ABSTRACT
========

INTRODUCTION
============

Radar observations provide a powerful tool for detailed
physical characterization of near-Earth objects and detailed reconstruction of
asteroid three-dimensional shapes.  Over the last decade detailed three-dimensional
shapes have been reported for 4769 Castalia (Hudson and Ostro 1994), 4179 Toutatis
(Hudson and Ostro 1995), 1620 Geographos (Hudson et al. 1999),
and 6489 Golevka (Hudson et al. 2000).  

Here we report detailed radar observations and a 3-D model of asteroid 1999 JM8,
our first look at a large, optically dark near-Earth asteroid.  The images reveal 
an object with an extremely slow, probably non-principal axis spin state, a highly
irregular shape, and numerous craters between ~100 m and 1.5 km in diameter. 

1999 JM8 was discovered by LINEAR on 1999 May 13, fortuitously more than 
two months prior to an encounter within 0.057 AU (22 lunar distances) of
Earth on 1999 July 29.  1999 JM8 was originally discovered at Palomar in April, 
1990 by E. F. Helin, but it was subsequently lost.  Its rediscovery on 1999 May 13 
occurred with sufficient lead time to prepare an extensive campaign of radar and 
optical observations.

1999 JM8 made an extended close encounter within 0.1 AU of Earth between July and
October of 1999 that offered an excellent opportunity for physical observations.
Pravec and Sarounova (Ondrejov), Hicks (Table Mountain), and Krugly (Kharkiv) 
obtained photometry that indicate very slow rotation and possibly
a non-principal axis rotation state.  Hicks also obtained photometric
colors at TMO that suggest that JM8 is an optically dark object.
Hicks, Buratti, and Hanner obrtained thermal radiometry with the 
5-m Hale telescope at Palomar.  Howell obtained an extensive set of vis-near IR 
spectroscopic measurements at McDonald Observatory during September of 1999, 
about 6 weeks after the radar observations concluded.  Table I summarizes 
the optically-determined physical properties of 1999 JM8.

We observed 1999 JM8 at Goldstone and Arecibo on 18 days between 1999 July 18 and
August 9, dates that spanned the asteroid's closest approach to within 0.057 AU
of Earth on 1999 July 29.  The asteroid's close approach, large size, and extremely
slow rotation provided an outstanding opportunity for radar observations. 
The best asteroid radar target that has ever been 

OBSERVATIONS
============

The first radar detection of JM8 was by CW on July 18.
The initial orbital solution (15) was very good due 
to the 9-year optical arc.  We measured a Doppler correction of 
+1.7 Hz at the epoch 1999 July 18 21:30:00 and updated the orbit to solution 17.
  
Attempts to range the asteroid during the first track were unsuccessful
due to problems resulting from the crash of the imaging DAS during a power
dip the night before the observations.

On the second track (July 20) we started with 2 CW runs, measured the Doppler
correction of -0.5 Hz, and then successfully obtained a range with coarse-
resolution 10 and 11 usec setups.  We completed this very short track with 
two 1-usec medium resolution ranging runs that resolved the target into
about 150 pixels.  We used the radar astrometry to generate solution 19.

During the July 21 track we verified the echoes with one CW
run and then we devoted the rest of the track to 1 us x 0.1 Hz imaging.
We updated the ephemeris to solution 21, which we used during the ensuing 
week.

Thereafter, our strategy during the Goldstone tracks was to do one or two
CW runs to verify that we had echoes and then devote the rest of the track
to high resolution imaging with progressively finer resolution until
after August 1 as the asteroid approached Earth.  For the Aug 7 and 8 
Goldstone tracks, the asteroid's distance increased by ~50% relative to
the minimum on July 29 so we backed off to a coarser-resolution 0.25 us x
0.075 Hz setup that still placed thousands of pixels on the target.  

We observed JM8 at Arecibo on August 1-6 and August 9.  We updated the orbit 
solution twice to incorporate additional radar and optical astrometry 
(solution 26). 

We used two imaging data acquisition systems at Arecibo: the Caltech 
Baseband Recorder (CBR), which was designed for observing pulsars and was 
graciously made available to us by the Caltech group (FIND OUT WHO!), and
a new system originally built by Jean-Luc Margot for observing 6489 Golevka 
(the Golevka sampling box, or GSB) that was then under development.  The 
prime reason for using each system was the ability to sample fast enough
to achieve 0.1 usec (15 meter) resolution.  The CBR has dual polarization 
capability but is more cumbersome to use for radar observations than the GSB; 
the GSB in August, 1999 had single polarization capability. We used both 
systems on each day, but the analyses reported here utilize the CBR data
exclusively due to the modestly stronger SNR (a few dB) and the dual-polarization
capability.  

