Secular Dynamics of Asteroids in the Inner Solar System

In the last three years we have carried out numerical and semi-analytical studies on the secular dynamical mechanisms in the region (semimajor axis a < 2 AU) where the NEA orbits evolve. Our numerical integrations (over a time span of a few Myr) have shown that: (i) the linear secular resonances with both the inner and the outer planets may play an important role in the dynamical evolution of NEAs; (ii) the apsidal secular resonance with Mars could provide an important dynamical transport mechanism by which asteroids in the Mars-crossing region eventually achieve Earth-crossing orbits; (iii) in this region, due to the interaction with the terrestrial planets, the Kozai resonance can occur at small inclinations, with the argument of perihelion ω librating around 0° or 180°, providing a temporary protection mechanism against close approaches to the planets. The location of the linear secular resonances in this zone has also been obtained by an automatic procedure using a semi-numerical method valid for all values of the inclinations and eccentricities of the small bodies, and also in the case of libration of the argument of perihelion. A map of the secular resonances in the (a, i) plane shows — in agreement with the numerical integrations — that all the resonances with the terrestrial and giant planets are present, and also that some of them overlap. Thus the way is now open to fully take into account secular resonances in modelling the dynamical evolution of NEAs. This revised version was published online in July 2006 with corrections to the Cover Date.     

Perturbation theory for asteroid motion in the gravitational field of a migrating planet

A new perturbation method for the determination of proper elements of an asteroid in the gravitational field of a migrating planet is developed. The article is published in the original.     

Secular perihelion advances of the inner planets and asteroid Icarus

A small effect expected from a recently proposed gravitational impact model (Wilhelm et al., 2013) is used to explain the remaining secular perihelion advance rates of the planets Mercury, Venus, Earth, Mars, and the asteroid (1566) Icarus—after taking into account the disturbances related to Newton’s Theory of Gravity. Such a rate was discovered by Le Verrier (1859) for Mercury and calculated by Einstein (1915, 1916) in the framework of his General Theory of Relativity (GTR). Accurate observations are now available for the inner Solar System objects with different orbital parameters. This is important, because it allowed us to demonstrate that the quantitative amount of the deviation from an 1/r potential is—under certain conditions—only dependent on the specific mass distribution of the Sun and not on the characteristics of the orbiting objects and their orbits. A displacement of the effective gravitational from the geometric centre of the Sun by about 4400 m towards each object is consistent with the observations and explains the secular perihelion advance rates.     

On the numerical transformation of variables in perturbation theory

Once the generating function of a Lie-type transformation is known, canonical variables can be transformed numerically by application of a Runge-Kutta type integration method or any other appropriate numerical integration algorithm. The proposed approach avails itself of the fact, that the transformation is defined by a system of differential equations with a small parameter as the independent variable. The integration of such systems arising in the perturbation theories of Hori and Deprit is discussed. The method allows to compute numerical values of periodic perturbations without deriving explicitly the perturbation series. This saving of an algebraic work is achieved at the expense of multiple evaluations of the generator's derivatives.     

Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location

In this paper a theoretical perturbation approach to the problem of the dynamics in secular resonance is exposed. This approach avoids any expansion of the main term of the Hamiltonian (linear term in the masses) with respect to the eccentricity or the inclination of the asteroid, in order to achieve results valid for any value of these variables. Moreover suitable action-angle variables are introduced to take properly into account the dynamics related to the motion of the argument of perihelion of the asteroid, which is relevant at high inclination. A class of secular resonances wider than that usually considered is found. An explicit computation of the location of the main secular resonances, estimating also the contribution of the quadratic term in the masses by means of classical series expansion, is reported in the last sections. The accuracy of computations obtained by series expansion is discussed in the paper.     

Radar observations and the shape of near-Earth asteroid 2008 EV5

We observed the near-Earth ASTEROID 2008 EV5 with the Arecibo and Goldstone planetary radars and the Very Long Baseline Array during December 2008. EV5 rotates retrograde and its overall shape is a 400 ± 50 m oblate spheroid. The most prominent surface feature is a ridge parallel to the asteroid’s equator that is broken by a concavity about 150 m in diameter. Otherwise the asteroid’s surface is notably smooth on decameter scales. EV5’s radar and optical albedos are consistent with either rocky or stony-iron composition. The equatorial ridge is similar to structure seen on the rubble-pile near-Earth asteroid (66391) 1999 KW4 and is consistent with YORP spin-up reconfiguring the asteroid in the past. We interpret the concavity as an impact crater. Shaking during the impact and later regolith redistribution may have erased smaller features, explaining the general lack of decameter-scale surface structure.     

