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.     

832 Karin: Absence of rotational spectral variations

832 Karin is the largest member of the young Karin cluster that formed 5.75±0.05 Myr ago in the outer main belt. Surprisingly, recent near-IR spectroscopy measurements [Sasaki, T., Sasaki, S., Watanabe, J., Sekiguchi, T., Yoshida, F., Kawakita, H., Fuse, T., Takato, N., Dermawan, B., Ito, T., 2004. Astrophys. J. 615 (2), L161-L164] revealed that Karin's surface shows different colors as a function of rotational phase. It was interpreted that 832 Karin shows us the reddish space-weathered exterior surface of the parent body as well as an interior face, which has not had time to become space-weathered. This result is at odds with recent results including seismic and geomorphic modeling, modeling of the Karin cluster formation and measurements of the space weathering rate. Consequently, we aimed to confirm/infirm this surprising result by sampling Karin's spectrum well throughout its rotation. Here, we present new visible (0.45-0.95 μm) and near-infrared (0.7-2.5 μm) spectroscopic observations of 832 Karin obtained in January and April 2006, covering most of Karin's longitudes. In the visible range, we find that Karin shows no rotational spectral variations. Similarly, we find that Karin exhibits very little (to none) spectral variations with rotation in the near-IR range. Our results imply that 832 Karin has a homogeneous surface, in terms of composition and surface age. Our results also imply that the impact that generated the family refreshed entirely Karin's surface, and probably the surfaces of all members.     

The surface properties of small asteroids: Peculiar Betulia—A case study

We present the results of extensive thermal-infrared observations of the C-type near-Earth Asteroid (1580) Betulia obtained in June 2002 with the 3-m NASA Infrared Telescope Facility (IRTF) on Mauna Kea, Hawaii. Betulia is a highly unusual object for which earlier radiometric observations, interpreted on the basis of simple thermal models, indicated a surface of high thermal inertia. A high thermal inertia implies a lack of thermally insulating regolith. Radiometric observations of other asteroids of comparable size indicate that regolith is present in nearly all cases. Knowledge of the surface thermal properties of small near-Earth asteroids is crucial for meaningful calculations of the Yarkovsky effect, which is invoked to explain the delivery of collisional fragments from the main belt into near-Earth orbits, and apparently has a significant influence on the orbital evolution of potentially hazardous near-Earth asteroids. Furthermore, apart from being an indicator of the presence of thermally insulating regolith on the surface of an asteroid, the thermal inertia determines the magnitude of the diurnal temperature variation and is therefore of great importance in the design of instrumentation for lander missions to small asteroids. In the case of Betulia our database is sufficiently broad to allow the use of more sophisticated thermal models than were available for earlier radiometric observations. The measured fluxes have been fitted with thermal-model emission continua to determine the asteroid's size and geometric albedo, pv. Fits obtained with a new thermophysical model imply an effective diameter of 4.57±0.46 km and an albedo of 0.077±0.015 and indicate a moderate surface thermal inertia of around 180 J m⁻² s^−0.5 K⁻¹. It is difficult to reconcile our results with earlier work, which indicate a larger diameter for Betulia and a high-thermal-inertia surface of bare rock.     

Karin cluster formation by asteroid impact

Insights into collisional physics may be obtained by studying the asteroid belt, where large-scale collisions produced groups of asteroid fragments with similar orbits and spectra known as the asteroid families. Here we describe our initial study of the Karin cluster, a small asteroid family that formed 5.8±0.2 Myr ago in the outer main belt. The Karin cluster is an ideal ‘natural laboratory’ for testing the codes used to simulate large-scale collisions because the observed fragments produced by the 5.8-Ma collision suffered apparently only limited dynamical and collisional erosion. To date, we have performed more than 100 hydrocode simulations of impacts with non-rotating monolithic parent bodies. We found good fits to the size-frequency distribution of the observed fragments in the Karin cluster and to the ejection speeds inferred from their orbits. These results suggest that the Karin cluster was formed by a disruption of an ≈33-km-diameter asteroid, which represents a much larger parent body mass than previously estimated. The mass ratio between the parent body and the largest surviving fragment, (832) Karin, is ≈0.15-0.2, corresponding to a highly catastrophic event. Most of the parent body material was ejected as fragments ranging in size from yet-to-be-discovered sub-km members of the Karin cluster to dust grains. The impactor was ≈5.8 km across. We found that the ejections speeds of smaller fragments produced by the collision were larger than those of the larger fragments. The mean ejection speeds of >3-km-diameter fragments were . The model and observed ejection velocity fields have different morphologies perhaps pointing to a problem with our modeling and/or assumptions. We estimate that ∼5% of the large asteroid fragments created by the collision should have satellites detectable by direct imaging (separations larger than 0.1 arcsec). We also predict a large number of ejecta binary systems with tight orbits. These binaries, located in the outer main belt, could potentially be detected by lightcurve observations. Hydrocode modeling provides important constraints on the interior structure of asteroids. Our current work suggests that the parent asteroid of the Karin cluster may have been an unfractured (or perhaps only lightly fractured) monolithic object. Simulations of impacts into fractured/rubble pile targets were so far unable to produce the observed large gap between the first and second largest fragment in the Karin cluster, and the steep slope at small sizes (≈6.3 differential index). On the other hand, the parent asteroid of the Karin cluster was produced by an earlier disruptive collision that created the much larger, Koronis family some 2-3 Gyr ago. Standard interpretation of hydrocode modeling then suggests that the parent asteroid of the Karin cluster should have been formed as a rubble pile from Koronis family debris. We discuss several solutions to this apparent paradox.     

