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.     

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.     

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.     

Spectral properties and geologic processes on Eros from combined NEAR NIS and MSI data sets

Abstract— From April 24 to May 14, 2000, the Near Earth Asteroid Rendezvous (NEAR) Shoemaker mission's near infrared spectrometer (NIS) obtained its highest resolution data of 433 Eros. High signal‐to‐noise ratio NIS reflectance spectra cover a wavelength range of 800–2400 nm, with footprint sizes from 213 times 427 m to 394 times 788 m. This paper describes improvement in instrument calibration by remediation of internally scattered light; derivation of a “pseudo channel” for NIS at 754 nm using Multispectral Imager (MSI) Eros approach maps at 951 and 754 nm; synthesis of a 3127‐spectrum high‐resolution data set with the improved calibration and expanded wavelength coverage; and investigation of global and localized spectral variation with respect to mineralogy, composition, and space weathering of Eros, comparing the findings with previous analyses. Scattered light removal reduces the “red” slope of Eros spectra, though not to the level seen by telescopic observations. The pseudo channel completes sampling of Eros' 1 micron (Band I) absorption feature, enabling direct comparison of NIS data with other asteroid and meteorite spectra without additional scaling or correction. Following scattered light removal and wavelength range extension, the spectral parameters of average Eros plot well inside the S(IV) field of Gaffey et al. (1993) and are consistent with the L6 chondrite meteorite fields of Gaffey and Gilbert (1998). Although Eros shows no evidence of mineralogical heterogeneity, modest spectral variations correlate with morphologically and geographically distinct areas of the asteroid. Eros bright‐to‐dark spectral ratios are largely consistent with laboratory “space weathering” experiment results and modeling of space weathering effects. Eros brightness variation unaccompanied by significant spectral variation departs from “lunar‐type”—where band depths, slopes, and albedoes all correlate—and “Ida‐type”—where significant spectral variation is unaccompanied by corresponding brightness variation. The brightest areas on Eros—steep crater walls—have lesser spectral slope and deeper Band I, consistent with exposure of “fresher,” less space weathered materials. Bright crater slope materials have opx/(opx + olv) of 0.24–0.29 and may be more representative of the subsurface mineralogy than “average” Eros, which is probably affected by space weathering. The floors of the large craters Psyche and Himeros have lower albedo and contain the most degraded or altered looking materials. NIS spectra retain a “red” spectral slope at greater than 2 microns. The recalibrated and expanded NIS spectra show better agreements with mixing models based on space weathering of chondritic mixtures.     

Spectrophotometry (0.33 to 1.07 μm) of 433 Eros and compositional implications

The spectral reflectance (0.33–1.07 μm) for the asteroid 433 Eros was determined as a function of rotational phase during January 28–30, and February 15, 1975. Interpretation of absorption features suggests Eros is composed of an undifferentiated assemblange of moderate to high temperature minerals (iron, pyroxene, and olivine, but no carbon). H-type ordinary chondrites are such assemblages, but it would be premature to conclude that Eros is like an H chondrite meteorite in composition until a better understanding is reached of possible physical differences between laboratory powders and asteroid regoliths for metal-bearing assemblages. There are no large-scale major compositional variations on the different sides of Eros.     

Ponded deposits on asteroid 433 Eros

Abstract— In late January 2001 the NEAR—Shoemaker spacecraft performed low‐altitude passes over the surface of 433 Eros. Coordinated observations of the asteroid surface were obtained at submeter resolution by the NEAR laser rangefinder and the multispectral imager. This paper presents three independent, coordinated observations of a 90 m pond adjacent to a granular debris flow, including the highest resolution altimetric measurements of ponded deposits on Eros. The ponded deposits appear to have been emplaced by fluid‐like motion of dry asteroidal regolith. A simple model of seismic agitation from impacts is developed to account for pond formation on Eros. The model predicts that ponds should form readily on Eros but not on the Moon, where ponds are not observed. The model also suggests that the absence of observable ponds in the largest craters of Eros, as well as on Phobos and Deimos, may be related to regolith depth.     

