Selecting candidate V-type asteroids from the analysis of the Sloan Digital Sky Survey colors

We present a systematic method to identify possible basaltic (V-type) asteroids using the Moving Objects Catalog (MOC) of the SDSS. The method is based on the Principal Components Analysis of the MOC colors combined with some refined criteria of segregation of the taxonomic classes. We found several V-type candidates outside the Vesta family, most of them in the inner asteroid belt. We also identified a few candidates in the middle/outer belt. Notwithstanding, their basaltic nature still needs to be conformed by spectroscopy, and these candidates are potential targets for observation using large telescopes.     

New V-type asteroids in near-Earth space

We present new visible and near-infrared spectroscopic observations of 4 small, previously unclassified, near-Earth objects (NEOs). They appear to have basaltic surfaces, and hence they can be classified as V-types. Their visible spectra exhibit a closer spectral match with the Main-Belt (MB) Asteroid (4) Vesta than the other, presently known, V-type NEOs and MB asteroids. The near-infrared spectrum of Asteroid 2003 FT3 shows—for the first time among NEOs—a peculiar shape of the 1 μm band, maybe suggesting an overabundance of olivine compared to the other V-types and to (4) Vesta. The presence of V-type objects among NEOs may be a consequence of the delivery processes connecting the inner MB to the near-Earth region. On the basis of the orbital parameters of the NEOs presented here, both the resonances (3:1 and ν₆), usually considered as the most relevant gateways for the production of near-Earth asteroids, should have been active to transfer the bodies from the MB region.     

Polarimetry of main belt asteroids: Wavelength dependence

New UBVRI polarimetric observations of ten asteroids, including space mission targets 1 Ceres and 21 Lutetia, are presented. These observations were obtained with the 1.25-m telescope of the Crimean Astrophysical Observatory and have been used to study the wavelength dependence of polarization for a sample of asteroids belonging to the M and low albedo classes. A more general analysis including also a larger data set of UBVRI polarimetric observations available in the literature for more than 50 main belt asteroids belonging to different taxonomic classes shows that the variation of the polarization degree Pr as a function of wavelength is generally well described by a linear trend. It typically does not exceed 0.2% in the studied spectral range 0.37-0.83 microns and tends to increase for increasing phase angle. Asteroids belonging to the S and M classes are found to exhibit a deeper negative branch and smaller positive polarization for increasing wavelength (negative sign of the slope of ΔPr/Δλ). Since the objects belonging to these classes are known to exhibit reddish reflectance spectra, the observed wavelength behavior of negative polarization contradicts the well-known inverse correlation of Pmin and albedo. Low albedo asteroids show larger dispersion of spectral slopes, but the overall trend is characterized by a shallower negative branch and a larger positive polarization for increasing wavelength (positive sign of the slope of ΔPr/Δλ). A few exceptions from this general trend are discussed. The observed variety in the wavelength dependence of asteroid polarization seems to be mainly attributed to surface composition.     

Physical properties and orbital stability of the Trojan asteroids

All the Trojan asteroids orbit about the Sun at roughly the same heliocentric distance as Jupiter. Differences in the observed visible reflection spectra range from neutral to red, with no ultra-red objects found so far. Given that the Trojan asteroids are collisionally evolved, a certain degree of variability is expected. Additionally, cosmic radiation and sublimation are important factors in modifying icy surfaces even at those large heliocentric distances. We search for correlations between physical and dynamical properties, we explore relationships between the following four quantities; the normalised visible reflectivity indexes (S^′), the absolute magnitudes, the observed albedos and the orbital stability of the Trojans. We present here visible spectroscopic spectra of 25 Trojans. This new data increase by a factor of about 5 the size of the sample of visible spectra of Jupiter Trojans on unstable orbits. The observations were carried out at the ESO-NTT telescope (3.5 m) at La Silla, Chile, the ING-WHT (4.2 m) and NOT (2.5 m) at Roque de los Muchachos observatory, La Palma, Spain. We have found a correlation between the size distribution and the orbital stability. The absolute-magnitude distribution of the Trojans in stable orbits is found to be bimodal, while the one of the unstable orbits is unimodal, with a slope similar to that of the small stable Trojans. This supports the hypothesis that the unstable objects are mainly byproducts of physical collisions. The values of S^′ of both the stable and the unstable Trojans are uniformly distributed over a wide range, from 0%/1000 Å to about 15%/1000 Å. The values for the stable Trojans tend to be slightly redder than the unstable ones, but no significant statistical difference is found.     

