Photoelectric lightcurves of asteroid 433 Eros

Photoelectric observations of the asteroid 433 Eros were carried out with the 50-cm reflector of the Astronomical Observatory of the University of Cluj-Napoca on January 21 and February 4 and 5, 1975.     

UBV lightcurves of asteroid 433 Eros

UBV photometry and lightcurves of Eros were obtained on nine dates between October 1974 and March 1975. The absolute V magnitude at photometric maximum extrapolated to a solar phase angle of zero is 10.75 while the linear phase coefficient is 0.026mag deg^?1. The mean colors at solar phase angles greater than 30° are B?V = 0.92 and U?B = 0.52mag. No significant color variations over the surface were detected.     

UBV photometry of asteroid 433 Eros

UBV observations of asteroid 433 Eros were conducted on 17 nights during the winter of 1974/75. The peak-to-peak amplitude of the lightcurve varied from about 0.3 mag to nearly 1.4mmag. The absolute V mag at maximum light, extrapolated to zero phase, is 10.85. Phase coefficients of 0.0233 mag/degree, 0.0009 mag/degree and 0.0004 mag/degree were derived for V, B-V, and U-B, respectively. The zero-phase color of Eros (B?V = 0.88, U?B = 0.50) is representative of an S (silicaceous) compositional type asteroid. The color does not vary with rotation. The photometric behavior of Eros can be modeled by a cylinder with rounded ends having an axial ratio of about 2.3:1. The asteroid is rotating about a short axis with the north pole at λ₀ = 15° and β₀ = 9°.     

Physical properties of asteroid 433 Eros

Newly available photometric, polarimetric, spectroscopic, thermal-radiometric, radar, and occultation results are synthesized in order to derive a coherent model for Eros. The geometric albedo is 0.19±0.01 at the visual wavelength, and the overall dimensions are approximately 13 × 15 × 36km. The rotation is about the short axis, in the direct sense, with a sidereal period of 5^h16^m13^s.4. The pole of rotation lies within a few degrees of ecliptic coordinates λ = 16° and β = + 11°.Eros is uniformly coated with a particulate surface layer several millimeters thick. It has an iron-bearing silicate composition, similar to that of a minority of main-belt asteroids, and probably identifiable with H-type ordinary chondrites.     

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.     

Five-color photoelectric photometry of asteroid 433 Eros

Five-color photoelectric lightcurves of asteroid 433 Eros were obtained on 9 nights during the 1974/75 apparition. Although color differences due to changing solar phase angle were detected, color differences during a single rotation of Eros are less than 1%. Amplitudes of up to 1^m.44 were measured, and there are indications that three reversals in the relative depths of the two minima occured between late December 1974 and late January 1975. The absolute visual magnitude at primary maximum, corrected to zero phase and to one AU from Earth and Sun, is about V₀(1,0) = 10^m.8.     

Origin and flatness of ponds on asteroid 433 Eros

NEAR‐Shoemaker Multi‐Spectral Imager data reveal several hundred “ponds” on 433 Eros: smooth deposits that sharply embay the bounding depressions in which they lie, and whose spectra appear blue relative to that of the surrounding terrain. We investigate the topography of these ponds on Eros using a new shape model derived from stereophotoclinometric analysis, and validated against altimetry from the NEAR Laser Rangefinder, to constrain the mode of pond formation from three existing models. We update the locations of 55 pond candidates identified in images registered to the new shape model. We classify the flatness of these features according to the behavior of the first and second derivatives of the topography. We find that less than half of pond candidates have clearly flat floors. Based on the pond topography, we favor an external origin for the ponds' deposits. We suggest that fine dust may be transported into bounding depressions by electrostatic levitation, but may adhere to slopes, and that seismic shaking may not be sufficient to bring the deposits to an equipotential surface. Disaggregation of a central boulder should result in an obvious break in slope, such a variation is only observed in roughly half the pond candidates.     

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.     

Radar constraints on asteroid regolith properties using 433 Eros as ground truth

Abstract— Radar data enable us to estimate an asteroid's near‐surface bulk density, thus providing a joint constraint on near‐surface porosity and solid density. We investigate two different approaches to simplifying this joint constraint: estimating solid densities by assuming uniform porosities for all asteroids; and estimating porosities by assuming uniform mineralogy within each taxonomic class. Methods used to estimate asteroids' near‐surface solid densities from radar data have not previously been calibrated via independent estimates. Recent spacecraft results on the chondritic nature of 433 Eros now permit such a check, and also support porosity estimation for S‐class objects. We use radar albedos and polarization ratios estimated for 36 main‐belt asteroids and nine near‐Earth asteroids to estimate near‐surface solid densities using two methods, one of which is similar to the uncalibrated algorithms used in previous studies, the other of which treats Eros as a calibrator. We also derive porosities for the same sample by assigning solid densities for each taxonomic class in advance. Density‐estimation results obtained for Eros itself are consistent with the uncalibrated method being valid in the mean; those derived for the full sample imply that uncalibrated solid densities are, at most, a few tens of percent too large on average. However, some derived densities are extremely low, whereas most porosity estimates are physically plausible. We discuss the relative merits of these two approaches.     