Dust transport in photoelectron layers and the formation of dust ponds on Eros

We investigate the electrostatic transport of charged dust in the photoelectron layer over the dayside surface of an asteroid. Micron-sized dust particles may be levitated above the surface in the photoelectron layer. Horizontal transport within the layer can then lead to net deposition of dust into shadowed regions where the electric field due to the photoelectron layer disappears. We apply a 2D numerical model simulating charged dust dynamics in the near-surface daytime plasma environment of Asteroid 433 Eros to the formation of dust deposits in craters. We find that dust tends to collect in craters and regions of shadow. This electrostatic dust transport mechanism may contribute to the formation of smooth dust ponds observed by the NEAR-Shoemaker spacecraft at Eros. The size distribution of transported dust depends on the particle density and work function, and the work function of the surface and solar wind electron temperature and density. With reasonable values for these parameters, μm-sized and smaller particles are levitated at Eros. Micrometeoroid bombardment is not a sufficient source mechanism for electrostatic transport to create the Eros dust ponds. Laboratory measurements of dust in a plasma sheath show that dust launched off the surface by direct electrostatic levitation can provide a sufficient source for transport to produce the observed Eros ponds.     

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°.     

Detection of Temperature-Dependent Spectral Variation on the Asteroid Eros and New Evidence for the Presence of an Olivine-Rich Silicate Assemblage

Data obtained by the near-infrared spectrometer carried by the NEAR-Shoemaker spacecraft show that the spectral properties of the asteroid Eros vary with temperature. The manner in which they vary demonstrates that the mineral olivine is a major constituent of the surface. The near-IR temperature-dependent spectral properties of Eros in the northern hemisphere, and for two individual regions on the surface, show clear evidence of the presence of the mineral olivine and are a close match to the temperature-spectral behavior of LL-type ordinary chondrite meteorites. While the presence of other olivine-rich meteorites cannot be excluded, H-type ordinary chondrites are clearly too pyroxene-rich to be permitted as a major surface component of Eros. The results of the thermal-spectral analysis are consistent with results from analysis of conventional reflectance spectra of the asteroid and contribute unambiguous detection of olivine to the understanding of the surface composition of Eros.     

Impact History of Eros: Craters and Boulders

Preliminary measurements of craters and boulders have been made in various locations on Eros from images acquired during the first nine months of NEAR Shoemaker's orbital mission, including the October 2000 low altitude flyover. (We offer some very preliminary, qualitative analysis of later LAF images and very high-resolution images obtained during NEAR's landing on 12 February 2001). Craters on Eros >100 m diameter closely resemble the saturated crater population of Ida; Eros is more heavily cratered than Gaspra but lacks the saturated giant craters of Mathilde. These craters and the other large-scale geological features were formed over a duration of very roughly 2 Gyr while Eros was in the main asteroid belt, between the time when its parent body was disrupted and Eros was injected into an Earth-approaching orbit (probably tens of Myr ago). Saturation equilibrium had been expected to shape Eros' crater population down to very small sizes, as on the lunar maria. However, craters <200 m diameter are instead progressively depleted toward smaller sizes and are a factor of ∼200 below empirical saturation at diameters of 4 m. Conversely, boulders and positive relief features (PRFs) rise rapidly in numbers (differential power-law index ∼−5) and those <10 m in size dominate the landscape at high resolutions. The pervasive boulders and minimal craters on Eros is radically different from the lunar surface at similar scales. This may be partly explained by a major depletion of meter-scale projectiles in the asteroid belt (due to the Yarkovsky Effect: Bell 2001), which thus form few small craters and destroy few boulders. Additionally, the small size and low gravity of Eros may result in redistribution or loss of ejecta due to seismic shaking, thus preferentially destroying small craters formed in such regolith. Possibly Eros has only a patchy, thin regolith of mobile fines; the smaller PRFs may then reflect exposures of fractured bedrock or piles of large ejecta blocks, which might further inhibit formation of craters <10 m in size. Eros may well have been largely detached dynamically and collisionally from the main asteroid belt for the past tens of Myr, in which case its cratering rate would have dropped by two orders of magnitude, perhaps enhancing the relative efficacy of other processes that would normally be negligible in competition with cratering. Such processes include thermal creep, electrostatic levitation and redistribution of fines, and space weathering (e.g., bombardment by micrometeorites and solar wind particles). Combined with other small-body responses to impact cratering (e.g., greater widespread distribution of bouldery ejecta), such processes may also help explain the unexpected small-scale character of geology on Eros. If there was a recent virtual hiatus in cratering of Eros (during which only craters <∼300 m diameter would be expected to have formed), space weathering may have reached maturity, thus explaining Eros' remarkable spectral homogeneity compared with Ida.     

70-cm radar observations of 433 Eros

Radar observations of 433 Eros were made at the Arecibo Observatory using a wavelength of 70 cm during the close approach of Eros to Earth in mid-January, 1975. A peak radar cross section of 39 ± 15 km² was observed. The spectral broadening obtained was approximately 30 Hz, which is consistent with a value of 16 km for the maximum radius of the asteroid. The surface of Eros appears to be relatively rough at the scale of a wavelength as compared to the surfaces of the terrestrial planets and the Moon. The composition of the surface is not well determined, except that it cannot be a highly conducting metal. A single measurement each of round-trip echo times delay and doppler shift was made.     