Nature of the small main belt Asteroid 3169 Ostro

We present a set of rotational lightcurve measurements of the small main belt Asteroid 3169 Ostro. Our observations reveal an unambiguous, double-peaked rotational lightcurve with a peak-to-peak variation up to 1.2±0.05 mag and a synodic period of 6.509±0.001 h. From the large flux variation and the overall shape of the lightcurves, we suggest that 3169 Ostro could be a tightly bound binary or a contact binary, similar to the Trojan Asteroid 624 Hektor. A shape model of this system is proposed on the assumption that 3169 Ostro is a Roche binary described by a pair of homogeneous elongated bodies, with a size ratio of 0.87, in hydrostatic equilibrium and in circular synchronous motion around each other. The direction of the spin axis is determined modulo 180° by its J2000 ecliptic coordinates λ₀=50±10°, β₀=±54±5°. The binary interpretation and the pole solution adequately fit the earlier photometric observations made in 1986 and 1988. However, additional supporting lightcurves are highly desirable especially in the next mutual events occurrence of 2008 and 2009 in order to remove the pole ambiguity and to confirm unambiguously the binary nature of 3169 Ostro.     

Dynamics of the Hungaria asteroids

To try to understand the dynamical and collisional evolution of the Hungaria asteroids we have built a large catalog of accurate synthetic proper elements. Using the distribution of the Hungaria, in the spaces of proper elements and of proper frequencies, we can study the dynamical boundaries and the internal structure of the Hungaria region, both within a purely gravitational model and also showing the signature of the non-gravitational effects. We find a complex interaction between secular resonances, mean motion resonances, chaotic behavior and Yarkovsky-driven drift in semimajor axis. We also find a rare occurrence of large scale instabilities, leading to escape from the region. This allows to explain the complex shape of a grouping which we suggest is a collisional family, including most Hungaria but by no means all; we provide an explicit list of non-members of the family. There are finer structures, of which the most significant is a set of very close asteroid couples, with extremely similar proper elements. Some of these could have had, in a comparatively recent past, very close approaches with low relative velocity. We argue that the Hungaria, because of the favorable observing conditions, may soon become the best known sub-group of the asteroid population.     

Identification of families among highly inclined asteroids

A dataset of 3652 high-inclination numbered asteroids was analyzed to search for dynamical families. A fully automated multivariate data analysis technique was applied to identify the groupings. Thirteen dynamical families and twenty-two clumps were found. When taxonomic information is available, the families show cosmochemical consistency and support an interpretation based on a common origin from a single parent body. Four families and three clumps found in this work show a size distribution which is compatible with a formation due to a cratering event on the largest member of the family, and also three families have B- or related taxonomic types members, which represents a 14% of the B-types classified by Bus and Binzel [2002. Icarus 158, 146-177].     

Photometry and spin rate distribution of small-sized main belt asteroids

Photometry results of 32 asteroids are reported from only seven observing nights on only seven fields, consisting of 34.11 cumulative hours of observations. The data were obtained with a wide-field CCD (^40.5′×^27.3′) mounted on a small, 46-cm telescope at the Wise Observatory. The fields are located within ±1.5° from the ecliptic plane and include a region within the main asteroid belt. The observed fields show a projected density of ∼23.7 asteroids per square degree to the limit of our observations. 13 of the lightcurves were successfully analyzed to derive the asteroids' spin periods. These range from 2.37 up to 20.2 h with a median value of 3.7 h. 11 of these objects have diameters in order of two kilometers and less, a size range that until recently has not been photometrically studied. The results obtained during this short observing run emphasize the efficiency of wide-field CCD photometry of asteroids, which is necessary to improve spin statistics and understand spin evolution processes. We added our derived spin periods to data from the literature and compared the spin rate distributions of small main belt asteroids (5>D>0.15 km) with that of bigger asteroids and of similar-sized NEAs. We found that the small MBAs do not show the clear Maxwellian-shaped distribution as large asteroids do; rather they have a spin rate distribution similar to that of NEAs. This implies that non-Maxwellian spin rate distribution is controlled by the asteroids' sizes rather than their locations.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