The pole orientation of asteroid 433 Eros determined by photometric astrometry

Refinements to the pole-determination method photometric astrometry (PA) were completed in 1983 (R. C. Taylor and E. F. Tedesco, 1983, Icarus54, 13–22). A goal is to redo the pole analysis for every asteroid whose pole had been determined from earlier versions of PA: Previous PA poles are reviewed in this paper. Asteroid 433 Eros is in that collection and has redone. The result are prograde rotation; a sidereal period of 0.219588 ± 0.000005 day; and a north pole at 22° longitude, +9° latitude. The uncertainty of the pole is 10°. The pole position of Eros determined by C.D. Vesely (1971, In Physical Studies of Minor Planets (T. Gehrels, Ed.), pp. 133–140, NASA SP-267) and Dunlap (1976, Icarus28, 69–78), using earlier versions of photometric astrometry, were within 21 and 7°, respectively, of the present result.     

Radar observations at 3.5 and 12.6 cm wavelength of asteroid 433 Eros

A study of the asteroid 433 Eros using 3.5 and 12.6 cm radar waves indicates that the surface is very much rougher than any planetary or lunar surface observed by this method. A surface completely covered with sharp edges, pits, subsurface holes, or embedded chunks with scale sizes on the order of our wavelengths seems to be indicated. A model based on a rough rotating triaxial ellipsoid having radii in the rotation equator of 18.6 and 7.9 km agrees well with our data, although a strong wobble in the apparent center frequency of the spectra as rotation progresses indicates that one side may be more reflective than the other, or more likely, that the projected axis of rotation does not equally divide the projected area.     

Upper limit to the 2 cm brightness temperature of asteroid 433 Eros

The brightness temperature of 433 Eros was less than 460°K during the close opposition in January 1975.     

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.     

X‐ray fluorescence measurements of the surface elemental composition of asteroid 433 Eros

Abstract— We report major element ratios determined for the S‐class asteroid 433 Eros using remote‐sensing x‐ray fluorescence spectroscopy with the near‐Earth asteroid rendezvous Shoemaker x‐ray spectrometer (XRS). Data analysis techniques and systematic errors are described in detail. Data acquired during five solar flares and during two extended “quiet Sun” periods are presented; these results sample a representative portion of the asteroid's surface. Although systematic uncertainties are potentially large, the most internally consistent and plausible interpretation of the data is that Eros has primitive Mg/Si, Al/Si, Ca/Si and Fe/Si ratios, closely similar to H or R chondrites. Global differentiation of the asteroid is ruled out. The S/Si ratio is much lower than that of chondrites, probably reflecting impact‐induced volatilization and/or photo‐ or ion‐induced sputtering of sulfur at the surface of the asteroid. An alternative explanation for the low S/Si ratio is that it reflects a limited degree of melting with loss of an FeS‐rich partial melt. Size‐sorting processes could lead to segregation of Fe‐Ni metal from silicates within the regolith of Eros; this could indicate that the Fe/Si ratios determined by the x‐ray spectrometer are not representative of the bulk Eros composition.     

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.     

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.     

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.     

Boulders and ponds on the Asteroid 433 Eros

There are ∼300 features on the Asteroid 433 Eros that morphologically resemble ponds (flat-floored and sharply embaying the bounding depression in which they sit). Because boulders on Eros are apparently eroding in place and because ponds with associated boulders tend to be larger than ponds without blocks, we propose that ponds form from thermally disaggregated and seismically flattened boulder material, under the assumption that repeated day/night cycling causes material fatigue that leads to erosion of the boulders. Results from a simple boulder emplacement/thermal erosion model with boulders emplaced in a few discrete events (i.e., large impacts) match well the observed size distribution. Under this scenario, the subtle color differences of ponds (somewhat bluer than the rest of the surface) might be due to some combination of less space-weathered material and density stratification of silicate-rich chondrules and more metal-rich matrix from a disaggregated boulder. Volume estimates of ponds derived from NEAR Laser Rangefinder profiles are consistent with what can be supplied by boulders. Ponds are also observed to be concentrated in regions of low slope and high elevation, which suggests the presence of a less mobile regolith and thus a contrast in the resistance to seismic shaking between the pond material and the material that makes up the bounding depression. Future tests include shake-table experiments and temperature cycling (fatigue) of ordinary chondrites to test the thermal erosion mechanism.     

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.     

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.