The Arecibo delay-Doppler images were reduced using full-length Fast-Fourier 
Transforms that were zero extended once achieve the finest frequency 
resolution possible (given that echo SNR was not an issue).  The resulting
frequency resolutions vary from 0.0098 Hz on August 1 to 0.0060 Hz on August
9 and are the finest S-band frequency resolutions ever obtained for any 
asteroid. 

1999 JM8's rotation is so slow that rotational smear was negligible during
each Arecibo track, so we grouped all the Arecibo images from each day into one 
weighted summed image.  We adopted the same approach for the Goldstone images
except for August 8, when the track was long enough (more than 7 hours) that 
subtle rotation was evident in weighted sums of images that each spanned 
~2.5 hours. 

Table "observations" summarizes the observations.

Satellite search
----------------
?

ASTROMETRY & ORBIT REFINEMENT
=============================

Refer to Jon's email about future/past encounters

Follow template of the Toutatis paper: combined optical and radar observations
from April 1990-present permit reliable computation of the orbit +/- 1000 years.
Over the upcoming millenium, no encounters closer than the one in 1999.  In the
past the August 1990 encounter was nearly a factor of two closer but at that time
1999 JM8 had been lost.  Impact probability over next ~1000 years: Zero.

Include a table of past and future close encounters with uncertainties.

The semimajor axis of 1999 JM8's orbit is presently within 0.006 AU (2.2 lunar 
distances) of a 2:9 mean motion resonance with Earth, which is
evident in the asteroid's recent pattern of close approaches in August of 1981 
(0.057 AU) and 1990 (0.034 AU) and in late July of 1999.  JM8 makes a distant 
encounter with Earth in 2008 (0.32 AU) and then the pattern of close approaches at
9-year intervals ceases.  

DISK-INTEGRATED PROPERTIES
==========================

X-band OC cross sections, bandwidths, SC/OC.  Show a sequence of X-band CW
spectra from each day.  Compare the nominal SC/OC with those of other 
radar-detected NEAs.  

DELAY-DOPPLER IMAGES
====================

Rotation period

Shape
-asymmetry
-dimensions
-angularity
-topography

Surface features:
-Concavities
   Four obviously large concavities seen on multiple days
   Smaller concavities: July 31, Aug 1, 4, 5, 6
   Radar-bright rim on July 28
   Implications of the concavities
-lineament
-Other features
-SC/OC images

Global view
-----------

Figure IMAGES shows a chronological sequence of OC delay-Doppler images 
from Goldstone and Arecibo and Table DELAY-DOPPLER DISPERSIONS gives 
the bandwidths and visible range extents on each day.  The maximum
visible delay extent was 5.3 km on August 6 and the maximum bandwidth
(when adjusted for the differences in wavelength between S- and X-band) 
was on Aug. 5.  The Arecibo images generally show larger delay extents 
than the Goldstone images due to the greater sensitivity at Arecibo 
(this is clearly evident on August 1, the only day of overlap at both
telescopes) and possibly due to differences in the asteroid's orientation.  

Rotation period
---------------
The echo bandwidths, visible range dispersions, and Eq. XX provide constraints
the apparent rotation period.  If we assume that the trailing edge of the
echoes is at the center of mass, and that the true diameer is twice
the visible range extent, then we obtain upper bounds on the
apparent rotation period that vary between 20.6 and 7 days with a mean
of 11.5 days.  The clear implication from this rough estimate is that 1999
JM8 is a very slow rotator.  

Additional evidence for slow rotation is available in time-resolved 
delay-Doppler images from each day.  We summed individual looks
spanning about 0.8 h 
from the beginning and end of each track and searched the resulting images
for evidence of rotation.  The only day in which rotation 
is clearly apparent is on August 8, when the observations
span 7.4 hours (Fig. IMAGES).   Careful inspection of the other
Goldstone images also shows very subtle differences in the shape of the 
leading edges on July 31 and August 1 that are probably attributable to 
rotation.  We found no evidence of rotation in the Arecibo images, which 
all span less than 1.4 hours.  The general lack of discernible rotation 
indicates that JM8 rotates with a period of at least several days.

