Deep Impact photometry of Comet 9P/Tempel 1

The photometric properties of the nucleus of Comet 9P/Tempel 1 are studied from the disk-resolved color images obtained by Deep Impact (DI). Comet Tempel 1 has typical photometric properties for comets and dark asteroids. The disk-integrated spectrum of the nucleus of Tempel 1 between 309 and 950 nm is linear without any features at the spectral resolution of the filtered images. At V-band, the red slope of the nucleus is 12.5±1% per 100 nm at 63° phase angle, translating to B-V=0.84±0.01, V-R=0.50±0.01, and R-I=0.49±0.02. No phase reddening is confirmed. The phase function of the nucleus of Tempel 1 is constructed from DI images and earlier ground-based observations found from the literature. The phase coefficient is determined to be β=0.046±0.007 mag/deg between 4° and 117° phase angle. Hapke's theoretical scattering model was used to model the photometric properties of this comet. Assuming a single Henyey-Greenstein function for the single-particle phase function, the asymmetry factor of Tempel 1 was fitted to be g=−0.49±0.02, and the corresponding single-scattering albedo (SSA) was modeled to be 0.039±0.005 at 550 nm wavelength. The SSA spectrum shows a similar linear slope to that of the disk-integrated spectrum. The roughness parameter is found to be 16°±8°, and independent of wavelength. The Minnaert k parameter is modeled to be 0.680±0.014. The photometric variations on Tempel 1 are relatively small compared to other comets and asteroids, with a ∼20% full width at half maximum of albedo variation histogram, and ∼3% for color. Roughness variations are evident in one small area, with a roughness parameter about twice the average and appearing to correlate with the complex morphological texture seen in high-resolution images.     

Near-infrared spectrophotometry of Asteroid 25143 Itokawa from NIRS on the Hayabusa spacecraft

A photometric analysis of the S-type Asteroid 25143 Itokawa is performed over multiple wavelengths ranging from 0.85 to 2.10 μm based on disk-resolved reflectance spectra obtained with the Hayabusa near-infrared spectrometer (NIRS). We derive the global photometric properties of Itokawa in terms of Hapke's photometric model. We find that Itokawa has a single-scatter albedo that is 35-40% less than that of Asteroid 433 Eros. Itokawa also has a single-particle phase function that is more strongly back-scattering than that of Eros. Despite its hummocky surface strewn with large boulders, Itokawa exhibits an opposition effect. However, the total amplitude of the opposition surge for Itokawa was estimated to be less than unity while Eros and other S-type asteroids have been found to have model values exceeding unity. The wavelength dependence of the opposition surge width reveals that coherent backscatter contributes to the opposition effect on Itokawa's surface. The photometric roughness of Itokawa is well constrained to a value of 26° ± 1° which is similar to Eros, suggesting that photometric roughness models the smallest surface roughness scale for which shadows exist.     

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.     

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-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.     

Asteroid Observations at Low Phase Angles: II. 5 Astraea, 75 Eurydike, 77 Frigga, 105 Artemis, 119 Althaea, 124 Alkeste, and 201 Penelope

The results of photometric observations of seven main-belt asteroids with moderate surface albedos are presented. New magnitude-phase dependences were obtained for these asteroids: 5 Astraea (down to a phase angle of 0.3°, S type), 75 Eurydike (0.1°, M), 77 Frigga (0.9°, M), 105 Artemis (0.3°, C), 119 Althaea (0.3°, S), 124 Alkeste (0.1°, S), and 201 Penelope (0.5°, M). The parameters of approximating functions and the amplitudes of the opposition effect of these asteroids were determined. The obtained data allowed us to improve values of the rotation periods for some of them: 5 Astraea (16.815±0.002 h), 105 Artemis (18.56±0.01 h), 119 Althaea (11.466±0.001 h), and 124 Alkeste (9.907±0.001 h).     

Global photometric properties of Asteroid (4) Vesta observed with Dawn Framing Camera

