Shape of small solar system bodies

The morphometric parameters are examined for the shape of fragments of ordinary chondrites, iron meteorites, S- and C-class stony asteroids, metallic asteroids, and icy small bodies of the Solar System. All small Solar System bodies are shown to have, depending on their composition and, hence, physical and mechanical properties, a specific shape that is unique to a given composition. C-class asteroids, the strength of which is almost three times less than that of S asteroids, differ from the latter in their less elongated shape. No systematic change is observed in the morphometric parameters (increased roundness or sphericity) of small bodies of differing compositions depending on their mass, which suggests that the hypothesis of creep in small Solar System bodies is unlikely to be true. The absence of creep confirms that, regardless of their composition, all small Solar System bodies are solid elastic bodies having an ultimate strength (tensile strength and compressive strength) and a yield strength.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

Ultraviolet observations of small bodies in the solar system by OAO-2

Broadband filter photometry from 2100 to 4300 Å has been obtained by OAO-2 for the following objects: The Galilean satellites; Titan; the rings of Saturn; and three asteroids. Agreement with independent ground-based photometry in the region of overlap is good. The previously known decrease in reflectivity from visual to ground-based ultraviolet wavelengths continues to 2590 Å for all these objects. Europa's reflectivity continues to decline towards 2110 Å, and the rings' reflectivity levels off from 2590 to 2110 Å. Other targets were too faint at 2110 Å to be measured reliably by OAO-2.The low ultraviolet albedo of Titan has important implications for that planet's atmospheric structure (Caldwell, Larach, and Danielson, 1973; Danielson, Caldwell, and Larach, 1973; Caldwell, 1974b). The ultraviolet reflectivity of Saturn's rings is suggestive of a two-component system, one being pure H₂O particles. The ultraviolet albedos of the Galilean satellites are consistent with existing upper limits for atmospheric abundances, but require either that former estimates of the fractional coverage of H₂O frost are too high, an unlikely circumstance, or that the frost has been darkened by some external agent in the space environment.     

Modelling the outcomes of high-velocity impacts between small solar system bodies

We present a self-consistent numerical algorithm aimed at predicting the outcomes of high-velocity impacts between asteroids (or other small bodies of the solar system), based on a set of model input parameters which can be estimated from the available experimental evidence, and including the possible gravitational reaccumulation of ejected fragments whose velocity is less than a suitably defined escape velocity. All the fragment mass distributions are modelled by truncated power laws, and a possible correlation between fragment ejection velocity and mass is taken into account in different ways, including a probabilistic one. We analyze in particular the effectiveness of the gravitational reaccumulation process in terms of different choices of the collisional parameters and the assumed relationship between fragment speed and mass. Both the transition size beyond which solid targets are likely to reaccumulate a large fraction of the fragment mass and the collision energy needed to disperse most of the fragments are sensitive functions of the assumed fragment velocity versus mass relationship. We also give some examples of how our algorithm can be applied to study the origin and collisional history of small solar system bodies, including the asteroid 951 Gaspra (recently imaged by the Galileo probe) and the asteroid families.     

Very small bodies in the solar system: The Earth's atmosphere as detector

Particles of mass less than about 1 gm are a minor fraction of the total matter impinging on the Earth averaged over millennia time scales. However, these particles dominate during a single particular year and produce the most obvious evidence of incoming extra-terrestrial matter in the form of ablation trails in the atmosphere which are visible at night as meteors.Observations of meteors give astronomical information on the composition, structure, and cometary associations of the particles. The composition is deduced from optical spectra of meteors, whilst telescopic studies of the trails during formation give information on the physical structure of the particles. Any cometary associations are deduced from measurement of meteor orbits determined photographically, using television, or by radar.Meteors occur in the atmosphere at heights from about 70 to 120 km. Optical observations are restricted to night-time and usually under conditions of low moonlight. A typical television based detector can record +8^M meteors with a sporadic rate of 15–20 per hour and velocities accurate to about 3%. The luminosity of the trail is strongly dependent on the velocity of the meteoroid (to about the third power).Radar observations of meteors are unrestricted by weather or time of day, and can readily detect meteors at least two orders of magnitude smaller in mass than those detectable optically. Again the observations are heavily biased toward the higher velocities as the electron line density varies approximately asV ^3.5. However, the higher the velocity of the meteoroid the greater the height of the meteor trail, and the reduced probability of radar detection due to rapid diffusion of the trail. Thus radar observations tend to select meteors in the intermediate velocity range 30–40 km s^–1.     