The accuracy of proper orbital elements and the properties of asteroid families: Comparison with the linear theory

The accuracy and reliability of the proper orbital elements used to define asteroid families are investigated by simulating numerically the dynamical evolution of families assumed to arise from the “explosion” of a parent object. The orbits of the simulated family asteroids have then been integrated in the frame of the elliptic restricted three-body problem Sun-Jupiter-asteroid, for times of the order of the circulation periods of perihelia and nodes. By filtering out short-periodic perturbations, we have monitored the behavior of the proper eccentricities and inclinations, computed according to the linear secular perturbation theory. Significant long-period variations have been found especially for families having nonnegligible eccentricities and/or inclinations (like the Eos family), and strong disturbances due to the proximity of mean motion commensurabilities with Jupiter have been evidenced (for instance, in the case of the Themis family). These phenomena can cause a significant “noise” on the proper eccentricities and inclinations, probably affecting in some cases the derived family memberships. They can also give rise to a spurious anisotropy in the fragment ejection velocity fields computed from the dispersion in proper elements observed in each family, and this could explain the puzzling anisotropies of this kind actually found in real families by D. Brouwer (1951, Astron. J. 56, 9–32) and by V. Zappalà, P. Farinella, Z. Knežević, and P. Paolicchi (1984), Icarus 59, 261–285).     

Explicit Semianalytical Theory of Asteroid Motion

A new semianalytical theory of asteroid motion is presented. The theory is developed on the basis of Kaula's expansion of the disturbing function including terms up to the second order with respect to the masses of disturbing bodies. The theory is constructed in explicit form that gives the possibility to study separately the influence of different perturbations in the dynamics of minor planets. The mean-motion resonances with major planets as well as mixed three-body resonances can also be taken into account. For the non-resonant case the formulas obtained can be used for deriving the second transformation to calculate the proper elements of an asteroid orbit in closed form with respect to inclinations and eccentricities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Space weathering and the interpretation of asteroid reflectance spectra

Lunar-style space weathering is well understood, but cannot be extended to asteroids in general. The two best studied Asteroids (433 Eros and 243 Ida) exhibit quite different space weathering styles, and neither exhibits lunar-style space weathering. It must be concluded that at this time the diversity and mechanisms of asteroid space weathering are poorly understood. This introduces a significant unconstrained variable into the problem of analyzing asteroid spectral data. The sensitivity of asteroid surface material characterizations to space weathering effects - whatever their nature - is strongly dependent upon the choice of remote sensing methodology. The effects of space weathering on some methodologies such as curve matching are potentially devastating and at the present time essentially unmitigated. On other methodologies such as parametric analysis (e.g., analyses based on band centers and band area ratios) the effects are minimal. By choosing the appropriate methodology(ies) applied to high quality spectral data, robust characterizations of asteroid surface mineralogy can be obtained almost irrespective of space weathering. This permits sophisticated assessments of the geologic history of the asteroid parent bodies and of their relationships to the meteorites. Investigations of the diversity of space weathering processes on asteroid surfaces should be a fruitful area for future efforts.     

Asteroid Mean Elements: Higher Order and Iterative Theories

Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation; they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step, used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory, resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete, fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements, incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamical erosion of the asteroid belt and implications for large impacts in the inner Solar System

The cumulative effects of weak resonant and secular perturbations by the major planets produce chaotic behavior of asteroids on long timescales. Dynamical chaos is the dominant loss mechanism for asteroids with diameters in the current asteroid belt. In a numerical analysis of the long-term evolution of test particles in the main asteroid belt region, we find that the dynamical loss history of test particles from this region is well described with a logarithmic decay law. In our simulations the loss rate function that is established at persists with little deviation to at least . Our study indicates that the asteroid belt region has experienced a significant amount of depletion due to this dynamical erosion—having lost as much as ∼50% of the large asteroids—since 1 Myr after the establishment of the current dynamical structure of the asteroid belt. Because the dynamical depletion of asteroids from the main belt is approximately logarithmic, an equal amount of depletion occurred in the time interval 10-200 Myr as in 0.2-4 Gyr, roughly ∼30% of the current number of large asteroids in the main belt over each interval. We find that asteroids escaping from the main belt due to dynamical chaos have an Earth-impact probability of ∼0.3%. Our model suggests that the rate of impacts from large asteroids has declined by a factor of 3 over the last 3 Gyr, and that the present-day impact flux of objects on the terrestrial planets is roughly an order of magnitude less than estimates currently in use in crater chronologies and impact hazard risk assessments.     

