A Global Solution for the Gravity Field, Rotation, Landmarks, and Ephemeris of Eros

As part of the NEAR Radio Science investigation, a global solution that includes both spherical and ellipsoidal harmonic gravity fields of Eros, Eros pole and rotation rate, Eros ephemeris, and landmark positions from the optical data was generated. This solution uses the entire one-year in orbit collection of X-band radiometric tracking (Doppler and range) from the Deep Space Network and landmark tracking observations generated from the NEAR spacecraft images of Eros. When compared to a constant density shape model, the gravity field shows a nearly homogeneous Eros. The Eros landmark solutions are in good agreement with the Eros shape model, and they reduce the center-of-mass and center-of-figure offset in the z direction to 13 m. Most of the NEAR spacecraft orbits are determined in all directions to an accuracy of several meters. The solution for the ephemeris of Eros constrains the mass of Vesta to 18.2±0.4 km³/s² and reduces the uncertainty in the Earth-Moon mass ratio.     

Photometric analysis of Eros from NEAR data

A photometric model of (433) Eros at wavelengths from 450 to 1050 nm is constructed using the combination of the images from the multispectral imager (MSI) obtained during the one-year long orbital phase of the NEAR mission, ground-based lightcurves from earlier observations, and our theoretical forward modeling simulations coupled with the NEAR shape model. The single scattering albedo is found to be 0.33±0.03 at 550 nm, which is smaller than past findings by 30%. The amplitude and width of the opposition effect are 1.4±0.1 and 0.010±0.004 from ground based lightcurves. It is confirmed that the asymmetry factor of the single-particle phase function and the surface roughness parameter do not depend on wavelength from 450 to 1050 nm, and their values are estimated to be −0.25±0.02 and 28°±3°, respectively, comparable with the earlier measurements from the NEAR NIS data. The geometric albedo and the Bond albedo at 550 nm are calculated to be 0.23 and 0.093, respectively, which make Eros less reflective than previous models, but still slightly more reflective than average S-type asteroids. The lower albedos of Eros are more consistent with our forward modeling simulations, as well as with its spectrum. Eros is a typical S-type asteroid like (951) Gaspra and (243) Ida, and has similar surface regolith properties. Combining the single-scattering albedo with the olivine composition of ordinary chondrites, taking into account space weathering darkening, we constrain the grain size of the regolith particles on Eros to a range of 50 to 100 μm.     

NEAR Infrared Spectrometer Photometry of Asteroid 433 Eros

We present near-infrared spectrometer (NIS) observations (0.8 to 2.4 μm) of the S-type asteroid 433 Eros obtained by the NEAR Shoemaker spacecraft and report results of our Hapke photometric model analysis of data obtained at phase angles ranging from 1.2° to 111.0° and at spatial resolutions of 1.25×2.5 to 2.75×5.5 km/spectrum. Our Hapke model fits successfully to the NEAR spectroscopic data for systematic color variations that accompany changing viewing and illumination geometry. Model parameters imply a geometric albedo at 0.946 μm of 0.27±0.04, which corresponds to a geometric albedo at 0.550 μm of 0.25±0.05. We find that Eros exhibits phase reddening of up to 10% across the phase angle range of 0-100°. We observe a 10% increase in the 1-μm band depth at high phase angles. In contrast, we observe only a 5% increase in continuum slope from 1.486 to 2.363 μm and essentially no difference in the 2-μm band depth at higher phase angles. These contrasting phase effects imply that there are phase-dependent differences in the parametric measurements of 1- and 2-μm band areas, and in their ratio. The Hapke model fits suggest that Eros exhibits a weaker opposition surge than either 951 Gaspra or 243 Ida (the only other S-type asteroids for which we possess disk-resolved photometric observations). On average, we find that Eros at 0.946 μm has a higher geometric albedo and a higher single-scatter albedo than Gaspra or Ida at 0.56 μm; however, Eros's single-particle phase function asymmetry and average surface macroscopic roughness parameters are intermediate between Gaspra and Ida. Only two of the five Hapke model parameters exhibit a notable wavelength dependence: (1) The single-scatter albedo mimics the spectrum of Eros, and (2) there is a decrease in angular width of the opposition surge with increasing wavelength from 0.8 to 1.7 μm. Such opposition surge behavior is not adequately modeled with our shadow-hiding Hapke model, consistent with coherent backscattering phenomena near zero phase.     

