linear polarimetry and broadband V and I photometry. We have modelled the observations in terms of the coherent-backscattering mechanism to constrain the surface properties of the object. Polarimetric observations of Eris show a small negative linear polarization without opposition surge in the phase angle range of 0.15-0.5 degrees. The photometric data allow us to suppose a brightness opposition peak at phase angles below 0.2-0.3 degrees. The data obtained suggest possible similarity to the polarimetric and photometric phase curves of Pluto. The measured absolute magnitude and broadband colors of Eris are H_V=-1.15, V-R=0.41, and V-I=0.75., Accepted by A&A

We show that the new ephemeris-space multiple-address-comparison (eMAC) method solves asteroid linking problems despite large parallaxes by applying the method to astrometric asteroid observation sets obtained nearly simultaneously with the Spitzer space telescope, the Canada–France–Hawaii Telescope (CFHT), and European Southern Observatory's Very Large Telescope (VLT). For main-belt asteroids, the parallax between Spitzer and the Earth-based telescopes is approximately one degree which is large as compared to a typical parallax for solely Earth-based telescopes in the arcseconds regime. In the eMAC method, we reduce the initially huge amount of possible linkages between observation sets by comparing samples of ephemerides that have been computed separately for all sets at, say, three common dates. If the non-zero ephemeris probability densities overlap at all common dates, we try to find an orbit solution for these so-called trial linkages. If there exists an orbit which reproduces all the astrometric observations assuming predefined observational errors, we call it a linkage. Known asteroids are independently identified among Spitzer, CFHT, and VLT astrometry, and comparing the identified observations to the linkages found shows that the method found all known correct linkages present in the data. In addition, we also found five previously unpublished linkages between Spitzer astrometry and Earth-based astrometry. Based on our simulations, we found virtually all Spitzer-related linkages between two single-night observation sets, and more than 99.4% of linkages between two single-night observation sets obtained by Earth-based observatories. Virtually all correct linkages consisting of at least three single-night sets were also detected. The results show that large-parallax discovery observations made from a spacecraft can be linked to Earth-based follow-up observations to ensure that the objects are not lost. Furthermore, we compute the heliocentric and Spitzer-centric distances as well as the corresponding solar phase angles at the dates of Spitzer observations. Based on comparisons to simulated geocentric observations, we also show that, for typical nearly-simultaneous observations, the parallax reduces the distance uncertainties by several orders of magnitude.

We present measurements of the complete scattering matrix as a function of the scattering angle of a sample of Sahara sand particles collected from a dune in Libya. The measurements were performed at a wavelength of 632.8 nm in the scattering angle range from 4° to 174°. To facilitate the use of the experimental data for multiple-scattering calculations with polarization included, we present a synthetic scattering matrix based on the measurements and defined in the full angle range from 0° to 180°. The Libyan sample consists of large particles distributed over a narrow size distribution which makes it an interesting test case for the Ray Optics Approximation (ROA) that provides accurate results for particles with curvature radii much larger than the wavelength. Numerical simulations using the ROA are compared with the experimental data. Moreover, the traditional ROA was modified with ad hoc simple schemes of Lambertian surface elements and internal screens to study the effects of small-scale surface roughness and internal structures, respectively. Model particle shapes used in the simulations are based on a shape analysis of our sample. The traditional ray optics approximation does not reproduce the experimental data although a significant improvement is obtained if unrealistically spiky particle shapes are used. When the Lambertian schemes are applied the agreement with the experimental data improves. Still, to get a good agreement with the experimental data we need unrealistic spiky particles together with the inclusion of external Lambertian reflections. This seems to indicate that a more refined treatment is needed to reproduce the scattering effects of the small-scale surface roughness of the Libyan sand particles.

According to current plans of the European space agency, Gaia will be launched in 2011. By performing a systematic survey of the whole sky down to magnitude V = 20, this mission will provide a fundamental contribution in practically all branches of modern Astrophysics. Gaia will be able to survey with repeated observations spanning over 5 years several 100,000 s asteroids. It will directly measure sizes of about 1,000 objects, obtain the masses of about 100 of them, derive spin properties and overall shapes of more than 10,000 objects, yield much improved orbits and taxonomic classification for most of the observed sources. The final harvest will very likely include new discoveries of objects orbiting at heliocentric distances less than 1 AU. At the end of the mission, we will know average densities of about 100 objects belonging to all the major taxonomic classes, have a much more precise knowledge of the inventory and size and spin distributions of the population, of the distribution of taxonomic classes as a function of heliocentric distance, and of the dynamical and physical properties of dynamical families.

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Context. The scattering of light by an asteroid’s surface depends on the properties of its particles, volume density, and roughness. It is described by the reflection coefficient which, upon integration over the illuminated and observed part of the surface, yields the disk-integrated photometric brightness of the asteroid. The Lommel-Seeliger reflection coefficient is applicable to dark, low-albedo C-class asteroids, with prospects for moderate-albedo S-class and M-class asteroids.Aims. We calculate the disk-integrated brightness for an ellipsoidal asteroid with a Lommel-Seeliger reflection coefficient (LS ellipsoid). Furthermore, we calculate the photocenter for the LS ellipsoid, that is, the distance of the center of light from the barycenter. Methods. Because of their analytical nature, the closed-form expressions can be readily utilized in numerical simulations.Results. We show lightcurves and photocenter variations for realistic examples of ellipsoidal shapes for a number of pole orientations. The results highlight the reciprocity principle of the radiative-transfer theory and suggest a nontrivial dependence of the photocenter on the pole orientation and viewing geometry.Conclusions. Finally, we outline a number of applications and future prospects.