Asteroid families: evidence of ageing of the proper elements

In recent times it has been emphasized that the present kinematical structures of asteroid families should be evolved with respect to the original post-impact situations, according to numerical simulations performed taking into account also the previously neglected Yarkovsky effect. In this paper we show that also a “classical” approach based on an analysis of the current kinematical properties of families leads to conclude that the distributions of proper eccentricities and semimajor axes of family members exhibit evidence of an evolution. The importance of this approach is that it yields a fully independent and quantitative estimate of an evolutionary spreading of the proper elements. In particular, we find that the original post-impact families had to be on the average about twice more compact than the families we observe now, when considering family members down to about 5 km in size. This result can be used in future analyses to derive estimates of the ages of different families, and to better constrain the typical values of the ejection velocities of the fragments in family-forming events.     

Fundamentally distinct outcomes of asteroid collisional evolution and catastrophic disruption

The outcomes of asteroid collisional evolution are presently unclear: are most asteroids larger than 1 km size gravitational aggregates reaccreted from fragments of a parent body that was collisionally disrupted, while much smaller asteroids are collisional shards that were never completely disrupted? The 16 km mean diameter S-type asteroid 433 Eros, visited by the NEAR mission, has surface geology consistent with being a fractured shard. A ubiquitous fabric of linear structural features is found on the surface of Eros and probably indicates a globally consolidated structure beneath its regolith cover. Despite the differences in absolute scale and in lighting conditions for NEAR and Hayabusa, similar features should have been found on 25143 Itokawa if present. This much smaller, 320 m diameter S-asteroid was visited by the Hayabusa spacecraft. Comparative analyses of Itokawa and Eros geology reveal fundamental differences, and interpretation of Eros geology is illuminated by comparison with Itokawa. Itokawa lacks a global lineament fabric, and its blocks, craters, and regolith may be inconsistent with formation and evolution as a fractured shard, unlike Eros. An object as small as Itokawa can form as a rubble pile, while much larger Eros formed as a fractured shard. Itokawa is not a scaled-down Eros, but formed by catastrophic disruption and reaccumulation.     

Binary asteroid systems: Tidal end states and estimates of material properties

The locations of the fully despun, double synchronous end states of tidal evolution, where the rotation rates of both the primary and secondary components in a binary system synchronize with the mean motion about the center of mass, are derived for spherical components. For a given amount of scaled angular momentum J/J′, the tidal end states are over-plotted on a tidal evolution diagram in terms of mass ratio of the system and the component separation (semimajor axis in units of primary radii). Fully synchronous orbits may not exist for every combination of mass ratio and angular momentum; for example, equal-mass binary systems require J/J′ > 0.44. When fully synchronous orbits exist for prograde systems, tidal evolution naturally expands the orbit to the stable outer synchronous solution. The location of the unstable inner synchronous orbit is typically within two primary radii and often within the radius of the primary itself. With the exception of nearly equal-mass binaries, binary asteroid systems are in the midst of lengthy tidal evolutions, far from their fully synchronous tidal end states. Of those systems with unequal-mass components, few have even reached the stability limit that splits the fully synchronous orbit curves into unstable inner and stable outer solutions.Calculations of material strength based on limiting the tidal evolution time to the age of the Solar System indicate that binary asteroids in the main belt with 100-km-scale primary components are consistent with being made of monolithic or fractured rock as expected for binaries likely formed from sub-catastrophic impacts in the early Solar System. To tidally evolve in their dynamical lifetime, near-Earth binaries with km-scale primaries or smaller created via a spin-up mechanism must be much weaker mechanically than their main-belt counterparts even if formed in the main belt prior to injection into the near-Earth region. Small main-belt binaries, those having primary components less than 10 km in diameter, could bridge the gap between the large main-belt binaries and the near-Earth binaries, as, depending on the age of the systems, small main-belt binaries could either be as strong as the large main-belt binaries or as weak as the near-Earth binaries. The inherent uncertainty in the age of a binary system is the leading source of error in calculation of material properties, capable of affecting the product of rigidity μ and tidal dissipation function Q by orders of magnitude. Several other issues affecting the calculation of μQ are considered, though these typically affect the calculation by no more than a factor of two. We also find indirect evidence within all three groups of binary asteroids that the semimajor axis of the mutual orbit in a binary system may evolve via another mechanism (or mechanisms) in addition to tides with the binary YORP effect being a likely candidate.     