Main Belt Comets: A new class of small bodies in the solar system

Comets and asteroids have traditionally been considered two distinct separate populations of small bodies in the solar system, according to their different dynamical, observational, and compositional characteristics.The discovery of a new class of objects, the so-called, Main Belt Comets (MBCs), exhibiting a clear cometary activity but having at the same time orbits indistinguishable from the ones of asteroids in the Main Belt provided further evidence that asteroids and comets, rather than two distinct separate classes, represent the end-members of a continuum of small bodies, with compositions from the very rocky to the very icy.Their study is nowadays deepening our knowledge of the formation mechanisms of the solar system and of the distribution of volatile materials in the protoplanetary disk.In this paper the present knowledge of MBCs is reviewed in terms of physical properties derived from observations, dynamical studies about the origin and formation, thermal modeling of the nuclei, investigations about the activation mechanisms, and the eventual contribution to the presence of water on our planet. An overview of the large-scale surveys dedicated to their discovery and of the detection techniques used so far is also given. Moreover, open question and indications for future observations and modeling are outlined.     

Observations of distant solar system bodies

Multicolour VRI photometry and astrometry of one Centaur and seven Edgeworth-Kuiper objects were obtained. One object, 1994 JQ₁ may be as red as 5145 Pholus, the reddest minor planet previously known. The Centaur 1995 DW₂ has more moderate colour indices, similar to main-belt asteroids. Seven R-magnitudes were obtained for 1994 JS, 1995 FB₂₁, and 1995 GY₇. No light variation above the expected noise is evident, apart from a few outliers. A total of 47 astrometric positions were obtained for the eight objects. The four nights of observations with the ESO New Technology Telescope covered 0.52 square degrees. Two previosuly unknown object, 1995 FB₂₁ and 1995 GY₇, were discovered. We estimate the density of Edgeworth-Kuiper objects brighter than R = 24 to 5.3 per square degree of sky near the ecliptic.     

Gravitational potential of solid bodies in the solar system

The gravitational potential of a solid body is expanded without approximation in any moving reference frame, in terms of harmonic coefficients relative to fixed axis in the body.     

THERMAP: a mid-infrared spectro-imager for space missions to small bodies in the inner solar system

We present THERMAP, a mid-infrared spectro-imager for space missions to small bodies in the inner solar system, developed in the framework of the MarcoPolo-R asteroid sample return mission. THERMAP is very well suited to characterize the surface thermal environment of a NEO and to map its surface composition. The instrument has two channels, one for imaging and one for spectroscopy: it is both a thermal camera with full 2D imaging capabilities and a slit spectrometer. THERMAP takes advantage of the recent technological developments of uncooled microbolometer arrays, sensitive in the mid-infrared spectral range. THERMAP can acquire thermal images (8–18 μm) of the surface and perform absolute temperature measurements with a precision better than 3.5 K above 200 K. THERMAP can acquire mid-infrared spectra (8–16 μm) of the surface with a spectral resolution Δλ of 0.3 μm. For surface temperatures above 350 K, spectra have a signal-to-noise ratio >60 in the spectral range 9–13 μm where most emission features occur.     

Astrometric baseline observations of solar system bodies

The use of ground-based and space baseline observations of Solar System bodies is considered. Baseline observations allow one to determine the distance to observed objects and (in some cases) the parameters of their orbital motion. Certain results of baseline observations of near-Earth asteroids and the results of model analysis of spacecraft observations are presented.     

Method of determining the orbits of the small bodies in the solar system based on an exhaustive search of orbital planes

A universal method of determining the orbits of newly discovered small bodies in the Solar System using their positional observations has been developed. The proposed method suggests determining geocentric distances of a small body by means of an exhaustive search for heliocentric orbital planes and subsequent determination of the distance between the observer and the points at which the chosen plane intersects with the vectors pointing to the object. Further, the remaining orbital elements are determined using the classical Gauss method after eliminating those heliocentric distances that have a fortiori low probabilities. The obtained sets of elements are used to determine the rms between the observed and calculated positions. The sets of elements with the least rms are considered to be most probable for newly discovered small bodies. Afterwards, these elements are improved using the differential method.     