Near-IR Reflectance Spectroscopy of 433 Eros from the NIS Instrument on the NEAR Mission: I. Low Phase Angle Observations

From February 13 to May 13, 2000, the near-infrared spectrometer (NIS) instrument on the Near Earth Asteroid Rendezvous (NEAR) spacecraft obtained more than 200,000 spatially resolved 800- to 2500-nm reflectance spectra of the S-type asteroid 433 Eros. An important subset of the spectra was obtained during a unique opportunity on February 13 and 14, when the NEAR spacecraft flew directly through the 0° phase angle point between Eros and the Sun just prior to the orbital insertion maneuver. This low phase flyby (LPF) dataset consists of ∼2000 spectra of the northern hemisphere of Eros, obtained from 1° to 47° phase angle and at spatial resolutions of between 6×12 km to 1.25×2.50 km per spectrum. The spectra were calibrated to radiance factor (I/F, where I=observed radiance and πF=solar input radiance) and then photometrically corrected to normal albedo. The average northern hemisphere spectrum of Eros is similar to the asteroid's unresolved telescopic spectrum and exhibits absorption features near 1000 nm (Band I) and 2000 nm (Band II) consistent with an orthopyroxene to orthopyroxene+olivine (opx+ol) mixing ratio of approximately 0.38±0.08. The ensemble of NIS LPF spectra falls primarily within the S(IV) to upper S(III) fields of the Gaffey et al. (1993) S-asteroid classification scheme and exhibits Band I and Band II properties similar to those of ordinary chondrite meteorites. While some small spatially coherent spectral variations have been detected, neither the opx/opx+ol) mixing ratio nor other spectral parameters vary spatially by more than ∼1σ across the entire northern hemisphere of the asteroid, suggesting a remarkable homogeneity of the composition and mineralogy of the uppermost regolith. Spectral mixture modeling suggests that the presence of glass and/or a reddening agent like nanophase iron, likely formed from exposure of the regolith to the space environment, is a component of the surface of Eros. Reddening and darkening components could also explain the dissimilarity in overall spectral slope and albedo between Eros and other S(IV) asteroids and ordinary chondrite meteorites. The largest (but still weak) spectral variations across the surface are seen in the depths of Band I and Band II, which are greatest in and around the largest craters and at the 0° longitude “nose” of the asteroid, and in the Band II/Band I area ratio between the large impact craters Psyche and Himeros. These subtle NIS spectral variations are usually associated with albedo and surface slope variations seen in NEAR imaging and topographic data and appear to be related to downslope movement of regolith materials.     

Disk-Integrated Photometry of 433 Eros

Analysis of the disk-integrated solar phase curve of 433 Eros, as derived from ground-based telescopic and NEAR Shoemaker spacecraft measurements, shows that Eros's surface properties are typical of average S-type asteroids. Eros displays the same single-particle scattering characteristics and porosity vs theoretical grain size relationships as typical S-asteroids, as does Ida. Eros's single-scattering albedo, however, is higher. The geometric albedo at 550 nm derived for Eros (0.29±0.02) is higher than Ida's but is equivalent to Gaspra's within the error bars. The phase integral (0.39±0.02) and Bond albedo (0.12±0.02) for Eros are higher than those estimated for average S-type asteroids but commensurate with the values obtained for Gaspra.     