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.     

Polarimetric evidence of close similarity between members of the Karin and Koronis dynamical families

We present the results of a campaign of polarimetric observations of small asteroids belonging to the Karin and Koronis families, carried out at the ESO Cerro Paranal Observatory using the VLT-Kueyen 8-m telescope. The Karin family is known to be very young, having likely been produced by the disruption of an original member of the Koronis family less than 6 Myr ago. The purpose of our study was to derive polarimetric properties for a reasonable sample of objects belonging to the two families, in order to look for possible systematic differences between them, to be interpreted in terms of differences in surface properties, in particular albedo. In turn, systematic albedo differences might be caused by different times of exposure to space weathering processes experienced by the two groups of objects. The results of our analysis indicate that no appreciable difference exists between the polarimetric properties of Karin and Koronis members. We thus find that space-weathering mechanisms may be very efficient in affecting surface properties of S-class asteroids on very short timescales. This result complements some independent evidence found by recent spectroscopic studies of very young families.     

The cool surfaces of binary near-Earth asteroids

Here we show results from thermal-infrared observations of km-sized binary near-Earth asteroids (NEAs). We combine previously published thermal properties for NEAs with newly derived values for three binary NEAs. The η value derived from the near-Earth asteroid thermal model (NEATM) for each object is then used to estimate an average thermal inertia for the population of binary NEAs and compared against similar estimates for the population of non-binaries. We find that these objects have, in general, surface temperatures cooler than the average values for non-binary NEAs as suggested by elevated η values. We discuss how this may be evidence of higher-than-average surface thermal inertia. This latter physical parameter is a sensitive indicator of the presence or absence of regolith: bodies covered with fine regolith, such as the Earth’s moon, have low thermal inertia, whereas a surface with little or no regolith displays high thermal inertia. Our results are suggestive of a binary formation mechanism capable of altering surface properties, possibly removing regolith: an obvious candidate is the YORP effect.We present also newly determined sizes and geometric visible albedos derived from thermal-infrared observations of three binary NEAs: (5381) Sekhmet, (153591) 2001 SN₂₆₃, and (164121) 2003 YT₁. The diameters of these asteroids are 1.41 ± 0.21 km, 1.56 ± 0.31 km, and 2.63 ± 0.40 km, respectively. Their albedos are 0.23 ± 0.13, 0.24 ± 0.16, and 0.048 ± 0.015, respectively.     

Radar observations of E-class Asteroids 44 Nysa and 434 Hungaria

We observed the E-class main-belt Asteroids (MBAs) 44 Nysa and 434 Hungaria with Arecibo Observatory's S-band (12.6 cm) radar. Both asteroids exhibit polarization ratios higher than those measured for any other MBA: Nysa, μc=0.50±0.02 and Hungaria, μc=0.8±0.1. This is consistent with the high polarization ratios measured for every E-class near-Earth asteroid (NEA) observed by Benner et al. [Benner, L.A.M., and 10 collegues, 2008. Icarus, submitted for publication] and suggests a common cause. Our estimates of radar albedo are 0.19±0.06 for Nysa and 0.22±0.06 for Hungaria. These values are higher than those of most MBAs and, when combined with their high polarization ratios, suggest that the surface bulk density of both asteroids is high. We model Nysa as an ellipsoid of dimension 113×67×65 km (±15%) giving an effective diameter Deff=79±10 km, consistent with previous estimates. The echo waveforms are not consistent with a contact binary as suggested by Kaasalainen et al. [Kaasalainen, M., Torppa, J., Piironen, J., 2002. Astron. Astrophys. 383, L19-L22]. We place a constraint on Hungaria's maximum diameter, Dmax?11 km consistent with previous size estimates.     