Dawn spacecraft orbited Vesta for more than one year and collected a huge volume of multispectral, high-resolution data in the visible wavelengths with the Framing Camera. We present a detailed disk-integrated and disk-resolved photometric analysis using the Framing Camera images with the Minnaert model and the Hapke model, and report our results about the global photometric properties of Vesta. The photometric properties of Vesta show weak or no dependence on wavelengths, except for the albedo. At 554 nm, the global average geometric albedo of Vesta is 0.38 ± 0.04, and the Bond albedo range is 0.20 ± 0.02. The bolometric Bond albedo is 0.18 ± 0.01. The phase function of Vesta is similar to those of S-type asteroids. Vesta’s surface shows a single-peaked albedo distribution with a full-width-half-max ∼17% relative to the global average. This width is much smaller than the full range of albedos (from ∼0.55× to >2× global average) in localized bright and dark areas of a few tens of km in sizes, and is probably a consequence of significant regolith mixing on the global scale. Rheasilvia basin is ∼10% brighter than the global average. The phase reddening of Vesta measured from Dawn Framing Camera images is comparable or slightly stronger than that of Eros as measured by the Near Earth Asteroid Rendezvous mission, but weaker than previous measurements based on ground-based observations of Vesta and laboratory measurements of HED meteorites. The photometric behaviors of Vesta are best described by the Hapke model and the Akimov disk-function, when compared with the Minnaert model, Lommel–Seeliger model, and Lommel–Seeliger–Lambertian model. The traditional approach for photometric correction is validated for Vesta for >99% of its surface where reflectance is within ±30% of global average.     

Keck observations of near-Earth asteroids in the thermal infrared

We present the results of thermal-infrared observations of 20 near-Earth asteroids (NEAs) obtained in the period March 2000-February 2002 with the 10-m Keck-I telescope on Mauna Kea, Hawaii. The measured fluxes have been fitted with thermal-model emission continua to determine sizes and albedos. This work increases the number of NEAs having measured albedos by 35%. The spread of albedos derived is very large (p_v=0.02−0.55); the mean value is 0.25, which is much higher than that of observed main-belt asteroids. In most cases the albedos are in the ranges expected for the spectral types, although some exceptions are evident. Our results are consistent with a trend of increasing albedo with decreasing size for S-type asteroids with diameters below 20 km. A number of objects are found to have unexpectedly low apparent color temperatures, which may reflect unusual thermal properties. However, the results from our limited sample suggest that high thermal-inertia, regolith-free objects may be uncommon, even amongst NEAs with diameters of less than 1 km. We discuss the significance of our results in the light of information on these NEAs taken from the literature and the uncertainties inherent in applying thermal models to near-Earth asteroids.     

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.     

A survey of Karin cluster asteroids with the Spitzer Space Telescope

The Karin cluster is one of the youngest known families of main-belt asteroids, dating back to a collisional event only 5.8±0.2 Myr ago. Using the Spitzer Space Telescope we have photometrically sampled the thermal continua (3.5-22 μm) of 17 Karin cluster asteroids of different sizes, down to the smallest members discovered so far, in order to make the first direct measurements of their sizes and albedos and study the physical properties of their surfaces. Our targets are also amongst the smallest main-belt asteroids observed to date in the mid-infrared. The derived diameters range from 17.3 km for 832 Karin to 1.5 km for 75176, with typical uncertainties of 10%. The mean albedo is pv=0.215±0.015, compared to 0.20±0.07 for 832 Karin itself (for H=11.2±0.3), consistent with the view that the Karin asteroids are closely related physically as well as dynamically. The albedo distribution (0.12?pv?0.32) is consistent with the range associated with S-type asteroids but the variation from one object to another appears to be significant. Contrary to the case for near-Earth asteroids, our data show no evidence of an albedo dependence on size. However, the mean albedo is lower than expected for young, fresh “S-type” surfaces, suggesting that space weathering can darken main-belt asteroid surfaces on very short timescales. Our data are also suggestive of a connection between surface roughness and albedo, which may reflect rejuvenation of weathered surfaces by impact gardening. While the available data allow only estimates of lower limits for thermal inertia, we find no evidence for the relatively high values of thermal inertia reported for some similarly sized near-Earth asteroids. Our results constitute the first observational confirmation of the legitimacy of assumptions made in recent modeling of the formation of the Karin cluster via a single catastrophic collision 5.8±0.2 Myr ago.     

Radar Observations of Asteroid 3908 Nyx

We report Doppler-only (cw) radar observations of basaltic near-Earth asteroid 3908 Nyx obtained at Arecibo and Goldstone in September and October of 1988. The circular polarization ratio of 0.75±0.03 exceeds ∼90% of those reported among radar-detected near-Earth asteroids and it implies an extremely rough near-surface at centimeter-to-decimeter spatial scales. Echo power spectra over narrow longitudinal intervals show a central dip indicative of at least one significant concavity. Inversion of cw spectra yields two statistically indistinguishable shape models that have similar shapes and dimensions but pole directions that differ by ∼100°. We adopt one as our working model and explore its implications. It has an effective diameter of 1.0±0.15 km and radar and visual geometric albedos of 0.15±0.075 and 0.16^+0.08_−0.05. The visual albedo supports the interpretation by D. P. Cruikshank et al. (1991, Icarus89, 1-13) that Nyx has a thermal inertia consistent with that of bare rock. The model is irregular, modestly asymmetric, and topographically rugged.     

