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.     

Spin rate distribution of small asteroids

The spin rate distribution of main belt/Mars crossing (MB/MC) asteroids with diameters 3-15 km is uniform in the range from f=1 to 9.5 d⁻¹, and there is an excess of slow rotators with f<1 d⁻¹. The observed distribution appears to be controlled by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The magnitude of the excess of slow rotators is related to the residence time of slowed down asteroids in the excess and the rate of spin rate change outside the excess. We estimated a median YORP spin rate change of ≈0.022 d⁻¹/Myr for asteroids in our sample (i.e., a median time in which the spin rate changes by 1 d⁻¹ is ≈45 Myr), thus the residence time of slowed down asteroids in the excess is ≈110 Myr. The spin rate distribution of near-Earth asteroids (NEAs) with sizes in the range 0.2-3 km (∼5 times smaller in median diameter than the MB/MC asteroids sample) shows a similar excess of slow rotators, but there is also a concentration of NEAs at fast spin rates with f=9-10 d⁻¹. The concentration at fast spin rates is correlated with a narrower distribution of spin rates of primaries of binary systems among NEAs; the difference may be due to the apparently more evolved population of binaries among MB/MC asteroids.     

Taxonomy of asteroids in the Cybele region from the analysis of the Sloan Digital Sky Survey colors

In this paper we search for photometric data of asteroids in the outer region of the Hecuba gap in the Moving Object Catalogue of the Sloan Digital Sky Survey to find the spectrophotometric characteristics of small members of this group. We found that the correlation between size and spectral slope previously identified for Cybele asteroids is correct only for large objects (H_V<12) but it is not supported by data obtained for the small ones. This result argues against the scenario suggesting that D-type objects are more fragile than P-types, favoring disruptive collisions of precursors of the first type and resulting in a larger fraction of the smaller body population being collisional fragments from a few large D-type precursors. A statistical comparison of the spectral slope histograms of Cybeles and Hildas showed that it is not possible to reject the hypothesis that both samples were obtained from the same population at a confident limit of 90%. This result could be indicative of certain homogeneity in the taxonomic distributions of the outer belt populations due to a similar original composition and/or a similar resurfacing processes of these distant bodies. Despite the intrinsic limitations of the five band photometry of the Sloan Digital Sky Survey, the analysis presented is based mainly in the detection of spectral slopes thus providing sufficient indication of the taxonomic type of these asteroids and making us confident about our conclusions.     

Hilda asteroids among Jupiter family comets

Hilda asteroids and comets are similar from the compositional point of view. The D-taxonomic class prevailing among Hildas has all the characteristics found in cometary spectra. Jupiter Family Comets (JFCs) coming from the trans-neptunian region are under the gravitational control of Jupiter, making them a dynamically unstable population with a mean dynamical lifetime of 10⁴ to ¹⁰⁵ years. In contrast, Hilda asteroids residing in the 3:2 mean motion resonance with Jupiter are a very stable population. But once they escape from the resonance, they are dynamically controlled by Jupiter, and in this sense their behavior resembles that of JFC. We performed a numerical simulation to analyze the dynamical evolution that Hildas follow after escaping from the resonance, and their contribution to the JFC population. We found that 8% of the particles leaving the resonance end up impacting Jupiter. 98.7% of the escaped Hildas live at least 1000 years as a JFC, with a mean lifetime of 1.4×¹⁰⁶ years. In particular, escaped Hildas stay mainly in the region of perihelion distances greater than 2.5 AU. On the other hand, the number of escaped Hildas reaching the inner Solar System (q<2.5 AU) is negligible. So, there are almost no Hilda asteroids among the NEO population. We also analyzed the possibility that the Shoemaker-Levy 9 were an escaped Hilda asteroid. In this case, it would be possible to give stronger constraints to its pre-capture orbital elements.     