The images on each day are distinctly different between July 20 and 31, but 
the August 1 image bears a striking resemblance to the lower-resolution 
image obtained on July 24.  This suggests that a major component of the asteroid's
rotation has a period that is close to 8 days and it is independent 
confirmation of the slow rotation that Pravec et al. obtained from lightcurves.
However, decoupling the effects of rotation and sky motion generally 
requires modeling for the asteroid's shape and estimating the spin 
vector (Hudson 1993), so our constraint on the rotation period based on 
visual inspection of the echoes should be treated as a preliminary estimate. 

The bandwidth increased between July 24 and August 1 by a factor of about 1.8,
which, if we ignore the NPA rotation that is suggested by the lightcurves, 
suggests that the instantaneous subradar latitude moved south from about
72 to 57 degrees (cf. Ostro 1987).  
If we adopt Pravec et al.'s nominal rotation period of 6.76 days, then the 
July 24 and August 1 bandwidths correspond to lower bounds on the maximum 
pole-on dimension of about 9.2 km, or somewhat
more than twice the observed range extent.  This is close to what we expect
if the asteroid's center-of-mass is near the trailing edge in the images.
1999 JM8's 50 degrees of westerly motion (i.e., toward decreasing right ascension) 
indicates that the sense of rotation between July 24 and August 1, an 
interval of 7.8 days, must be retrograde in order for the apparent rotation 
to be longer than the rotation period from the lightcurves.  A period of close 
to 7 days is also suggested by the similarity of the August 8 images to
those obtained on July 24 and August 1.

Shape and elongation
--------------------

The images provide strong evidence that 1999 JM8 has an irregular and asymmetric
shape.  For example, the leading edge is rounded on July 24, 31, and August
1, 2, 8, and 9, but portions of it are distinctly angular on July 27, 
August 5, and 6.  In the July 28 image two hill-like features are evident 
on the leading edge that extend about 400 meters toward the radar relative 
to their surroundings.  The August 5 image shows an extended, gently undulating 
leading edge.  A rotated view of the same feature on August 6, when the 
feature is oriented closer to the line of sight, shows that it 
is close to 5 km in its maximum dimension.
Using the 2-sigma level as a threshold for detection, then there is a 
maximum factor of 1.5 difference in the visible delay extent among
the Arecibo images and a factor of 1.7 difference in the Goldstone images.  
Although the shape of 1999 JM8 is apparently irregular, 1999 JM8 is
not bifurcated, in contrast with Toutatis (Ostro et al.
1995, Hudson and Ostro 1995), Castalia (Ostro et al. 1990, Hudson and Ostro
1994), and Bacchus (Benner et al. 1999).  

We estimated the elongation of JM8 from extrema in the echo bandwidths 
between August 1 and 9, when we obtained the strongest images with the 
highest frequency resolution.  The August 1 and 8 images are similar 
and their echo bandwidths have a ratio of 1.1, suggesting that the 42 
degrees of sky motion did not substantially alter the subradar latitude
between the two days and that variations in the bandwidth during the 
intervening days result mostly from the asteroid's shape.  The ratio of 
the maximum (Aug 5) to the minimum (Aug 2 and 3) bandwidths is only 1.2, 
suggesting that 1999 JM8 is not very elongated.  This is comparable to the 
three lowest NEA elongations reported from radar observations to date: 
2100 Ra-Shalom (Shepard et al. 2000), 7822 (1991 CS) (Benner et al. 1999a), 
and 1998 KY26 (Ostro et al. 1999b).  Ultimately a more accurate estimate of 
the asteroid's elongation will come from the shape reconstruction, which
will explicitly remove bandwidth variations caused by sky motion on the
apparent subradar latitude and the effects of non-principal axis rotation.

Several of the images show a distal arc or linear extension of pixels
(July 24 August 1 and 8).  The sequence of daily images between July 31 and 
August 9 makes it clear that this feature is the "indentation" that is 
prominent on the approaching limb on August 5.  