Thermal infrared and optical observations of four near-Earth asteroids

We present thermal infrared photometry and spectrophotometry of four near-Earth asteroids (NEAs), namely (433) Eros, (66063) 1998 RO₁, (137032) 1998 UO₁, and (138258) 2000 GD₂, using the United Kingdom Infrared Telescope (UKIRT) in 2002. For two objects, i.e. (433) Eros and (137032) 1998 UO₁, quasi-simultaneous optical observations were also obtained, using the Jacobus Kapteyn Telescope (JKT). For (127032) 1998 UO₁, we obtain a rotation period P=3.0±0.1 h and an absolute visual magnitude HV=16.7±0.4. The Standard Thermal Model (STM), Fast Rotating Model (FRM) and near-Earth asteroid Thermal Model (NEATM) have been fitted to the IR fluxes to determine effective diameters Deff, geometric albedos pv, and beaming parameters η. The derived values are (433) Eros: Deff=23.3±3.5 km (at lightcurve maximum), pv=0.24±0.07, η=0.95±0.19; (66063) 1998 RO₁: , ; (137032) 1998 UO₁: Deff<1.13 km, pv>0.29; (138258) 2000 GD₂: Deff=0.27±0.04 km, , η=0.74±0.15. (66063) 1998 RO₁ is a binary asteroid from lightcurve characteristics [Pravec, P., and 56 colleagues, 2006. Icarus 181, 63-93] and we estimate the effective diameter of the primary (Dp) and secondary (Ds) components: and . The diameter and albedo of (138258) 2000 GD₂ are consistent with the trend of decreasing diameter for S- and Q-type asteroids found by Delbó et al. [Delbó, M., Harris, A.W., Binzel, R.P., Pravec, P., Davies, J.K., 2003. Icarus 166, 116-130]. A possible trend of increasing beaming parameter with diameter for small (less than about 3 km) S- and Q-type asteroids is found.     

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.     

Albedo and size determination of potentially hazardous asteroids: (99942) Apophis

The near-Earth object (99942) Apophis will make an extremely close approach to the Earth in 2029, and currently has approximately a one-in-45,000 chance of impacting our planet in 2036 (JPL Sentry, November 2006). Computation of the orbital evolution of this object is limited by insufficient knowledge of physical properties required to determine the role played by non-gravitational effects. Using polarimetric observations, we have obtained the first reliable determination of the albedo of Apophis, obtaining 0.33±0.08. We also derive an updated estimate of the asteroid's absolute magnitude: H=19.7±0.4. Using this albedo and H, we find that Apophis has a diameter of 270±60 m, slightly smaller than preliminary estimates based upon an assumed albedo. Our observations demonstrate the feasibility of polarimetric observations aimed at obtaining albedos and sizes of small, potentially hazardous asteroids.     

Properties of the Hermean Regolith: II. Disk-Resolved Multicolor Photometry and Color Variations of the “Unknown” Hemisphere

Multicolor photometric observations of the “unknown” hemisphere of Mercury have been performed with the Swedish Vacuum Solar Telescope on La Palma at maximal elongations from the Sun in 1997 and 1998. A set of six interference filters with central wavelengths from 450 to 940 nm were used. Multicolor photometry of Mercury was performed on disk-resolved images of the unknown hemisphere (longitudes 160°-340°) with a highest resolution of ∼200 km (J. Warell and S. Limaye 2001, Planet. Space Sci.49, 1531-1552).Disk-integrated spectrophotometry shows that (1) the spectrum of Mercury displays a linear slope from 650 to 940 nm, indicating that the average mercurian regolith is considerably more mature than relatively immature pure anorthosite regions on the Moon; (2) there is negative evidence for the presence of the putative 1-μm absorption feature near 940 nm due to the presence of ferrous iron (Fe²⁺) in pyroxenes; and (3) no effect of phase reddening of the integrated disk is observed between phase angles of 63° and 84°.For the first time, disk-resolved spectrophotometry of Mercury's surface has been obtained, from which it is inferred that (4) the scattering properties of Mercury's regolith are more homogeneous than for the Moon and that there is no clear relation between reflectance and chemical properties at spatial scales of ∼300 km on the unknown hemisphere and (5) there exists an inverse relation of spectral slope with emission angle which is larger for Mercury than for the Moon, indicating that the average mercurian regolith is more backscattering and that this effect increases with wavelength.Finally, from filter ratio images of Mercury's disk it is found that (6) no color variations larger that 2% with respect to the surroundings are detected at a spatial resolution of ∼300 km.     