Observations of X/M asteroids across multiple wavelengths

We have conducted a radar-driven observational campaign of main-belt asteroids (MBAs) focused on X/M class asteroids using the Arecibo radar and NASA Infrared Telescope Facilities (IRTF). M-type asteroids have been identified as metallic, enstatite chondrites and/or heavily altered carbonaceous chondrites [Bell, J.F., Davis, D., Hartmann, W.K., Gaffey, M.J., 1989. In: Binzel, R.P., Gehrels, T., Matthews, M.S. (Eds.), Asteroids II. Univ. of Arizona Press, Tucson, pp. 921-948; Gaffey, M.J., McCord, T.B., 1979. In: Gehrels, T., Matthews, M.S. (Eds.), Asteroids. Univ. of Arizona Press, Tucson, pp. 688-723; Vilas, F., 1994. Icarus 111, 456-467]. Radar wavelength observations can determine whether an asteroid is metallic and provide information about the porosity and regolith depth. Near-infrared observations can help determine the grain size, porosity and composition of an object. Concurrent observations with these tools can give us a wealth of information about an object. Our objectives for this observation program were to (a) determine if there are any consistent relationships between spectra in the near-infrared wavelengths and radar signatures and (b) look for rotationally resolved relationships between asteroid radar properties and near-infrared spectral properties. This paper describes preliminary results of an ongoing survey of near-infrared observations of M-type asteroids and is a companion paper to radar observations reported by Shepard [Shepard, M.K., and 19 colleagues, 2008a. Icarus 195, 184-205]. In the analysis of 16 asteroid near-infrared spectra and nine radar measurements, we find a trend indicating a correlation between continuum slope from 1.7 to 2.45 μm and radar albedo—an asteroid with a steep continuum slope also has a bright radar albedo, which suggests a significant metal content. This may provide a means to use near-IR observations to predict the most likely metallic candidates for radar studies.     

The fossilized size distribution of the main asteroid belt

Planet formation models suggest the primordial main belt experienced a short but intense period of collisional evolution shortly after the formation of planetary embryos. This period is believed to have lasted until Jupiter reached its full size, when dynamical processes (e.g., sweeping resonances, excitation via planetary embryos) ejected most planetesimals from the main belt zone. The few planetesimals left behind continued to undergo comminution at a reduced rate until the present day. We investigated how this scenario affects the main belt size distribution over Solar System history using a collisional evolution model (CoEM) that accounts for these events. CoEM does not explicitly include results from dynamical models, but instead treats the unknown size of the primordial main belt and the nature/timing of its dynamical depletion using innovative but approximate methods. Model constraints were provided by the observed size frequency distribution of the asteroid belt, the observed population of asteroid families, the cratered surface of differentiated Asteroid (4) Vesta, and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr. Using CoEM, we solved for both the shape of the initial main belt size distribution after accretion and the asteroid disruption scaling law . In contrast to previous efforts, we find our derived function is very similar to results produced by numerical hydrocode simulations of asteroid impacts. Our best fit results suggest the asteroid belt experienced as much comminution over its early history as it has since it reached its low-mass state approximately 3.9-4.5 Ga. These results suggest the main belt's wavy-shaped size-frequency distribution is a “fossil” from this violent early epoch. We find that most diameter D?120 km asteroids are primordial, with their physical properties likely determined during the accretion epoch. Conversely, most smaller asteroids are byproducts of fragmentation events. The observed changes in the asteroid spin rate and lightcurve distributions near D∼100-120 km are likely to be a byproduct of this difference. Estimates based on our results imply the primordial main belt population (in the form of D<1000 km bodies) was 150-250 times larger than it is today, in agreement with recent dynamical simulations.     