The Trojan asteroid belt: Proper elements,stability, chaos and families

I have computed proper elements for 174 asteroids in the 1 : 1 resonance with Jupiter, that is for all the reliable orbits available (numbered and multi-opposition). The procedure requires numerical integration, under the perturbations by the four major planets, for 1,000,000 years; the output is digitally filtered and compressed into a synthetic theory (as defined within theLONGSTOP project). The proper modes of oscillation of the variables related to eccentricity, perihelion, inclination and node define proper elements. A third proper element is defined as the amplitude of the oscillation of the semimajor axis associated with the libration period; because of the strong nonlinearity of the problem, this component cannot be determined by a simple Fourier transform to the frequency domain. I therefore give another definition, which results in very good stability with time. For 87% of the computed orbits, the stability of the proper elements-at least over 1M yr-is within the following bounds: 0.001AU in semimajor axis, 0.0025 in eccentricity and sine of inclination. Half of the cases with degraded stability of the proper elements are found to be chaotic, with e-folding times between 16,000 and 660,000yr; in some other cases, chaotic behaviour does not result in a significantly decreased stability of the proper elements (stable chaos). The accuracy and stability of these proper elements is good enough to allow a search for asteroid families; however, the dynamical structure of the Trojan belt is very different from the one of the main belt, and collisional events among Trojans can result in a distribution of fragments difficult to identify. The occurrence of couples of Trojans with very close proper elements is proven not to be statistically significant in almost all cases. As the only exception, the couple 1583 Antilochus — 3801 Thrasimedes is significant; however, it is not easy to account for it by a conventional collisional theory. The Menelaus group is confirmed as a strong candidate collisional family; Teucer and Sarpedon could be considered as significant clusters. A number of other clumps are detected (by the same automated clustering method used for the main belt by Zappalà et al., 1990, 1992), but the total number of Trojans with reliable orbits is not large enough to detect many significant candidate families.     

The primordial excitation and clearing of the asteroid belt—Revisited

We have performed new simulations of two different scenarios for the excitation and depletion of the primordial asteroid belt, assuming Jupiter and Saturn on initially circular orbits as predicted by the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465]. First, we study the effects of sweeping secular resonances driven by the depletion of the solar nebula. We find that these sweeping secular resonances are incapable of giving sufficient dynamical excitation to the asteroids for nebula depletion timescales consistent with estimates for solar-type stars, and in addition cannot cause significant mass depletion in the asteroid belt or produce the observed radial mixing of different asteroid taxonomic types. Second, we study the effects of planetary embryos embedded in the primordial asteroid belt. These embedded planetary embryos, combined with the action of jovian and saturnian resonances, can lead to dynamical excitation and radial mixing comparable to the current asteroid belt. The mass depletion driven by embedded planetary embryos alone, even in the case of an eccentric Jupiter and Saturn, is roughly 10-20× less than necessary to explain the current mass of the main belt, and thus a secondary depletion event, such as that which occurs naturally in the Nice Model, is required. We discuss the implications of our new simulations for the dynamical and collisional evolution of the main belt.     

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.     

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.     

Global survey of color variations on 433 Eros: Implications for regolith processes and asteroid environments

High-resolution imaging acquired with the Near Earth Asteroid Rendezvous Shoemaker (NEAR Shoemaker) spacecraft is used to elucidate the spectral properties and spatial distribution of color units on Asteroid 433 Eros. Previous workers mapped four distinct types of color units on the surface (bright streaks, dark soils, ponded materials, average regolith). These units exhibit albedo and color boundaries but there is no evidence to indicate they represent distinct rock types. Rather the units are thought to show evidence of complex regolith transport and sorting processes. Here we report the results of a comprehensive study of all viable color MultiSpectral Imager (MSI) data to identify and characterize the distribution and nature of color units across the whole asteroid. Due to a spacecraft upset that resulted in contamination of the MSI optics, color images are affected with a scattered light problem that hampers interpretation of subtle color contrasts, even after a rigorous remediation. To constrain interpretations of the MSI color data we characterize this residual scattered light and demonstrate how complete correction would affect derived color ratios. Results of our comprehensive study are consistent with previous mapping—confirming that bright streaks, average regolith and dark soils fall on a mixing line, consistent with space weathering effects. We find that the ponded deposits do not fall on this putative mixing line. The color and reflectance of the ponded deposits are consistent with some combination of compositional, grain size and maturity variations from the average regolith. Additionally we show that spectral separation of the four units on ratio plots would only increase with full removal of residual scattered light, especially for features that are small in terms of pixels. Global analysis of the Eros color units illustrates complex regolith processes and grain sorting that may hold clues to understanding space weathering processes and the link between asteroids and meteorites.