Phase curves of nine Trojan asteroids over a wide range of phase angles

We have observed well-sampled phase curves for nine Trojan asteroids in B-, V-, and I-bands. These were constructed from 778 magnitudes taken with the 1.3-m telescope on Cerro Tololo as operated by a service observer for the SMARTS consortium. Over our typical phase range of 0.2-10°, we find our phase curves to be adequately described by a linear model, for slopes of 0.04-0.09 mag/° with average uncertainty less than 0.02 mag/°. (The one exception, 51378 (2001 AT33), has a formally negative slope of −0.02 ± 0.01 mag/°.) These slopes are too steep for the opposition surge mechanism to be shadow-hiding (SH), so we conclude that the dominant surge mechanism must be coherent backscattering (CB). In a detailed comparison of surface properties (including surge slope, B-R color, and albedo), we find that the Trojans have surface properties similar to the P and C class asteroids prominent in the outer main belt, yet they have significantly different surge properties (at a confidence level of 99.90%). This provides an imperfect argument against the traditional idea that the Trojans were formed around Jupiter’s orbit. We also find no overlap in Trojan properties with either the main belt asteroids or with the small icy bodies in the outer Solar System. Importantly, we find that the Trojans are indistinguishable from other small bodies in the outer Solar System that have lost their surface ices (such as the gray Centaurs, gray Scattered Disk Objects, and dead comets). Thus, we find strong support for the idea that the Trojans originally formed as icy bodies in the outer Solar System, were captured into their current orbits during the migration of the gas giant planets, and subsequently lost all their surface ices.     

Evidence for asteroid space weathering from the Sloan Digital Sky Survey

By studying color variations between young and old asteroid families we find evidence for processes that modify colors of asteroids over time. We show that colors of aging surfaces of S-type asteroids become increasingly ‘redder’ and measure the rate of these spectral changes. We estimate that the mean spectral slope between 0.35 and 0.9 μm increases with time t (given in My) as ≈0.01 μm⁻¹×log₁₀t. This empirical fit is valid only for 2.5?t?3000 My (the time interval where we have data) and for the mean spectral slope determined from wide-wavelength filter photometry obtained by the Sloan Digital Sky Survey. We also find that Gy-old terrains of S-type asteroids reflect about 15% more light at ∼1-μm wavelengths than an ∼5-My-old S-type asteroid surface when the flux is normalized by the reflected light at 0.55 μm. We attribute these effects to space weathering. This result has important implications for asteroid geology and the origin of meteorites that reach the Earth. Our results also suggest that surfaces of C-type asteroids exhibit color alterations opposite to those of the S-type asteroids.     

Spectroscopic observations of Jupiter Trojans

We present the results of a campaign of spectroscopic observations of Jupiter Trojan asteroids. Thirty-four objects were observed during three runs in July and November 1998, and March 2002 using the Danish 1.54-m telescope at ESO. The covered spectral range was between 5000 and 9000 Å. Our observations include objects belonging both L₄ to L₅ clouds. According to analyses of previous investigations of Trojans, the spectra of different taxonomic classes can be separated on the basis of the slope of the reflectance spectrum. The large majority of the objects of our sample have been found to belong to the D taxonomic class, but we found also objects of P- and C-type. In two cases, we found also evidence of blueish spectral trends. Our data are important, since they allow us to substantially enlarge the whole data set of available Trojan spectra.     

Submillimeter photometry and lightcurves of Ceres and other large asteroids

Photometry and thermal lightcurves of six large asteroids (1-Ceres, 2-Pallas, 3-Juno, 12-Victoria, 85-Io and 511-Davida) have been observed at 870 μm (345 GHz) using the MPIfR 19-Channel Bolometer of the Heinrich-Hertz Submillimeter Telescope. Only Ceres displayed a lightcurve with an amplitude (∼50%, peak to peak) that was significantly greater than the uncertainty in the observations. When thermal fluxes and brightness temperatures are corrected for heliocentric distance and albedo, there is a significant relation with the sub-solar latitude of the asteroid, or the local season of the asteroid. No such trend can be found between observations with solar phase angle. These results are evidence that most of the submillimeter thermal radiation is emitted from below the diurnal thermal wave. Comparing the observed trend with model output suggests that the submillimeter radiation from all the asteroids we observed is best modeled by surface material with low thermal inertia (<15 J m⁻² s^−0.5 K⁻¹, consistent with mid-infrared observations of large main-belt asteroids) and a refractive index closer to unity relative to densities inferred from radar experiments, implying a veneer of material over the asteroid surface with a density less than 1000 kg m⁻³. More data with better signal-to-noise and aspect coverage could improve these models and constrain physical properties of asteroid surface materials. This would also allow asteroids to be used as calibration sources with accurately known and stable, broadband fluxes at long wavelengths.     