Thermal inertia of near-Earth asteroids and implications for the magnitude of the Yarkovsky effect

Thermal inertia determines the temperature distribution over the surface of an asteroid and therefore governs the magnitude the Yarkovsky effect. The latter causes gradual drifting of the orbits of km-sized asteroids and plays an important role in the delivery of near-Earth asteroids (NEAs) from the main belt and in the dynamical spreading of asteroid families. At present, very little is known about the thermal inertia of asteroids in the km size range. Here we show that the average thermal inertia of a sample of NEAs in the km-size range is . Furthermore, we identify a trend of increasing thermal inertia with decreasing asteroid diameter, D. This indicates that the dependence of the drift rate of the orbital semimajor axis on the size of asteroids due to the Yarkovsky effect is a more complex function than the generally adopted D⁻¹ dependence, and that the size distribution of objects injected by Yarkovsky-driven orbital mobility into the NEA source regions is less skewed to smaller sizes than generally assumed. We discuss how this fact may help to explain the small difference in the slope of the size distribution of km-sized NEAs and main-belt asteroids.     

Young Asteroid 832 Karin shows no rotational spectral variations

We have made near-IR spectral observations of the very young (5.75 Myr) S-type asteroid 832 Karin, well sampled in rotational phase over its 18.35-h period. We find no significant variations in its reflectance spectrum. Karin, the brightest member of the Karin cluster (a sub-family of the larger, older Koronis dynamical family), was shown to be exceptionally young by Nesvorný et al. [Nesvorný, D., Bottke, W.F., Dones, L., Levison, H., 2002. Nature 417, 720-722], using backward numerical integration of orbital elements of cluster members. Their precise dating of the collisional breakup gives us an opportunity, for the first time and without age-dating of physical samples, to monitor time-evolution of processes, like space weathering, that operate on timescales of ∼1-10 Myr. Sasaki et al. [Sasaki, T., Sasaki, S., Watanabe, J., Sekiguchi, T., Yoshida, F., Kawakita, H., Fuse, T., Takato, N., Dermawan, B., Ito, T., 2004. Astrophys. J. 615, L161-L164; Sasaki, T., Sasaki, S., Watanabe, J., Sekiguchi, T., Yoshida, F., Ito., T., Kawakita, H., Fuse, T., Takato, N., Dermawan, B., 2005. Lunar Planet. Sci. XXXVI. Abstract #1590] had made similar measurements of Karin, although more sparsely sampled than ours, and claimed dramatically different colors as a function of rotational phase. Sasaki et al. interpreted their data to be showing the reddish, space-weathered exterior surface of the precursor asteroid, as well as an interior face, which had not had time to become space-weathered. On five nights over 2006 January 7-14 UT, we observed Karin with the SpeX (0.8-2.5 μm) spectrometer of the IRTF. We analyze data in 30° intervals of rotational longitude, some of which we sampled on two different nights. The spectra are consistent with little or no spectral variation as the asteroid rotates; certainly there are no changes as large as previously reported. The previous observations were probably spurious. Our average spectrum resembles the “blue” spectrum of Sasaki et al., which they interpreted to be the “fresh” surface. Karin is not quite as red as typical S-types, yet has rather shallow absorption bands. We surmise that the space-weathering process affecting Karin has had time to reduce spectral contrast, but has not operated long enough to redden its spectrum—an intermediate case of space weathering, which has gone to completion for most main-belt asteroids. This work sets an important constraint on the timescale for the ubiquitous space-weathering process affecting S-types, namely that its effects are evident, but not yet complete, at ∼6 Myr.     

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.     

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.     

Interplanetary dust particles collected from the stratosphere: physical, chemical, and mineralogical properties and implications for their sources

The suggestion that significant quantities of interplanetary dust are produced by both main-belt asteroids and comets is based on the Infrared Astronomical Satellite detection of dust trails or bands associated with these objects. Gravitational focusing strongly biases all near-Earth collections of interplanetary dust in favor of particles with the lowest geocentric velocities, that is the dust from main-belt asteroids spiraling into the Sun under the influence of Poynting-Robertson radiation drag.

The major dust bands in the main-belt appear to be associated with the catastrophic disruptions which produced the Eos, Themis and Koronis families of asteroids. If dust particles are produced in the catastrophic collision process, then Poynting-Robertson radiation drag is such an efficient transport mechanism from the main-belt to 1 AU that near-Earth collections of interplanetary dust should include, and perhaps be dominated by, this material. The physical, chemical and mineralogical properties of this asteroidal dust can provide constraints on the properties of the asteroidal parent bodies.

Interplanetary dust particles from 5 to 100 μm in diameter have been recovered from the stratosphere of the Earth by NASA sampling aircraft since the mid1970s. The densities of a large fraction of these interplanetary dust particles are significantly lower than the densities of their constituent silicate mineral phases, indicating significant porosities. Direct examination of ultra-microtome thin-sections of interplanetary dust particles also shows significant porosities. The majority of the particles are chemically and mineralogically similar to, but not identical to, the carbonaceous chondrite meteorites.