Aims. Two C-type main-belt asteroids (171) Ophelia and (360) Carlova are studied for their spin parameters and shapes in the present paper. Although it was suspected that Ophelia was a binary system owing to the eclipse features in the light curve obtained in 1977, no direct evidence has been obtained to confirm the binarity. To verify the previous findings, the spin parameters and shape of Ophelia are derived by analyzing the photometric data. To understand the dispersion in the previous determination of Carlova's spin parameters, new observational data and existing photometric data are reanalyzed to find a homogenous solution for its spin parameters and shape. Methods. The spin parameters and shapes of two asteroids were determined from photometric data using the convex inversion technique. The simplified virtual-observation Markov chain Monte Carlo method was applied to estimate the uncertainties of the spin parameters and to understand the divergence of derived shapes. Results. A pair of possible poles for Ophelia are derived, the spin periods corresponding to the two poles are nearly the same. The convex shape of Ophelia shows binary characteristics. For Carlova, a unique pole solution and its convex shape are ascertained together with the occultation observations. The convex shape of Carlova shows that it is a rough ellipsoid.

International audience

Methodology and applications of the Ray Optics Method (ROM) are shown for polarized light scattering by large nonspherical particles. Particle geometries under consideration are hexagonal columns, various types of dendrites, fractal polycrystals, and Gaussian random spheres. The two latter particle shapes serve as examples for highly irregularly shaped scatterers as they can be found in atmospheric ice clouds and interplanetary dust particles. After briefly discussing the applicability of ROM in terms of size parameter and absorption strength, the effects of particle shape and orientation on the phase matrix elements P11, P22, P33, P44, P12, and P34 are discussed. In general it is shown that the polarization information from single scattering can be used to distinguish between hexagonal columns, plates, and irregular particles as well as between 3D randomly and horizontally oriented particles. The scattering characteristics of Gaussian random particles are illustrated through ray-tracing computations using the refractive index of ice. Similarities to scattering by the fractal crystal particle are found in the case of highly irregular, fractal Gaussian particles with power law correlation functions.

The light scattered by a small particle near a planar interface may be expressed to high accuracy as the superposition of the contributions of four weighted rays. We provide experimental evidence that demonstrates the model may be used to predict polarization of scattered light from larger irregular particles near planar surfaces. This system is of interest because the two reciprocal-ray components, whose interference contributes to the narrow, asymmetric polarization opposition effect, do not decrease significantly relative to the other two ray components when the separation distance between the particle and the planar interface increases. As a result, we demonstrate that for this particular scattering system the wide, parabolically shaped negative polarization branch also is the result of the interference of these reciprocal rays.

Polarization is a powerful remote-sensing method to investigate solar system bodies. It is an especially sensitive diagnostic tool to reveal physical properties of the bodies whose observational characteristics are governed by small scatterers (dust, regolith surfaces). For these objects, at small phase angles, a negative polarization is observed, i.e., the electric vector E oscillates predominantly in the scattering plane, contrary to what is typical for rather smooth homogeneous surfaces. The behavior of negative polarization with phase angle depends on the size, composition and packing of the scatterers. These characteristics can be unveiled by modelling the light scattering by the dust or regolith in terms of the coherent backscattering mechanism. We have investigated the surface properties of TNOs and Centaurs by means of polarimetric observations with FORS1 of the ESO VLT. TNOs Ixion and Quaoar, and Centaur Chiron show a negative polarization surge. The Centaur Chiron has the deepest polarization minimum (-1.5 - 1.4%). The two TNOs show differing polarization curves: for Ixion, the negative polarization increases rapidly with phase; for Quaoar, the polarization is relatively small (~ -0.6%), and nearly constant at the observed phase angles. For all three objects, modelling results suggest that the surface contains an areal mixture of at least two components with different single-scatterer albedos and photon mean-free paths., 11 pages, 7 postscript figures, accepted by A&A; astro-ph abstract has been replaced with a more complete one

Near-Earth objects Radiometric Observatory (NERO) is one of the six studies for possible missions dedicated to near-Earth objects, that were funded by the European Space Agency (ESA) in 2002–2003. It is a further development of some previous studies already submitted to ESA (Sysiphos, Spaceguard-1). The general concept is that a small satellite equipped with both a detector for visible wavelengths and an array for thermal IR measurements around 10 μm would be an ideal platform to obtain simultaneously two of the major objectives of current NEO science, namely the physical characterization of the objects and the discovery of those NEOs that are difficult to detect from the ground because their orbits are entirely or partly inside the Earth’s orbit. The NERO study includes a comprehensive analysis of the advantages and drawbacks of different orbital options for the satellite (including L2 of Earth and L2 of Venus) and a preliminary simulation of the effectiveness of orbit determination based on NERO observations of newly detected objects. The main results of this study, including also a preliminary sketch of the payload design (optics, detectors, cooling system, etc.) are briefly summarized.

The Advanced Moon micro-Imager Experiment (AMIE), on-board SMART-1, the first European mission to the Moon, is an imaging system with scientific, technical and public outreach objectives. The science objectives are to image the lunar South Pole, permanent shadow areas (ice deposit), eternal light (crater rims), ancient lunar non-mare volcanism, local spectrophotometry and physical state of the lunar surface, and to map high latitudes regions (south) mainly at far side (South Pole Aitken basin). The technical objectives are to perform a Laserlink experiment (detection of laser beam emitted by ESA/Tenerife ground station), flight demonstration of new technologies and on-board autonomy navigation. The public outreach and educational objectives are to promote planetary exploration and space. We present here the first results obtained during the cruise phase. � 2005 Published by Elsevier Ltd on behalf of COSPAR.