Hidden Mass in the Asteroid Belt

The total mass of the asteroid belt is estimated from an analysis of the motions of the major planets by processing high precision measurements of ranging to the landers Viking-1, Viking-2, and Pathfinder (1976-1997). Modeling of the perturbing accelerations of the major planets accounts for individual contributions of 300 minor planets; the total contribution of all remaining small asteroids is modeled as an acceleration caused by a solid ring in the ecliptic plane. Mass M_ring of the ring and its radius R are considered as solve-for parameters. Masses of the 300 perturbing asteroids have been derived from their published radii based mainly on measured fluxes of radiation, making use of the corresponding densities. This set of asteroids is grouped into three classes in accordance with physical properties and then corrections to the mean density for each class are estimated in the process of treating the observations. In this way an improved system of masses of the perturbing asteroids has been derived.The estimate M_ring≈(5±1)×10⁻¹⁰M_⊙ is obtained (M_⊙ is the solar mass) whose value is about one mass of Ceres. For the mean radius of the ring we have R≈2.80 AU with 3% uncertainty. Then the total mass M_belt of the main asteroid belt (including the 300 asteroids mentioned above) may be derived: M_belt≈(18±2)×10⁻¹⁰M_⊙. The value M_belt includes masses of the asteroids which are already discovered, and the total mass of a large number of small asteroids—most of which cannot be observed from the Earth. The second component M_ring is the hidden mass in the asteroid belt as evaluated from its dynamical impact onto the motion of the major planets.Two parameters of a theoretical distribution of the number of asteroids over their masses are evaluated by fitting to the improved set of masses of the 300 asteroids (assuming that there is no observational selection effect in this set). This distribution is extrapolated to the whole interval of asteroid masses and as a result the independent estimate M_belt≈18×10⁻¹⁰M_⊙ is obtained which is in excellent agreement with the dynamical finding given above.These results make it possible to predict the total number of minor planets in any unit interval of absolute magnitude H. Such predictions are compared with the observed distribution; the comparison shows that at present only about 10% of the asteroids with absolute magnitude H<14 have been discovered (according to the derived distribution, about 130,000 such asteroids are expected to exist).     

The surface properties of small asteroids: Peculiar Betulia—A case study

We present the results of extensive thermal-infrared observations of the C-type near-Earth Asteroid (1580) Betulia obtained in June 2002 with the 3-m NASA Infrared Telescope Facility (IRTF) on Mauna Kea, Hawaii. Betulia is a highly unusual object for which earlier radiometric observations, interpreted on the basis of simple thermal models, indicated a surface of high thermal inertia. A high thermal inertia implies a lack of thermally insulating regolith. Radiometric observations of other asteroids of comparable size indicate that regolith is present in nearly all cases. Knowledge of the surface thermal properties of small near-Earth asteroids is crucial for meaningful calculations of the Yarkovsky effect, which is invoked to explain the delivery of collisional fragments from the main belt into near-Earth orbits, and apparently has a significant influence on the orbital evolution of potentially hazardous near-Earth asteroids. Furthermore, apart from being an indicator of the presence of thermally insulating regolith on the surface of an asteroid, the thermal inertia determines the magnitude of the diurnal temperature variation and is therefore of great importance in the design of instrumentation for lander missions to small asteroids. In the case of Betulia our database is sufficiently broad to allow the use of more sophisticated thermal models than were available for earlier radiometric observations. The measured fluxes have been fitted with thermal-model emission continua to determine the asteroid's size and geometric albedo, pv. Fits obtained with a new thermophysical model imply an effective diameter of 4.57±0.46 km and an albedo of 0.077±0.015 and indicate a moderate surface thermal inertia of around 180 J m⁻² s^−0.5 K⁻¹. It is difficult to reconcile our results with earlier work, which indicate a larger diameter for Betulia and a high-thermal-inertia surface of bare rock.     