Color Variations on Eros from NEAR Multispectral Imaging

NEAR multispectral imaging was obtained at seven wavelengths (450-1050 nm) to characterize hemispheric and regional color properties of Eros. The highest-resolution whole-disk data, 180 m/pixel, were obtained during the last pre-orbit insertion sequence on 12 February 2000. The same areas were imaged again in color at 10-20 m/pixel from high orbit in March-April 2000, and selected targets have been studied in color at resolutions as high as 4 m/pixel from low orbit. Whole-disk spectra are in close agreement with ground-based observations. These and the disk-resolved measurements show little variation in visible-wavelength color, but they do reveal spatial variation of several percent in the 950-nm/760-nm reflectance ratio, used here as a proxy for depth of the 1-μm olivine-pyroxene absorption band. After photometric correction to i=30° e=0° using both a Hapke correction and a modified empirical phase function, the disk-resolved images show reproducible spatial variations in albedo and 950-nm/760-nm reflectance ratio. The northern hemisphere exhibits average reflectances at i=30°, e=0° of 0.136±0.007 at 760 nm and 0.115±0.006 at 950 nm, equivalent to geometric albedos of 0.30±0.02 and 0.26±0.02, respectively. There is more than factor of 2 spatial variation in reflectance, but only about 10% variation in the 950-nm/760-nm reflectance ratio. Reflectance and color ratio are highly correlated, with the highest reflectances in discrete, sharp-edged patches on slopes exceeding 20°, consistent with material being exposed by downslope movement. Eros is also conspicuously deficient in small, bright, spectrally distinctive craters which are found on the other two S asteroids, Gaspra and Ida, imaged by spacecraft at close range. Eros exhibits a larger range of albedos than other S asteroids, but its color variations are much more subtle: variation in the 950-nm/760-nm reflectance ratio with 760-nm reflectance is several times less than on those asteroids or in the lunar maria. Of the different mechanisms possibly responsible for reflectance and color differences on Eros, spatial differences in the extent of regolith aging by space weathering are most consistent with Eros's observed properties. However, the effects of this process are both qualitatively and quantitatively different than in the lunar maria.     

Implementation of the First Asteroid Landing

Spacecraft have successfully landed on the Moon, Venus, and Mars, and have penetrated the atmosphere of Jupiter. On 2001 February 12, the Near-Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft landed on the surface of the asteroid (433) Eros after a year of observations in orbit about the asteroid. NEAR Shoemaker was not designed to land on an asteroid, complicating the design of operations needed to accomplish this feat. However, the NEAR Shoemaker team wanted to attempt a landing after the year of orbital operations that consumed most of the remaining spacecraft fuel, operations funding, and planned Deep Space Network tracking. This would be a fitting end to the mission, and it would be possible to obtain images at much greater resolution during the descent than could be obtained from orbit. The operations were more successful than the NEAR Shoemaker team had hoped, obtaining 70 high-resolution images during the descent and two weeks of gamma-ray spectrometer data from the surface after the successful soft landing.     

Direct measurement of the size, shape, and pole of 511 Davida with Keck AO in a single night

Using the high-quality data set of 165 images taken at 11 epochs over the 5.13 h rotation of the large C-type Asteroid 511 Davida, we find the dimensions of its triaxial ellipsoid model to be 357±2×294±2×231±50 km. The images were acquired with the adaptive optics system on the 10 m Keck II telescope on December 27, 2002. The a and b diameters are much better determined than previously estimated from speckle interferometry and indirect measurements, and our mean diameter, (abc)^1/3=289±21 km, is 19% below previous estimates. We find the pole to lie within 2° of [RA=295°; Dec=0°] or in Ecliptic coordinates [λ=297°; β=+21°], a significant improvement to the pole direction. Otherwise, previous determinations of the axial ratios agree with our new results. These observations illustrate that our technique of finding the dimensions and pole of an asteroid from its changing projected size and shape is very powerful because it can be done in essentially one night as opposed to decades of lightcurves. Average departures of 3% (5 km) of the asteroid's mean radius from a smooth outline are detected, with at least two local positive-relief features and at least one flat facet showing approximately 15 km deviations from the reference best-fit ellipsoid. The facet is reminiscent of large global-scale craters on Asteroid 253 Mathilde (also a C-type) when seen edge-on in close-up images from the NEAR mission flyby. We show that giant craters (up to 150 km diameter, the size of the largest facets seen on Davida) can be expected from the impactor size distribution, without likelihood of catastrophic disruption of Davida.     

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.     

Forced obliquities and moments of inertia of Ceres and Vesta

We examine models of secular variations in the orbit and spin poles of Ceres and Vesta, the two most massive bodies in the main asteroid belt. If the spin poles are fully damped, then the current values of obliquity, or angular separation between spin and orbit poles, are diagnostic of the moments of inertia and thus indicative of the extent of differentiation of these bodies. Using existing shape models and assuming uniform density, the present obliquity values are predicted to be 12.31° for Ceres and 15.66° for Vesta. Part of this difference is related to differing orbital inclinations; a more centrally condensed internal structure would yield more rapid spin pole precession, and larger obliquity. Time scales for tidal damping are expected to be rather long. However, at least for Vesta, current estimates of the spin pole location are consistent with its obliquity being fully damped. When the degree two gravity coefficients and spin pole orientations are determined by the Dawn spacecraft, it will allow accurate determination of the moments of inertia of these bodies, assuming the obliquities are damped.     