Concavities
-----------

The 1999 JM8 images contain numerous examples of relatively bright pixels 
surrounding rounded clusters of radar dark pixels.  These are the signatures of 
concavities that may be impact craters, as have previously been
seen in delay-Doppler images of Touatatis (Ostro et al. 1995, Hudson and Ostro
1995) and Geographos (Ostro et al. 1996, Hudson and Ostro 1999).  Figure
CRATERS identifies possible concavities.  Our concavity identifications
are somewhat subjective due to the delay-Doppler resolution; the variable to low 
SNRs across portions of the images, particularly near the trailing edges; the 
modest contrast in echo power between the dark pixels and surrounding brighter 
pixels of some features; and due to delay-Doppler projection effects that 
may explain why several features are elliptical or tear-shaped.  Most of the
possible concavities have been identified in images on at least two days; 
several of the largest have been seen on as many as six days and are clearly real.
It is possible that we may have missed some features or even included
some features that are not concavities, but in what follows we will assume 
that the features we have identified are craters and explore the implications.

We estimated the visible range extents of the features from the delay-Doppler 
images.  For features visible on multiple days, the maximum range
extents are consistent for some features but are different by as much 
as several tens of percent for others, differences that in some cases result 
from changes in the projected shape of the features from one day to the next 
in the images, perhaps due to projection effects as the asteroid
spins, and also due to the weak SNR of some features near the trailing edges
of the echoes that make identifying concavities difficult.  
Much more robust estimates of the geographic distribution and dimensions
of impact craters will become available upon completion of the 3-D shape model.

We identified about 40 concavities that have visible range extents between 
about 0.1 and 1.6 km.  Features in the ~200-400 m size range comprise about
~50% of the total.  There appear to be at least 5 concavities larger than 
about 500 meters and 3 larger than about 1 km.  

The upper limit has considerable uncertainty:
there's clearly at least one significant, nearly central concavity visible 
on July 24, Aug 1, 2, 3, 8, and 9, but the maximum dimension is
difficult to estimate because most of the concavity is in shadow.
The best view seems to be on August 8 when the concavity is prominent along the 
trailing edge at frequencies just negative of zero Hz.  On that day the feature 
has a visible range extent of about 1.5 km, but on August 1 and 2 it appears 
to be close to 2 km in visible extent.  

The three days when the most concavities are visible are August 5, when we 
counted about 25, and August 4 and 6, when about 15 are visible.  In 
contrast, if we consider only the days with the highest delay resolution 
(19 m/pixel at Goldstone on July 31 and August 1 and 15 m/pixel at Arecibo
on August 1-6 and August 9), then the fewest number of concavities that are 
discernible, less than 5, is on August 9.  

We do not have a 3-D shape model of 1999 JM8 so we cannot reliably estimate 
how large these concavities are relative to the asteroid's effective 
diameter, but if the effective diameter of 1999 JM8 is as large as ~8.4 km,
which is about twice the mean visible range extent in the Arecibo images, 
then the largest concavity may be close to 20% of the asteroid's diameter.  
This would suggest that 1999 JM8 is not a small version of 243 Mathilde, which 
has at least 7 craters larger than 47% of its diameter, which greatly
exceeds the apparent abundance of relatively large craters on 1999 JM8 
(Veverka et al. 1997, Chapman et al. 1999).  

The largest concavities are visible on July 24, 31, Aug 1, 2, 
3, 8, and 9, days that, except for August 3, do not show many small craters.
This suggests that there may be a global asymmetry in the distribution of
the largest craters.  

The days in which we see the most large craters are days in which we do
not see many 

Several of the days in which the four largest concavities are visible 
(Jul 24, 31, Aug 1-3, 8, and 9) show fewer concavities are also characterized 
by a general paucity of abundant smaller craters.  

Is the apparent difference in the distribution of concavities real, or is it
an artifact of geometry, SNR, and resolution?  If it's real, then the implication
is that the largest craters obscured the many smaller craters that likely preceded
them.  Then the question is why more smaller craters aren't visible on top of
the large ones?  Are the large craters geologically young?  It could be that there
_are_ craters in the larger ones but the geometry, SNR, and resolution prevent
us from seeing them.

These craters
appear to be on the opposite hemisphere from craters seen on July 24, 31, August 1-3
and August 8-9 so I suspect that they aren't the same.  The craters on the other 
days were less numerous and much larger.  These crude estimates of the geographic 
distribution seem to indicate a significant difference in the abundance of large
and small craters between hemispheres.  Why would one side have more
much larger craters than the other?  Perhaps the side with large craters might not have
as many small ones because the big craters could have "erased" the smaller ones.

Curiously, an asymmetric distribution of the largest craters was also seen on Ida.