Physical properties of asteroid dust bands and their sources

Disruptive collisions in the main belt can liberate fragments from parent bodies ranging in size from several micrometers to tens of kilometers in diameter. These debris bodies group at initially similar orbital locations. Most asteroid-sized fragments remain at these locations and are presently observed as asteroid families. Small debris particles are quickly removed by Poynting-Robertson drag or comminution but their populations are replenished in the source locations by collisional cascade. Observations from the Infrared Astronomical Satellite (IRAS) showed that particles from particular families have thermal radiation signatures that appear as band pairs of infrared emission at roughly constant latitudes both above and below the Solar System plane. Here we apply a new physical model capable of linking the IRAS dust bands to families with characteristic inclinations. We use our results to constrain the physical properties of IRAS dust bands and their source families. Our results indicate that two prominent IRAS bands at inclinations ≈2.1° and ≈9.3° are byproducts of recent asteroid disruption events. The former is associated with a disruption of a ≈30-km asteroid occurring 5.8 Myr ago; this event gave birth to the Karin family. The latter came from the breakup of a large >100-km-diameter asteroid 8.3 Myr ago that produced the Veritas family. Using an N-body code, we tracked the dynamical evolution of ≈10⁶ particles, 1 μm to 1 cm in diameter, from both families. We then used these results in a Monte Carlo code to determine how small particles from each population undergo collisional evolution. By computing the thermal emission of particles, we were able to compare our results with IRAS observations. Our best-fit model results suggest the Karin and Veritas family particles contribute by 5-9% in 10-60-μm wavelengths to the zodiacal cloud's brightness within 50° latitudes around the ecliptic, and by 9-15% within 10° latitudes. The high brightness of the zodiacal cloud at large latitudes suggests that it is mainly produced by particles with higher inclinations than what would be expected for asteroidal particles produced by sources in the main belt. From these results, we infer that asteroidal dust represents a smaller fraction of the zodiacal cloud than previously thought. We estimate that the total mass accreted by the Earth in Karin and Veritas particles with diameters 20-400 μm is ≈15,000-20,000 tons per year (assuming 2 g cm⁻³ particles density). This is ≈30-50% of the terrestrial accretion rate of cosmic material measured by the Long Duration Exposure Facility. We hypothesize that up to ≈50% of our collected interplanetary dust particles and micrometeorites may be made up of particle species from the Veritas and Karin families. The Karin family IDPs should be about as abundant as Veritas family IDPs though this ratio may change if the contribution of third, near-ecliptic source is significant. Other sources of dust and/or large impact speeds must be invoked to explain the remaining ≈50-70%. The disproportional contribution of Karin/Veritas particles to the zodiacal cloud (only 5-9%) and to the terrestrial accretion rate (30-50%) suggests that the effects of gravitational focusing by the Earth enhance the accretion rate of Karin/Veritas particles relative to those in the background zodiacal cloud. From this result and from the latitudinal brightness of the zodiacal cloud, we infer that the zodiacal cloud emission may be dominated by high-speed cometary particles, while the terrestrial impactor flux contains a major contribution from asteroidal sources. Collisions and Poynting-Robertson drift produce the size-frequency distribution (SFD) of Karin and Veritas particles that becomes increasingly steeper closer to the Sun. At 1 AU, the SFD is relatively shallow for small particle diameters D (differential slope exponent of particles with D?100 μm is ≈2.2-2.5) and steep for D?100 μm. Most of the mass at 1 AU, as well as most of the cross-sectional area, is contributed by particles with D≈100-200 μm. Similar result has been found previously for the SFD of the zodiacal cloud particles at 1 AU. The fact that the SFD of Karin/Veritas particles is similar to that of the zodiacal cloud suggests that similar processes shaped these particle populations. We estimate that there are ≈5×¹⁰²⁴ Karin and ≈10²⁵ Veritas family particles with D>30 μm in the Solar System today. The IRAS observation of the dust bands may be satisfactorily modeled using ‘averaged’ SFDs that are constant with semimajor axis. These SFDs are best described by a broken power-law function with differential power index α≈2.1-2.4 for D?100 μm and by α?3.5 for 100 μm?D?1 cm. The total cross-sectional surface area of Veritas particles is a factor of ≈2 larger than the surface area of the particles producing the inner dust bands. The total volumes in Karin and Veritas family particles with 1 μm<D<1 cm correspond to D=11 km and D=14 km asteroids with equivalent masses ≈1.5×¹⁰¹⁸ g and ≈3.0×¹⁰¹⁸ g, respectively (assuming 2 g cm⁻³ bulk density). If the size-frequency and radial distribution of particles in the zodiacal cloud were similar to those in the asteroid dust bands, we estimate that the zodiacal cloud represents ∼3×¹⁰¹⁹ g of material (in particles with 1 μm<D<1 cm) at ±10° around the ecliptic and perhaps as much as ∼¹⁰²⁰ g in total. The later number corresponds to about a 23-km-radius sphere with 2 g cm⁻³ density.     