A spectroscopic comparison of HED meteorites and V-type asteroids in the inner Main Belt

V-type asteroids in the inner Main Belt (a < 2.5 AU) and the HED meteorites are thought to be genetically related to one another as collisional fragments from the surface of the large basaltic Asteroid 4 Vesta. We investigate this relationship by comparing the near-infrared (0.7-2.5 μm) spectra of 39 V-type asteroids to laboratory spectra of HED meteorites. The central wavelengths and areas spanned by the 1 and 2 μm pyroxene-olivine absorption bands that are characteristic of planetary basalts are measured for both the asteroidal and meteoritic data. The band centers are shown to be well correlated, however the ratio of areas spanned by the 1 and 2 μm absorption bands are much larger for the asteroids than for the meteorites. We argue that this offset in band area ratio is consistent with our currently limited understanding of the effects of space weathering, however we cannot rule out the possibility that this offset is due to compositional differences. Several other possible causes of this offset are discussed.Amongst these inner Main Belt asteroids we do not find evidence for non-Vestoid mineralogies. Instead, these asteroids seem to represent a continuum of compositions, consistent with an origin from a single differentiated parent body. In addition, our analysis shows that V-type asteroids with low inclinations (i < 6°) tend to have band centers slightly shifted towards long wavelengths. This may imply that more than one collision on Vesta’s surface was responsible for producing the observed population of inner belt V-type asteroids. Finally, we offer several predictions that can be tested when the Dawn spacecraft enters into orbit around Vesta in the summer of 2011.     

Surface composition of Hilda asteroids from the analysis of the Sloan Digital Sky Survey colors

In this paper we search for photometric data of asteroids in the Hilda region in the Moving Object Catalogue of the Sloan Digital Sky Survey to find the spectral characteristics of small members of this group. We found that the correlation between size and spectral slope previously suggested for Hilda asteroids is correct only for large objects (H<12) but it is not supported by data obtained for the small ones. The best possibility to explain this behavior is that a space weathering process affecting the surface properties of these primitive objects is operating, modulated by a collisional resurfacing process affected by the lack of small projectiles in the population. Despite the intrinsic limitations of the few band photometry of the Sloan Digital Sky Survey, the analysis presented is based mainly in the detection of spectral slopes providing enough good indication about the taxonomic type of these asteroids and making us confident about our conclusions.     

The distribution of basaltic asteroids in the Main Belt

We present the observational results of a survey designed to target and detect asteroids whose photometric colors are similar to those of Vesta family members and thus may be considered as candidates for having a basaltic composition. Fifty basaltic candidates were selected with orbital elements that lie outside of the Vesta dynamical family. Optical and near-infrared spectra were used to assign a taxonomic type to 11 of the 50 candidates. Ten of these were spectroscopically confirmed as V-type asteroids, suggesting that most of the candidates are basaltic and can be used to constrain the distribution of basaltic material in the Main Belt. Using our catalog of V-type candidates and the success rate of the survey, we calculate unbiased size-frequency and semi-major axis distributions of V-type asteroids. These distributions, in addition to an estimate for the total mass of basaltic material, suggest that Vesta was the predominant contributor to the basaltic asteroid inventory of the Main Belt, however scattered planetesimals from the inner Solar System (a<2.0 AU) and other partially/fully differentiated bodies likely contributed to this inventory. In particular, we infer the presence of basaltic fragments in the vicinity of Asteroid 15 Eunomia, which may be derived from a differentiated parent body in the middle Main Belt (2.5<a<2.8). We find no asteroidal evidence for a large number of previously undiscovered basaltic asteroids, which agrees with previous theories suggesting that basaltic fragments from the ∼100 differentiated parent bodies represented in meteorite collections have been “battered to bits” [Burbine, T.H., Meibom, A., Binzel, R.P., 1996. Meteorit. Planet. Sci. 31, 607-620].     

A radar survey of M- and X-class asteroids

We observed ten M- and X-class main-belt asteroids with the Arecibo Observatory's S-band (12.6 cm) radar. The X-class asteroids were targeted based on their albedos or other properties which suggested they might be M-class. This work brings the total number of main-belt M-class asteroids observed with radar to 14. We find that three of these asteroids have rotation rates significantly different from what was previously reported. Based on their high radar albedo, we find that only four of the fourteen—16 Psyche, 216 Kleopatra, 758 Mancunia, and 785 Zwetana—are almost certainly metallic. 129 Antigone has a moderately high radar albedo and we suggest it may be a CH/CB/Bencubbinite parent body. Three other asteroids, 97 Klotho, 224 Oceana, and 796 Sarita have radar albedos significantly higher than the average main belt asteroid and we cannot rule out a significant metal content for them. Five of our target asteroids, 16 Psyche, 129 Antigone, 135 Hertha, 758 Mancunia, and 785 Zwetana, show variations in their radar albedo with rotation. We can rule out shape and composition in most cases, leaving variations in thickness, porosity, or surface roughness of the regolith to be the most likely causes. With the exception of 129 Antigone, we find no hydrated M-class asteroids (W-class; Rivkin, A.S., Howell, E.S., Lebofsky, L.A., Clark, B.E., Britt, D.T., 2000. Icarus 145, 351-368) to have high radar albedos.     