Elemental composition of 433 Eros: New calibration of the NEAR-Shoemaker XRS data

We present a new calibration of the elemental-abundance data for Asteroid 433 Eros taken by the X-ray spectrometer (XRS) aboard the NEAR-Shoemaker spacecraft. (NEAR is an acronym for “Near-Earth Asteroid Rendezvous.”) Quantification of the asteroid surface elemental abundance ratios depends critically on accurate knowledge of the incident solar X-ray spectrum, which was monitored simultaneously with asteroid observations. Previously published results suffered from incompletely characterized systematic uncertainties due to an imperfect ground calibration of the NEAR gas solar monitor. The solar monitor response function and associated uncertainties have now been characterized by cross-calibration of a large sample of NEAR solar monitor flight data against contemporary broadband solar X-ray data from the Earth-orbiting GOES-8 (Geostationary Operational Environmental Satellite). The results have been used to analyze XRS spectra acquired from Eros during eight major solar flares (including three that have not previously been reported). The end product of this analysis is a revised set of Eros surface elemental abundance ratios with new error estimates that more accurately reflect the remaining uncertainties in the solar flare spectra: Mg/Si=0.753+0.078/−0.055, Al/Si=0.069±0.055, S/Si=0.005±0.008, Ca/Si=0.060+0.023/−0.024, and Fe/Si=1.678+0.338/−0.320. These revised abundance ratios are consistent within cited uncertainties with the results of Nittler et al. [Nittler, L.R., and 14 colleagues, 2001. Meteorit. Planet. Sci. 36, 1673-1695] and thus support the prior conclusions that 433 Eros has a major-element composition similar to ordinary chondrites with the exception of a strong depletion in sulfur, most likely caused by space weathering.     

Apollo 15 gravity analysis from theS-band transponder experiment

TheS-Band Transponder experiment used precision doppler tracking data of the command and service module, the lunar module and the subsatellite to provide detailed information about the near side gravity field. No special instruments are required other than the existingS-Band transponder used for real time navigation. The data consists of variations in the spacecraft speed as measured by the earth-based radio tracking system, which has a resolution of 0.65 mm/s.Initial data reduction has been concentrated on the low altitude CSM data ( 20 km) which provides new detailed gravity profiles of the Serenitatis and Crisium mascons. The results are in good agreement with Apollo 14 analysis and strongly suggest that the mascons are near surface features with a mass distribution per unit area of approximately 800 kg/cm². The Apennines reveal themselves as a local gravity high of 85 mgal and Marius Hills likewise have a gravity high of 62 mgal.The subsatellite data is too sparse at present to definitely determine new gravity anomaly locations. The spacecraft is functioning well and a dense data block is being obtained, which will provide a new gravity map from ±95° longitude to ±30 latitude. Since periapsis altitudes are following relatively close to predicted altitudes, it seems fairly safe at this point to believe the subsatellite lifetime will be at least one year.     

The NEAR‐Shoemaker x‐ray/gamma‐ray spectrometer experiment: Overview and lessons learned

Abstract— The near‐Earth asteroid rendezvous (NEAR)‐Shoemaker remote‐sensing x‐ray/gamma‐ray spectrometer (XGRS) completed more than a year of operation in orbit and on the surface of 433 Eros. Elemental compositions for a number of regions on the surface of Eros have been derived from analyses of the characteristic x‐ray and gamma‐ray emission spectra. The NEAR XGRS detection system was included as part of the interplanetary network (IPN) for the detection and localization of gamma‐ray bursts (GRBs). Preliminary results for both the elemental composition of the surface of Eros and the detection of GRBs have been obtained. In addition to the science results, the design and operation of the NEAR XGRS is considered. Significant information important for the design of future remote sensing XGRS systems has been obtained and evaluated. We focus on four factors that became particularly critical during NEAR: (1) overall spacecraft design, (2) selection of materials, (3) increase of the signal‐to‐noise ratio and (4) knowledge of the incident solar x‐ray spectrum.     