Keck observations of the 2002-2003 jovian ring plane crossing

We present new observations of Jupiter's ring system at a wavelength of 2.2 μm obtained with the 10-m W.M. Keck telescopes on three nights during a ring plane crossing: UT 19 December 2002, and 22 and 26 January 2003. We used conventional imaging, plus adaptive optics on the last night. Here we present detailed radial profiles of the main ring, halo and gossamer rings, and interpret the data together with information extracted from radio observations of Jupiter's synchrotron radiation. The main ring is confined to a 800-km-wide annulus between 128,200 and 129,000 km, with a ∼5000 km extension on the inside. The normal optical depth is 8×¹⁰⁻⁶, 15% of which is provided by bodies with radii a?5 cm. These bodies are as red as Metis. Half the optical depth, τ≈4×¹⁰⁻⁶, is attributed to micron-sized dust, and the remaining τ≈3×¹⁰⁻⁶ to grains tens to hundreds of μm in size. The inward extension consists of micron-sized (a?10 μm) dust, which probably migrates inward under Poynting-Robertson drag. The inner limit of this extension falls near the 3:2 Lorentz resonance (at orbital radius r=122,400 km), and coincides with the outer limit of the halo. The gossamer rings appear to be radially confined, rather than broad sheets of material. The Amalthea ring is triangularly shaped, with a steep outer dropoff over ∼5000 km, extending a few 1000 km beyond the orbit of Amalthea, and a more gradual inner dropoff over 15,000-20,000 km. The inner edge is near the location of the synchronous orbit. The optical depth in the Amalthea ring is ∼5×¹⁰⁻⁷, up to 20% of which is comprised of macroscopic material. The optical depth in the Thebe ring is a factor of 3 smaller.     

Dust production from the hypervelocity impact disruption of the Murchison hydrous CM2 meteorite: Implications for the disruption of hydrous asteroids and the production of interplanetary dust