Positional observations of small solar system bodies with the SBG telescope at the Astronomical Observatory of the Ural Federal University

The telescope SBG (D = 0.42 m, F = 0.76 m) at the Kourovka Astronomical Observatory of the Ural Federal University has undergone an upgrade in 2005–2006. A CCD camera (Apogee Alta U32) and a new drive system were installed, and a new system for telescope and observation control was implemented. This upgrade required verifying the astrometric quality of the telescope. The data processing approaches tested when searching for the optimum CCD image processing technique combined TYCHO2 and UCAC2 catalogues with various reduction models and methods for choosing reference stars. Lorentzian and Moffat profiles were used in the measurement of pixel coordinates. It was demonstrated that the accuracy of SBG observations of main-belt asteroids with precisely determined orbits depends on their brightness and varies from 0.06” (11.5 ^m ) to 0.4” (18.5 ^m ). Regular SBG observations of comets and asteroids (mostly near-Earth and potentially hazardous ones) have been performed since 2007. Coordinates of 8515 positions of 720 asteroids and more than 1000 positions of 40 comets were obtained. The RMS deviations of observed coordinates from their calculated values are typically smaller than 1”: the average deviations for asteroids are 0.33” (in right ascension) and 0.34” (in declination); the corresponding values for comets are 0.37” (in α) and 0.38” (in δ). The results of observations are sent to the Minor Planet Center and are used to determine orbits more accurately and solve other fundamental and applied problems.     

Radiation forces on small particles in the solar system

We present a new and more accurate expression for the radiation pressure and Poynting-Robertson drag forces; it is more complete than previous ones, which considered only perfectly absorbing particles or artificial scattering laws. Using a simple heuristic derivation, the equation of motion for a particle of mass m and geometrical cross section A, moving with velocity v through a radiation field of energy flux density S, is found to be (to terms of order $\text{v}\text{c}$)

$\text{m}\text{v}\text{?}\text{= (}\text{SA}\text{c}\text{)Q}{}_{\mathrm{<mtext>pr</mtext>}}\text{[(1 ?}\text{r}\text{?}\text{c}\text{)}\text{S}\text{?}\text{?}\text{v}\text{c}\text{]}$

, where ? is a unit vector in the direction of the incident radiation, $\text{r}\text{?}$ is the particle's radial velocity, and c is the speed of light; the radiation pressure efficiency factor Q_pr ≡ Q_abs + Q_sca(1 ? 〈cos α〉), where Q_abs and Q_sca are the efficiency factors for absorption and scattering, and 〈cos α〉 accounts for the asymmetry of the scattered radiation. This result is confirmed by a new formal derivation applying special relativistic transformations for the incoming and outgoing energy and momentum as seen in the particle and solar frames of reference. Q_pr is evaluated from Mie theory for small spherical particles with measured optical properties, irradiated by the actual solar spectrum. Of the eight materials studied, only for iron, magnetite , and graphite grains does the radiation pressure force exceed gravity and then just for sizes around 0.1 μm; very small particles are not easily blown out of the solar system nor are they rapidly dragged into the Sun by the Poynting-Robertson effect. The solar wind counterpart of the Poynting-Robertson drag may be effective, however, for these particles. The orbital consequences of these radiation forces-including ejection from the solar system by relatively small radiation pressures-and of the Poynting-Robertson drag are considered both for heliocentric and planetocentric orbiting particles. We discuss the coupling between the dynamics of particles and their sizes (which diminish due to sputtering and sublimation). A qualitative derivation is given for the differential Doppler effect, which occurs because the light received by an orbiting particle is slightly red-shifted by the solar rotation velocity when coming from the eastern hemisphere of the Sun but blue-shifted when from the western hemisphere; the ratio of this force to the Poynting-Robertson force is $\text{(}\text{R}{}_{\mathrm{\odot }}\text{r}\text{)}{}^2\text{[(}\text{w}{}_{\mathrm{\odot }}\text{n}\text{) ? 1]}$, where R_⊙ and w_⊙ are the solar radius and spin rate, and n is the particle's mean motion. The Yarkovsky effect, caused by the asymmetry in the reradiated thermal emission of a rotating body, is also developed relying on new physical arguments. Throughout the paper, representative calculations use the physical and orbital properties of interplanetary dust, as known from various recent measurements.     