The shape distribution of boulders on Asteroid 25143 Itokawa: Comparison with fragments from impact experiments

Laboratory impact experiments have found that the shape of fragments over a broad size range is distributed around the mean value of the axial ratio 2:√2:1, which is independent of a wide range of experimental conditions. We report the shape statistics of boulders with size of 0.1-30 m on the surface of Asteroid 25143 Itokawa based on high-resolution images obtained by the Hayabusa spacecraft in order to investigate whether their shape distribution is similar to the distribution obtained for fragments (smaller than 0.1 m) in laboratory impact experiments. We also investigated the shapes of boulders with size of 0.1-150 m on Asteroid 433 Eros using a few arbitrary selected images by the NEAR spacecraft, in order to compare those with the shapes on Asteroid Itokawa. In addition, the shapes of small- and fast-rotating asteroids (diameter <200 m and rotation period <1 h), which are natural fragments from past impact events among asteroids, were inferred from archived light curve data taken by ground-based telescopes. The results show that the shape distributions of laboratory fragments are similar to those of the boulders on Eros and of the small- and fast-rotating asteroids, but are different from those on Itokawa. However, we propose that the apparent difference between the boulders of Itokawa and the laboratory fragments is due to the migration of boulders. Therefore, we suggest that the shape distributions of the boulders ranging from 0.1 to 150 m in size and the small- and fast-rotating asteroids are similar to those obtained for the fragments generated in laboratory impact experiments.     

Radar observations and a physical model of Asteroid 4660 Nereus, a prime space mission target

Near-Earth Asteroid 4660 Nereus has been identified as a potential spacecraft target since its 1982 discovery because of the low delta-V required for a spacecraft rendezvous. However, surprisingly little is known about its physical characteristics. Here we report Arecibo (S-band, 2380-MHz, 13-cm) and Goldstone (X-band, 8560-MHz, 3.5-cm) radar observations of Nereus during its 2002 close approach. Analysis of an extensive dataset of delay-Doppler images and continuous wave (CW) spectra yields a model that resembles an ellipsoid with principal axis dimensions X=510±20 m, Y=330±20 m and . The pole direction is approximately located at ecliptic pole longitude and latitude of λ=+25°, β=+80° with the uncertainty radius of 10°. Our modeling yields a refined rotation period of 15.16±0.04 h. Nereus has a circular polarization (SC/OC) ratio of 0.74±0.08, which implies substantial near-surface centimeter-to-decimeter scale roughness. Dynamical analysis of our model suggests that YORP alteration of the rotation period may become evident within a few years. Nereus has two stable synchronous orbits where natural material may remain in orbit, while most asteroids observed to date do not have such stable synchronous orbits. We also find that spacecraft orbits about Nereus are feasible.     

The geology of 433 Eros

Abstract— The global high‐resolution imaging of asteroid 433 Eros by the Near‐Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft has made it possible to develop the first comprehensive picture of the geology of a small S‐type asteroid. Eros displays a variety of surface features, and evidence of a substantial regolith. Large scale facets, grooves, and ridges indicate the presence of at least one global planar structure. Directional and superposition relations of smaller structural features suggest that fracturing has occurred throughout the object. As with other small objects, impact craters dominate the overall shape as well as the small‐scale topography of Eros. Depth/diameter ratios of craters on Eros average ～0.13, but the freshest craters approach lunar values of ～0.2. Ejecta block production from craters is highly variable; the majority of large blocks appear to have originated from one 7.6 km crater (Shoemaker). The interior morphology of craters does not reveal the influence of discrete mechanical boundaries at depth in the manner of craters formed on lunar mare regolith and on some parts of Phobos. This lack of mechanical boundaries, and the abundant evidence of regolith in nearly every high‐resolution image, suggests a gradation in the porosity and fracturing with depth. The density of small craters is deficient at sizes below ～200 m relative to predicted slopes of empirical saturation. This characteristic, which is also found on parts of Phobos and lunar highland areas, probably results from the efficient obliteration of small craters on a body with significant topographic slopes and a thick regolith. Eros displays a variety of regolith features, such as debris aprons, fine‐grained “ponded” deposits, talus cones, and bright and dark streamers on steep slopes indicative of efficient downslope movement of regolith. These processes serve to mix materials in the upper loose fragmental portion of the asteroid (regolith). In the instance of “ponded” materials and crater wall deposits, there is evidence of processes that segregate finer materials into discrete deposits. The NEAR observations have shown us that surface processes on small asteroids can be very complex and result in a wide variety of morphologic features and landforms that today seem exotic. Future missions to comets and asteroids will surely reveal still as yet unseen processes as well as give context to those discovered by the NEAR Shoemaker spacecraft.     