More than half of the C-type asteroids, the dominant type of asteroid in the outer half of the main-belt, show evidence of hydration in their reflectance spectra. In order to understand the collisional evolution of asteroids and the production of interplanetary dust and to model the infrared signature of small particles in the Solar System it is important to characterize the dust production from primary impact disruption events, and compare the disruption of hydrous and anhydrous targets. We performed a hypervelocity impact disruption experiment on an ∼30 g target of the Murchison CM2 hydrated carbonaceous chondrite meteorite, and compared the results with our previous disruption experiments on anhydrous meteorites including Allende, a CV3 carbonaceous chondrite, and nine ordinary chondrites. Murchison is significantly more friable than the ordinary chondrites or Allende. Nonetheless, on a plot of mass of the largest fragment versus specific impact energy, the Murchison disruption plots within the field of the anhydrous meteorites points, suggesting that Murchison is at least as resistant to impact disruption as the anhydrous meteorites, which require about twice the energy for disruption as terrestrial anhydrous basalt targets. We determined the mass-frequency distribution of the debris from the Murchison disruption over a nine order-of-magnitude mass range, from ∼10⁻⁹ g to the mass of the largest fragment produced in the disruption. The cumulative mass-frequency distribution from the Murchison disruption is fit by three power-law segments. For masses >10⁻² g the slope is only slightly steeper than that of the corresponding segment from the disruption of most anhydrous meteorites. Over the range from ∼10⁻⁶ to 10⁻² g the slope is significantly steeper than that for the anhydrous meteorites. For masses <10⁻⁶ g the slopes of both the Murchison and the anhydrous meteorites are almost flat. Thus the Murchison disruption significantly over-produced small fragments (10⁻⁶-10⁻³ g) compared to anhydrous meteorite targets. If the Murchison results are representative of hydrous asteroids, the hydrous asteroids may dominate over anhydrous asteroids in the production of interplanetary dust >100 μm in size, the size of micrometeorites recovered from the polar ices, while both types of asteroids might produce comparable amounts of ∼10 μm interplanetary dust. This would explain the puzzle that polar micrometeorites (>100 μm in size) are similar to hydrous meteorites, while the majority of the ∼10 μm interplanetary dust particles are anhydrous.     

Physical characterization of the potentially hazardous high-albedo Asteroid (33342) 1998 WT24 from thermal-infrared observations

The potentially hazardous Asteroid (33342) 1998 WT₂₄ approached the Earth within 0.0125 AU on 2001 December 16 and was the target of a number of optical, infrared, and radar observing campaigns. Interest in 1998 WT₂₄ stems from its having an orbit with an unusually low perihelion distance, which causes it to cross the orbits of the Earth, Venus, and Mercury, and its possibly being a member of the E spectral class, which is rare amongst near-Earth asteroids (NEAs). We present the results of extensive thermal-infrared observations of 1998 WT₂₄ obtained in December 2001 with the 3-m NASA Infrared Telescope Facility (IRTF) on Mauna Kea, Hawaii and the ESO 3.6-m telescope in Chile. A number of thermal models have been applied to the data, including thermophysical models that give best-fit values of 0.35±0.04 km for the effective diameter, 0.56±0.2 for the geometric albedo, pv, and 100-300 J m⁻² s^−0.5 K⁻¹ for the thermal inertia. Our values for the diameter and albedo are consistent with results derived from radar and polarimetric observations. The albedo is one of the highest values obtained for any asteroid and, since no other taxonomic type is associated with albedos above 0.5, supports the suggested rare E-type classification for 1998 WT₂₄. The thermal inertia is an order of magnitude higher than values derived for large main-belt asteroids but consistent with the relatively high values found for other near-Earth asteroids. A crude pole solution inferred from a combination of our observations and published radar results is β=−52°, λ=355° (J2000), but we caution that this is uncertain by several tens of degrees.     

Are Main-Belt Asteroids a Sufficient Source for the Earth-Approaching Asteroids?

This paper predicts the size distribution of the Earth-approaching asteroids with diameterd= 10 m to 10 km, assuming they originate as the fragments of main-belt asteroids with a cumulative size distribution proportional tod^−2.5and that they have self-similar fragmentation properties. The resulting distribution is dominated by “fast-track” bodies originating from parent asteroids with orbits close to the 3:1 mean-motion resonance with Jupiter. Because the dynamical lifetimes of these Earth approachers are shorter than their collisional lifetimes, their size distribution is nearly proportional tod^−3.0, the production distribution in the main belt. This prediction, however, is at odds with the Spacewatch observations. The observed distribution is relatively flat ford> ∼100 m, and relatively steep ford< ∼100 m, so that the number of Earth approachers withd∼ 10 m to 0.3 km is overestimated. If these populations are predominantly of main-belt origin, then the size distribution in the main belt is not a simple power law. A nonuniform size distribution with wave-like oscillations, possibly caused by a cutoff at small sizes, would lead to Earth approachers with a size distribution in better agreement with the observations. If such wave-like oscillations are realistic, then the main belt is sufficient to supply the observed number of Earth approachers throughout the observed size range.     