Most stony interplanetary dust particles have carbon contents exceeding those of Allende, a carbonaceous chondrite meteorite having a low albedo. The population of interplanetary dust does not appear to exhibit the full range of compositional diversity inferred from reflection spectroscopy of the main-belt asteroids. In particular, higher albedo particles corresponding to S-type asteroids are underrepresented or absent from the stratospheric collections, and primitive carbonaceous particles seem to be overrepresented in the stratospheric collections compared to the fraction of mainbelt asteroids classified as primitive. This suggests that much of the interplanetary dust may be generated by a stochastic process, probably preferentially sampling a few most recent collisional events.     

Observational Constraints On Surface Characteristics Of Comet Nuclei

Direct observations of the nuclear surfaces of comets have been difficult; however a growing number of studies are overcoming observational challenges and yielding new information on cometary surfaces. In this review, we focus on recent determinations of the albedos, reflectances, and thermal inertias of comet nuclei. There is not much diversity in the geometric albedo of the comet nuclei observed so far (a range of 0.025 to 0.06). There is a greater diversity of albedos among the Centaurs, and the sample of properly observed TNOs(2) is still too small. Based on their albedos and Tisser and invariants, Fernández et al. (2001) estimate that about 5% of the near-Earth asteroids have a cometary origin, and place an upper limit of 10%. The agreement between this estimate and two other independent methods provide the strongest constraint to date on the fraction of objects that comets contribute to the population of near-Earth asteroids. There is a diversity of visible colors among comets, extinct comet candidates, Centaurs and TNOs. Comet nuclei are clearly not as red as the reddest Centaurs and TNOs. What Jewitt (2002) calls ultra-red matter seems to be absent from the surfaces of comet nuclei. Rotationally resolved observations of both colors and albedos are needed to disentangle the effects of rotational variability from other intrinsic qualities. New constraints on thermal inertia of comets are consistent with previous independent estimates. The thermal inertia estimates for Centaurs 2060 Chiron and 8405 Asbolus are significantly lower than predicted by thermal models, and also lower than the few upper limits or constraints known for active, ordinary nuclei.     

Physical characteristics of Hayabusa target Asteroid 25143 Itokawa

In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

MIDI observations of 1459 Magnya: First attempt of interferometric observations of asteroids with the VLTI

The Very Large Telescope Interferometer (VLTI) of the European Southern Observatory (ESO) can be used to obtain direct determination of the sizes and the albedos of asteroids. We present results of the first attempt to carry out interferometric observations of asteroids with the Mid Infrared Interferometric Instrument (MIDI) at the VLTI. Our target was 1459 Magnya. This is the only V-type asteroid known to exist in the outer main-belt, and its IRAS-albedo turns out to be rather low for an object of this taxonomic class. Interferometric fringes were not detected, very likely due to the fact that the flux emitted by the asteroid was lower than expected and below the MIDI threshold for fringe detection. However, by fitting the Standard Thermal Model to the N-band infrared flux measured by MIDI in photometric mode and to the visible absolute magnitude, obtained from quasi-simultaneous B- and V-band photometric observations, we have derived a geometric visible albedo of 0.37±0.06 and an effective diameter of 17±1 km. This new estimate of the albedo differs from that previously obtained by IRAS and is more consistent with the V-type taxonomic classification of 1459 Magnya.     

Radar detection of near-Earth Asteroids 1915 Quetzalcoatl, 3199 Nefertiti, 3757 (1982 XB), and 4034 (1986 PA)

We describe Arecibo (2380 MHz, 12.6 cm) Doppler-only radar detections of near-Earth Asteroids 1915 Quetzalcoatl, 3199 Nefertiti, 3757 (1982 XB), and 4034 (1986 PA) obtained between 1981 and 1989. Estimates of the echo spectral bandwidths, radar cross-sections, and circular polarization ratios of these objects constrain their sizes, radar albedos, surface roughnesses, taxonomic classes, rotation periods, and pole directions. Our radar constraints on the diameters of Quetzalcoatl and Nefertiti are most consistent with sizes determined using thermal-radiometry and the Fast Rotation Model (FRM); this consistency may indicate that these asteroids have surfaces of high thermal inertia (i.e., little or no regolith). Constraints on Quetzalcoatl's radar albedo rule out a “metallic M” classification. The radar constraints for Nefertiti are inconsistent with a rotation pole published by Kaasalainen et al. (2004, Icarus 167, 178). Our estimates of 1982 XB's size are consistent with previously published estimates. The radar bandwidth of 1986 PA places an upper bound of about 24 h on its rotation period.