Interpretation of the light curves of some non-atmospheric bodies in the solar system

A model to explain the phase curves of some non-atmospheric bodies in the solar system has been developed. It is found that, for instance, phase curves of the Moon, the Galilean satellites of Jupiter, some asteroids and Saturn's rings are in agreement with the given model.     

On the sputter alteration of regoliths of outer solar system bodies

This paper discussed several processes that are expected to occur when the porous regoliths on bodies without atmospheres in the outer Solar System are subjected to energetic ion bombardment. The conclusions reached in many of the papers involving sputtering published in the planetary literature are qualitatively or quantitatively incorrect because effects of soil porosity have been neglected. It is shown theoretically and experimentally that porosity reduces the effective sputtering yield of a soil by more than an order of magnitude. Between 90 and 97% of the sputtered atoms are trapped within the regolith, where they are fractionated by differential desorption. Experiments indicate that more volatile species have higher desorption probabilities. This process is the most important way in which alteration of chemical and optical properties occurs when a regolith is sputtered. When a basic silicate soil is irridiated these effects lead to sputter-deposited films enriched in metallic iron, while O, Na, and K are preferentially lost. The Na and K are present in the atmosphere above the sputtered silicate in quantities much greater than their abundances in the regolith. Icy regoliths of SO₂ should be enriched in elemental S and/or S₂O. This prediction is supported by the probable identification of S₂O and polysulfur oxide bands in the IR spectra of H-sputtered SO₂ reported by M. Moore (1984, Icarus 59, 114–128). When porous mixtures of water, ammonia, and methane frosts are sputtered, the loss of H and surface reactions of C, N, and O in the deposits should produce complex hydrocarbons and carbohydrates, some of which may be quite dark. Such reactions may have played a role in the formation of the matrix material of carbonaceous chondrites prior to agglomeration.     

Constraining the orbits of small solar system bodies using spectroscopic Doppler shift measurements – a preliminary study

In this short paper we examine whether the measurement of Doppler shifts in the solar light reflected off an asteroid surface may improve the accuracy of the determined orbit. Our results suggest it will be worthwhile to use high‐resolution spectrographs, of the exoplanet‐hunting type, to measure those Doppler shifts. Spectroscopic Doppler shifts might improve the accuracy of Earth‐impact predictions, help to recover “lost” near‐Earth objects, and may also significantly enhance the knowledge about dynamics of the Kuiper belt. Future high‐resolution spectrographs on the VLT and the E‐ELT may thus have an important role in studies of Solar‐System dynamics and kinematics. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coherent backscattering and opposition effects observed in some atmosphereless bodies of the solar system

The results of photometric and polarimetric observations carried out for some bright atmosphere-less bodies of the Solar system near the zero phase angle reveal the simultaneous existence of two spectacular optical phenomena, the so-called brightness and polarization opposition effects. In a number of studies, these phenomena were explained by the influence of coherent backscattering. However, in general, the interference concept of coherent backscattering can be used only in the case where the particles are in the far-field zones of each other, i.e., when the scattering medium is rather rarefied. Because of this, it is important to prove rigorously and to demonstrate that the coherent backscattering effect may also exist in densely packed scattering media like regolith surface layers of celestial bodies. From the results of the computer modeling performed with the use of numerically exact solutions of the macroscopic Maxwell equations for discrete random media with different packing densities of particles, we studied the origin and evolution of all the opposition phenomena predicted by the coherent backscattering theory for low-packing-density media. It has been shown that the predictions of this theory remain valid for rather high packing densities of particles that are typical, in particular, of regolith surfaces of the Solar system bodies. The results allow us to conclude that both opposition effects observed simultaneously in some high-albedo atmosphereless bodies of the Solar system are caused precisely by coherent backscattering of solar light in the regolith layers composed of microscopic particles.