Elemental composition from gamma‐ray spectroscopy of the NEAR‐Shoemaker landing site on 433 Eros

Abstract— Elemental composition and composition ratios derived from gamma‐ray measurements collected by the NEAR‐Shoemaker spacecraft while on the surface of 433 Eros are reported. Performance of the gamma‐ray spectrometer (GRS) during cruise and orbit is reviewed. The best gamma‐ray data were collected on the surface of Eros after the spacecraft's controlled descent on 2001 February 12. Methods used in spectral analysis, to convert peak areas to incident photons, and photons to elemental composition are described in some detail. The elemental abundance of K and the Mg/Si, Fe/Si, Si/O and Fe/O abundance ratios were determined. The Mg/Si and Si/O ratios and the K abundance are roughly chondritic, but the Fe/Si and Fe/O ratios are low compared to expected chondritic values. Three possible explanations for the apparent Fe depletion are considered.     

Small-Scale Topography of 433 Eros from Laser Altimetry and Imaging

The NEAR laser rangefinder (NLR) obtained more than 16 million range returns from asteroid 433 Eros. We present the first results from analyses of topographic profiles interpreted with the aid of simultaneous, boresighted images obtained by the NEAR multispectral imager (MSI). The location of the NLR boresight relative to that of MSI is determined by detailed correlations of ranging data and simultaneous images, including cases where the laser boresight slewed off and on the limb of the asteroid and cases where the laser illuminated a boulder close to the time of an image. In the data presented, the precision of the range measurements is about 1 m, with the minimum spot diameter under 5 m, and successive spots are contiguous or overlapping. Elevation on the irregular object Eros is given with respect to the gravitational and centrifugal potential. Landslides in craters are characterized. Possible crater benches are identified. Examples of infilled craters are presented. These observations suggest a depth of unconsolidated regolith, which is subject to sliding, of typically a few tens of meters. An example of structurally controlled cratering is presented. Examples of tectonic features are described. Surface roughness on Eros is approximately self-affine from scales of a few meters to hundreds of meters. A comparison of fractal statistics shows that Eros is extremely rough on observed scales, when compared to terrestrial a'a lava on submeter scales and undisturbed lunar regolith on subcentimeter scales.     

Spin axis of (2953) Vysheslavia and its implications

Photometric observations made during the years 2000-2005 are used to determine the pole orientation of (2953) Vysheslavia, a ?15-km size member of the Koronis family. We find admissible solutions for ecliptic latitude and longitude of the rotation pole P₃: βp=−64°±10° and λp=11°±8° or P₄: βp=−68°±8° and λp=192°±8°. These imply obliquity values γ=154°±14° and γ=157°±11°, respectively. The sidereal rotation period is Psid=0.2622722±0.0000018 day. This result is interesting for two reasons: (i) the obliquity value between 90° and 180° is consistent with a prediction done by Vokrouhlický et al. [Vokrouhlický, D., Bro?, M., Farinella, P., Kne?evi?, Z., 2001. Icarus 150, 78-93] that Vysheslavia might have been transported to its unstable orbit by the Yarkovsky effect, and (ii) with the obliquity close to 180°, Vysheslavia seems to belong to one of the two distinct groups in the Koronis family found recently by Slivan [Slivan, S.M., 2002. Nature 419, 49-51], further supporting the case of dichotomy in the spin axis distribution in this family. We also argue against the possibility that Vysheslavia reached its current orbit by a recent collisional breakup.     

An Estimate of Eros's Porosity and Implications for Internal Structure

Earth-based spectral measurements and NEAR Shoemaker magnetometer, X-ray, and near-infrared spectrometer data are all consistent with Eros having a bulk composition and mineralogy similar to ordinary chondrite meteorites (OC). By comparing the bulk density of 433 Eros (2.67±0.03 g/cm³) with that of OCs (3.40 g/cm³), we estimate the total porosity of the asteroid to be 21-33%. Macro (or structural) porosity, best estimated to be ∼20%, is constrained to be between 6 and 33%. We conclude that Eros is a heavily fractured body, but we find no evidence that it was ever catastrophically disrupted and reaccumulated into a rubble pile.