Visible spectroscopic and photometric survey of Jupiter Trojans: Final results on dynamical families

We present the results of a visible spectroscopic and photometric survey of Jupiter Trojans belonging to different dynamical families. The survey was carried out at the 3.5 m New Technology Telescope (NTT) of the European Southern Observatory (La Silla, Chile) in April 2003, May 2004 and January 2005. We obtained data on 47 objects, 23 belonging to the L5 swarm and 24 to the L4 one. These data together with those already published by Fornasier et al. [Fornasier, S., Dotto, E., Marzari, F., Barucci, M.A., Boehnhardt, H., Hainaut, O., de Bergh, C., 2004a. Icarus 172, 221-232] and Dotto et al. [Dotto, E., Fornasier, S., Barucci, M.A., Licandro, J., Boehnhardt, H., Hainaut, O., Marzari, F., de Bergh, C., De Luise, F., 2006. Icarus 183, 420-434], acquired since November 2002, constitute a total sample of visible spectra for 80 objects. The survey allows us to investigate six families (Aneas, Anchises, Misenus, Phereclos, Sarpedon, Panthoos) in the L5 cloud and four L4 families (Eurybates, Menelaus, 1986 WD and 1986 TS6). The sample that we measured is dominated by D-type asteroids, with the exception of the Eurybates family in the L4 swarm, where there is a dominance of C- and P-type asteroids. All the spectra that we obtained are featureless with the exception of some Eurybates members, where a drop-off of the reflectance is detected shortward of 5200 Å. Similar features are seen in main belt C-type asteroids and commonly attributed to the intervalence charge transfer transition in oxidized iron. Our sample comprises fainter and smaller Trojans as compared to the literature's data and allows us to investigate the properties of objects with estimated diameter smaller than 40-50 km. The analysis of the spectral slopes and colors versus the estimated diameters shows that the blue and red objects have indistinguishable size distribution, so any relationship between size and spectral slopes has been found. To fully investigate the Trojans population, we include in our analysis 62 spectra of Trojans available in literature, resulting in a total sample of 142 objects. Although the mean spectral behavior of L4 and L5 Trojans is indistinguishable within the uncertainties, we find that the L4 population is more heterogeneous and that it has a higher abundance of bluish objects as compared to the L5 swarm. Finally, we perform a statistical investigation of the Trojans's spectra property distributions as a function of their orbital and physical parameters, and in comparison with other classes of minor bodies in the outer Solar System. Trojans at lower inclination appear significantly bluer than those at higher inclination, but this effect is strongly driven by the Eurybates family. The mean colors of the Trojans are similar to those of short period comets and neutral Centaurs, but their color distributions are different.     

Impact cratering and break up of the small bodies of the Solar System

We consider the largest impact craters observed on small satellites and asteroids and the impact disruption of such bodies. Observational data are considered from 21 impact-like structures on 13 satellites and 8 asteroids (target body radii in the range 0.7-265 km). If the radius of the target body is R and the diameter of the largest crater observed on this body D, the ratio D/R is then the main observational parameter of interest. This is found on the observed bodies and compared to data obtained in the laboratory. Taking the largest observed value for D/R as a proxy for the ratio Dc/R (where Dc is the diameter of the largest crater that can be formed on a body without shattering it) it was found that for the observed icy satellites Dc,icy≈1.2R and for the asteroids and the rocky satellites Dc,rocky≈1.6R. In laboratory experiments with ice targets at impactor speeds of 1 to 3 km s⁻¹ we obtained Dc,icy≈1.64R.     

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.     