Asteroid observations at low phase angles: III. Brightness behavior of dark asteroids

The results of photometric observations of eight main-belt asteroids with low surface albedo are presented. The magnitude-phase dependences including low phase angles (<1 deg) have been obtained for Asteroids 76 Freia (down to phase angle 0.1 deg, P-type), 190 Ismene (0.3 deg, P-type), 303 Josephina (0.2 deg, C-type), 309 Fraternitas (0.1 deg, C-type), 313 Chaldaea (0.1 deg, C-type), 444 Gyptis (0.8 deg, P-type), 615 Roswitha (0.1 deg, C-type), and 954 Li (0.03 deg, FCX-type). The behavior of brightness in the range of opposition effect is found to be practically linear for 190 Ismene with amplitude of opposition effect only 0.03 mag. Amplitudes of the opposition effect for other asteroids are close to a mean for this type. The obtained data allowed us also to determine the rotation periods of asteroids: 303 Josephina (12.497±0.001 h), 309 Fraternitas (11.205±0.005 h), 615 Roswitha (4.422±0.001 h) and 954 Li (7.207±0.002 h). The color indexes B-V, V-R and R-I have been determined for some asteroids.     

Laboratory Study of the Bidirectional Reflectance of Powdered Surfaces: On the Asymmetry Parameter of Asteroid Photometric Data

We performed laboratory experiments on the bidirectional reflectance of powdered surfaces of dunite, graphite, and Allende (CV3) and Gao (H5) meteorites. The particle size of each sample varied from tens to hundreds of micrometers. The absolute bidirectional reflectance was determined for two ranges of phase angle: from 2° to 80° at 0° angle of incidence and from 2° to 155° at 75° angle of incidence. The phase angle was incremented every 1° in between 2° and 5° and every 10° between 10° and 150°. We determined the Hapke parameters and found that the values of the asymmetry parameter retrieved for most of the samples were positive when the coverage of the phase angle was wide, 2° to 155°, although the values derived from remote sensing instruments on asteroid flyby missions have been negative or nearly zero. Among our sample surfaces, only those of graphite, Allende, and Gao with particle sizes of hundreds micrometers show negative or nearly zero values. The single-scattering albedos determined for the Gao samples are comparable to the values of S-class asteroids, while those for the Allende samples are much larger than those of C-class asteroids.     

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.     

Determination of Shape, Gravity, and Rotational State of Asteroid 433 Eros

Prior to the Near Earth Asteroid Rendezvous (NEAR) mission, little was known about Eros except for its orbit, spin rate, and pole orientation, which could be determined from ground-based telescope observations. Radar bounce data provided a rough estimate of the shape of Eros. On December 23, 1998, after an engine misfire, the NEAR-Shoemaker spacecraft flew by Eros on a high-velocity trajectory that provided a brief glimpse of Eros and allowed for an estimate of the asteroid's pole, prime meridian, and mass. This new information, when combined with the ground-based observations, provided good a priori estimates for processing data in the orbit phase.After a one-year delay, NEAR orbit operations began when the spacecraft was successfully inserted into a 320×360 km orbit about Eros on February 14, 2000. Since that time, the NEAR spacecraft was in many different types of orbits where radiometric tracking data, optical images, and NEAR laser rangefinder (NLR) data allowed a determination of the shape, gravity, and rotational state of Eros. The NLR data, collected predominantly from the 50-km orbit, together with landmark tracking from the optical data, have been processed to determine a 24th degree and order shape model. Radiometric tracking data and optical landmark data were used in a separate orbit determination process. As part of this latter process, the spherical harmonic gravity field of Eros was primarily determined from the 10 days in the 35-km orbit. Estimates for the gravity field of Eros were made as high as degree and order 15, but the coefficients are determined relative to their uncertainty only up to degree and order 10. The differences between the measured gravity field and one determined from a constant density shape model are detected relative to their uncertainty only to degree and order 6. The offset between the center of figure and the center of mass is only about 30 m, indicating that Eros has a very uniform density (1% variation) on a large scale (35 km). Variations to degree and order 6 (about 6 km) may be partly explained by the existence of a 100-m, regolith or by small internal density variations. The best estimates for the J2000 right ascension and declination of the pole of Eros are α=11.3692±0.003° and δ=17.2273±0.006°. The rotation rate of Eros is 1639.38922±0.00015°/day, which gives a rotation period of 5.27025547 h. No wobble greater than 0.02° has been detected. Solar gravity gradient torques would introduce a wobble of at most 0.001°.