SOS: the visible spectroscopic survey of 820 asteroids

We present the results of a visible spectroscopic survey of 820 asteroids carried on between November 1996 and September 2001 at the 1.52 m telescope at ESO (La Silla). The instrumental set-up allowed an useful spectral range of about 4900 Å<λ<9200 Å. The global spatial distribution of the observed asteroids covers quite well all the region between 2.2 and 3.3 AU though some concentrations are apparent. These are due to the fact that several sub-sets of asteroids, such as families and groups, have been selected and studied during the development of the survey. The observed asteroids have been classified using the Tholen and the Bus taxonomies which, in general, agree quite well.     

On the shapes and spins of “rubble pile” asteroids

We examine the shape of a “rubble pile” asteroid as it slowly gains angular momentum by YORP torque, to the point where “landsliding” occurs. We find that it evolves to a “top” shape with constant angle of repose from the equator up to mid-latitude, closely resembling the shapes of several nearly critically spinning asteroids imaged by radar, most notably (66391) 1999 KW4 [Ostro, S.J., Margot, J.-L., Benner, L.A.M., Giorgini, J.D., Scheeres, D.J., Fahnestock, E.G., Broschart, S.B., Bellerose, J., Nolan, M.C., Magri, C., Pravec, P., Scheirich, P., Rose, R., Jurgens, R.F., De Jong, E.M., Suzuki, S., 2006. Science 314, 1276-1280]. Similar calculations for non-spinning extremely prolate or oblate “rubble piles” show that even loose rubble can sustain shapes far from fluid equilibrium, thus inferences based on fluid equilibrium are generally useless for inferring bulk properties such as density of small bodies. We also investigate the tidal effects of a binary system with a “top shape” primary spinning at near the critical limit for stability. We find that very close to the stability limit, the tide from the secondary can actually levitate loose debris from the surface and re-deposit it, in a process we call “tidal saltation.” In the process, angular momentum is transferred from the primary spin to the satellite orbit, thus maintaining the equilibrium of near-critical spin as YORP continues to add angular momentum to the system. We note that this process is in fact dynamically related to the process of “shepherding” of narrow rings by neighboring satellites.     

Exploration of faint absorption bands in the reflectance spectra of the asteroids by method of optimal smoothing: Vestoids

An optimization method of smoothing noisy spectra was developed to investigate faint absorption bands in the visual spectral region of reflectance spectra of asteroids and the compositional information derived from their analysis. The smoothing algorithm is called “optimal” because the algorithm determines the best running box size to separate weak absorption bands from the noise. The method is tested for its sensitivity to identifying false features in the smoothed spectrum, and its correctness of forecasting real absorption bands was tested with artificial spectra simulating asteroid reflectance spectra. After validating the method we optimally smoothed 22 vestoid spectra from SMASS1 [Xu, Sh., Binzel, R.P., Burbine, T.H., Bus, S.J., 1995. Icarus 115, 1-35]. We show that the resulting bands are not telluric features. Interpretation of the absorption bands in the asteroid spectra was based on the spectral properties of both terrestrial and meteorite pyroxenes. The bands located near 480, 505, 530, and 550 nm we assigned to spin-forbidden crystal field bands of ferrous iron, whereas the bands near 570, 600, and 650 nm are attributed to the crystal field bands of trivalent chromium and/or ferric iron in low-calcium pyroxenes on the asteroids' surface. While not measured by microprobe analysis, Fe³⁺ site occupancy can be measured with Mössbauer spectroscopy, and is seen in trace amounts in pyroxenes. We believe that trace amounts of Fe³⁺ on vestoid surfaces may be due to oxidation from impacts by icy bodies. If that is the case, they should be ubiquitous in the asteroid belt wherever pyroxene absorptions are found. Pyroxene composition of four asteroids of our set is determined from the band position of absorptions at 505 and 1000 nm, implying that there can be orthopyroxenes in all range of ferruginosity on the vestoid surfaces. For the present we cannot unambiguously interpret of the faint absorption bands that are seen in the spectra of 4005 Dyagilev, 4038 Kristina, 4147 Lennon, and 5143 Heracles. Probably there are other spectrally active materials along with pyroxenes on the surfaces of these asteroids.     

Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion

The main belt is believed to have originally contained an Earth mass or more of material, enough to allow the asteroids to accrete on relatively short timescales. The present-day main belt, however, only contains ∼5×¹⁰⁻⁴ Earth masses. Numerical simulations suggest that this mass loss can be explained by the dynamical depletion of main belt material via gravitational perturbations from planetary embryos and a newly-formed Jupiter. To explore this scenario, we combined dynamical results from Petit et al. [Petit, J. Morbidelli, A., Chambers, J., 2001. The primordial excitation and clearing of the asteroid belt. Icarus 153, 338-347] with a collisional evolution code capable of tracking how the main belt undergoes comminution and dynamical depletion over 4.6 Gyr [Bottke, W.F., Durda, D., Nesvorny, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H., 2005. The fossilized size distribution of the main asteroid belt. Icarus 175, 111-140]. Our results were constrained by the main belt's size-frequency distribution, the number of asteroid families produced by disruption events from diameter D>100 km parent bodies over the last 3-4 Gyr, the presence of a single large impact crater on Vesta's intact basaltic crust, and the relatively constant lunar and terrestrial impactor flux over the last 3 Gyr. We used our model to set limits on the initial size of the main belt as well as Jupiter's formation time. We find the most likely formation time for Jupiter was 3.3±2.6 Myr after the onset of fragmentation in the main belt. These results are consistent with the estimated mean disk lifetime of 3 Myr predicted by Haisch et al. [Haisch, K.E., Lada, E.A., Lada, C.J., 2001. Disk frequencies and lifetimes in young clusters. Astrophys. J. 553, L153-L156]. The post-accretion main belt population, in the form of diameter D?1000 km planetesimals, was likely to have been 160±40 times the current main belt's mass. This corresponds to 0.06-0.1 Earth masses, only a small fraction of the total mass thought to have existed in the main belt zone during planet formation. The remaining mass was most likely taken up by planetary embryos formed in the same region. Our results suggest that numerous D>200 km planetesimals disrupted early in Solar System history, but only a small fraction of their fragments survived the dynamical depletion event described above. We believe this may explain the limited presence of iron-rich M-type, olivine-rich A-type, and non-Vesta V-type asteroids in the main belt today. The collisional lifetimes determined for main belt asteroids agree with the cosmic ray exposure ages of stony meteorites and are consistent with the limited collisional evolution detected among large Koronis family members. Using the same model, we investigated the near-Earth object (NEO) population. We show the shape of the NEO size distribution is a reflection of the main belt population, with main belt asteroids driven to resonances by Yarkovsky thermal forces. We used our model of the NEO population over the last 3 Gyr, which is consistent with the current population determined by telescopic and satellite data, to explore whether the majority of small craters (D<0.1-1 km) formed on Mercury, the Moon, and Mars were produced by primary impacts or by secondary impacts generated by ejecta from large craters. Our results suggest that most small craters formed on these worlds were a by-product of secondary rather than primary impacts.     

Tidal encounters of ellipsoidal granular asteroids with planets

We investigate planetary fly-bys of asteroids using an approximate volume-averaged method that offers a relatively simple, but very flexible, approach to study the rotational dynamics of ellipsoids. The asteroid is considered to be a deformable, prolate ellipsoid, with its interior being modeled as a rigid-granular material. Effects due to the asteroid's rotation, its self-gravity and gravitational interaction with the planet are included. Using a simplified approach allows us to explore in detail the mechanics of asteroid's deformations and disruptions during planetary encounters. We also compare our results with those obtained by Richardson et al. [Richardson, D.C., Bottke Jr., W.F., Love, S.G., 1998. Icarus 134, 47-76] who used a large numerical code. We find that many of the features reported by them can indeed be captured by our rather simple methodology, and we discuss the reasons why some of our results differ from theirs.