Space weathering of small Koronis family members

The space weathering process and its implications for the relationships between S- and Q-type asteroids and ordinary chondrite meteorites is an often debated topic in asteroid science. Q-type asteroids have been shown to display the best spectral match to ordinary chondrites (McFadden, L.A., Gaffey, M.J., McCord, T.B. [1985]. Science 229, 160–163). While the Q-types and ordinary chondrites share some spectral features with S-type asteroids, the S-types have significantly redder spectral slopes than the Q-types in visible and near-infrared wavelengths. This reddening of spectral slope is attributed to the effects of space weathering on the observed surface composition. The analysis by Binzel et al. (Binzel, R.P., Rivkin, A.S., Stuart, J.S., Harris, A.W., Bus, S.J., Burbine, T.H. [2004]. Icarus 170, 259–294) provided a missing link between the Q- and S-type bodies in near-Earth space by showing a reddening of spectral slope in objects from 0.1 to 5 km that corresponded to a transition from Q-type to S-type asteroid spectra, implying that size, and therefore surface age, is related to the relationship between S- and Q-types. The existence of Q-type asteroids in the main-belt was not confirmed until Mothé-Diniz and Nesvorny (Mothé-Diniz, T., Nesvorny, D. [2008]. Astron. Astrophys. 486, L9–L12) found them in young S-type clusters. The young age of these families suggest that the unweathered surface could date to the formation of the family. This leads to the question of whether older S-type main-belt families can contain Q-type objects and display evidence of a transition from Q- to S-type. To answer this question we have carried out a photometric survey of the Koronis family using the Kitt Peak 2.1 m telescope. This provides a unique opportunity to compare the effects of the space weathering process on potentially ordinary chondrite-like bodies within a population of identical initial conditions. We find a trend in spectral slope for objects 1–5 km that shows the transition from Q- to S-type in the main-belt. This data set will prove crucial to our understanding of the space weathering process and its relevant timescales.     

Trojans’ Odyssey: Unveiling the early history of the Solar System

In our present understanding of the Solar System, small bodies (asteroids, Jupiter Trojans, comets and TNOs) are the most direct remnants of the original building blocks that formed the planets. Jupiter Trojan and Hilda asteroids are small primitive bodies located beyond the ‘snow line’, around respectively the L₄ and L₅ Lagrange points of Jupiter at ～5.2?AU (Trojans) and in the 2:3 mean-motion resonance with Jupiter near 3.9?AU (Hildas). They are at the crux of several outstanding and still conflicting issues regarding the formation and evolution of the Solar System. They hold the potential to unlock the answers to fundamental questions about planetary migration, the late heavy bombardment, the formation of the Jovian system, the origin and evolution of trans-neptunian objects, and the delivery of water and organics to the inner planets. The proposed Trojans’ Odyssey mission is envisioned as a reconnaissance, multiple flyby mission aimed at visiting several objects, typically five Trojans and one Hilda. It will attempt exploring both large and small objects and sampling those with any known differences in photometric properties. The orbital strategy consists in a direct trajectory to one of the Trojan swarms. By carefully choosing the aphelion of the orbit (typically 5.3?AU), the trajectory will offer a long arc in the swarm thus maximizing the number of flybys. Initial gravity assists from Venus and Earth will help reducing the cruise time as well as the ΔV needed for injection thus offering enough capacity to navigate among Trojans. This solution further opens the unique possibility to flyby a Hilda asteroid when leaving the Trojan swarm. During the cruise phase, a Main Belt Asteroid could be targeted if requiring a modest ΔV. The specific science objectives of the mission will be best achieved with a payload that will perform high-resolution panchromatic and multispectral imaging, thermal-infrared imaging/ radiometry, near- and mid-infrared spectroscopy, and radio science/mass determination. The total mass of the payload amounts to 50?kg (including margins). The spacecraft is in the class of Mars-Express or a down-scaled version of Jupiter Ganymede Orbiter. It will have a dry mass of 1200?kg, a total mass at launch of 3070?kg and a ΔV capability of 700?m/s (after having reached the first Trojan) and can be launched by a Soyuz rocket. The mission operations concept (ground segment) and science operations are typical of a planetary mission as successfully implemented by ESA during, for instance, the recent flybys of Main Belt asteroids Steins and Lutetia.