The infrared spectrum of asteroid 433 Eros

The mineralogical composition of asteroid Eros has been determined from its infrared spectrum (0.9–2.7μm; 28cm^?1 resolution). Major minerals include metallic NiFe and pyroxene; no spectroscopic evidence for olivine or plagioclase feldspar was found. The IR spectrum of Eros is most consistent with a stony-iron composition.     

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.     

Observations of 433 Eros from 1.25 to 3.35 microns

Abstract— We have spectrophotometrically observed 433 Eros, the target of the NEAR‐Shoemaker spacecraft, on 1995 December 4 from 1.25 to 3.35 μm. As expected, Eros shows no evidence of an absorption feature >5% in the 3 μm region, and is interpreted to have an anhydrous surface within observational uncertainties. Our observations in the JHK region agree with previous work by Chapman and Morrison (1976) and Murchie and Pieters (1996), but differ from the near‐infrared spectrometer spectra reported by Clark et al. (2001). Our calculations indicate that thermal flux from Eros is not responsible for this mismatch.     

Polarization of the reflected light of asteroid 433 Eros

Linear polarizations measured for asteroid 433 Eros at various wavelengths and at solar phase angles ranging from 9° to 53° are presented. The polarization results are entirely typical of main-belt S asteroids, and indicate a dusty surface with geometric albedo 0.20. The derived effective diameter at photometric maximum is 21 km. Eros is quite uniform polarimetrically; no dependence on aspect is detected, and the polarization is shown to be constant during a single rotation with a precision of one part in forty.     

Detecting crater ejecta‐blanket boundaries and constraining source crater regions for boulder tracks and elongated secondary craters on Eros

Abstract– We present results of a numerical model of the dynamics of ejecta emplacement on asteroid 433 Eros. Ejecta blocks represent the coarsest fraction of Eros’ regolith and are important, readily visible, “tracer particles” for crater ejecta‐blanket units that may be linked back to specific source craters. Model results show that the combination of irregular shape and rapid rotation of an asteroid can result in markedly asymmetric ejecta blankets (and, it follows, ejecta block spatial distribution), with locally very sharp/distinct boundaries. We mapped boulder number densities in NEAR‐Shoemaker MSI images across a portion of a predicted sharp ejecta‐blanket boundary associated with the crater Valentine and confirm a distinct and real ejecta‐blanket boundary, significant at least at the 3‐sigma level. Using our dynamical model, we “back track” the landing trajectories of three ejecta blocks with associated landing tracks in an effort to constrain potential source regions where those blocks were ejected from Eros’ surface in impact events. The observed skip distances of the blocks upon landing on Eros’ surface and the landing speeds and elevation angles derived from our model allow us to estimate the coefficient of restitution, ε, of Eros’ surface for impacts of 10‐m‐scale blocks at approximately 5 m s^?1 impact speeds. We find mean values of ε of approximately 0.09–0.18.     

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.     

Thermal properties of 433 Eros

We report on radiometric and reflected light observations of 433 Eros at high time resolution, high accuracy, and broad spectral coverage. We use a thermal inertia model to estimate the thermal inertia, albedo, and size of Eros. We find an albedo of 0.125 ± 0.025 with axes of 39.3 ± 2.0 × 16.1 ± 0.8 km. Our estimate of the albedo is about 30% lower than previous estimates.     

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.     

A precise modeling of Eros 433 rotation

Thanks to the recent data obtained from the NEAR space probe, we calculate in this paper, with a precision never reached so far for an asteroid, the precession and the nutation of Eros 433. In a preliminary step, we show that Eros obliquity has a remarkable value of 89.0° which tends to align its figure axis along the orbital plane. This very specific obliquity has some consequences on the motion of the axis of figure: one is the very small amplitude of the precession in longitude, for which we get the value . Moreover, we calculate Eros nutation for the figure axis due to the Sun, after developing the perturbing potential at the 4th order of the eccentricity. We show that the figure axis undergoes very large oscillations in the direction perpendicular to Eros orbital plane, due to the nutation in obliquity. Peak to peak, these oscillations reach 55″, which is far larger than the amplitudes of the nutations of the Earth due to the Sun (of the order of 2″). Moreover, we give the analytical developments of Δψ and Δε, both for the axis of angular momentum, and the axis of figure.