Are there any concavities with radar-bright annuli surrounding them?
Near the center of the July 28 image is a radar-bright annulus encompassing
a group of pixels that are about 100 m in diameter, suggesting a small impact crater 
with a radar-bright feature surrounding it.  Crater 37, which is visible on
July 31 and August 1 and has a range extent of ~170 m, also has a radar-bright 
annulus.  This feature is more
obvious in the Arecibo image than in the Goldstone image.  Crater 36 also 
appears to have a radar-bright loop that appears to overlap its rim in the
August 1, 2, and 3 images.  The ellipsoidal delay-Doppler distribution of
bright pixels associated with this feature suggest an oblique view, so perhaps
the "rim" is radar bright because of relatively abundant facets along the 
rim that are normal to the line of sight.  Radar-bright features surrounding 
impact craters have not been seen previously in radar images of asteroids, but
they have been found surrounding impact craters in Haystack (Thompson et al. 1981)
and Arecibo (Stacy et al. 1997) radar images of the Moon and in Arecibo 
(Burns and Campbell 1985, Campbell et al. 1990), Goldstone (Jurgens et al. 1988),
Venera (Basilevsky et al. 1987), and Magellan (Phillips et al. 1991) images of Venus.
Whether or not radar bright elliptical rings surrounding concavities on 1999 JM8
are extended features, perhaps due to near-surface roughness, or due to facets
oriented orthogonal to the line of sight, is not
clear due to the coarse resolution and S/N.  If these are roughness features, then
they have implications for regolith retention and/or near-surface shaking on JM8 
and the relative age of the concavities.  

None of the crater-like features on 1999 JM8 is complex: there are no central 
peaks, peak rings, or multi-ring basins, or craters that clearly overlap. 
Of course, complex crater structures are not
expected for such a small object due to its weak gravity (Melosh 1989).
We do not see any ejecta in the images.  There are suggestions of crater
clusters but we do not see clear evidence of overlapping concavities, thus
we cannot discern the stratigraphic sequence of surface features.
We do not see compelling evidence of terracing or slumping in any craters, 
but there are enigmatic groups of bright pixels that appear in two of the
largest craters that were best seen in Arecibo images on August 1 and 2.
There are hints, but not compelling evidence, that some of the concavities
may have irregularly shaped rims.  Ultimately we hope to understand the 
geographic and size distributions of craters on JM8 in order to compare its 
collisional history with those estimated from crater distributions on Gaspra, 
Ida, and Mathilde.   Ultimately the shape reconstruction will provide the best 
constraints on the abundance, dimensions, and geographic distribution of 
craters on 1999 JM8.

Linear features
---------------

The images show at least two approximately linear features that
to appear to be unrelated to impact craters.  The most prominent 
is seen on August 4 as a narrow undulatory curve of bright pixels extending 
about 0.5 Hz from the positive leading edge 
toward the negative leading edge.  This feature is also visible on August 3 and
5.  A second linear feature is evident in images obtained on July 31 and August 1.
In the July 31 image it occurs at positive frequencies between the 
leading edge and at least two craters, the larger of which it appears to 
intersect.  It is about 0.5 Hz wide on August 1.

A plausible interpretation is that the features are radar bright due 
orientation of facets nearly normal to the radar line of sight.  The origin
of the features is unknown, but they might be ridges, fault scarps, 
or grooves.  Grooves have been seen in spacecraft images of Gaspra (Veverka et
al. 1994) and Ida (Sullivan et al. 1996), and linear features were seen on 
Mathilde (Thomas et al. 1999), but no linear features have been seen previously 
on any NEAs imaged by radar.

Other surface features
----------------------

Collection of radar bright pixels inside craters on August 1 and 2.  The August 2
pixels are associated with the high SC/OC feature.  

Surface features
----------------

The first hint of surface features appears in the July 21 image in the 
form of two groups of dark pixels (near the trailing edge) that are surrounded 
by annuli of relatively bright pixels, which may correspond to concavities.
The July 23 image has a diffuse group of relatively bright pixels beyond the
negative leading edge, suggesting an intervening topographic low.  

The first obvious surface features are two tear-shaped clusters of radar-dark 
pixels surrounded by much brighter pixels that appear on either side 
of zero Hz in the July 24 image.  These are the delay-Doppler signature 
of concavities and a plausible interpretation is that they may be 
impact craters.  The July 24 image also reveals a concavity ~1.4 km in diameter
near the trailing edge; this may be the same apparent concavity that was seen 
on July 23.  There appear to be other surface features near the sub-radar
point and along the approaching limb, but it is not clear what they are.
The July 24 images span about 2 hours, so we checked
images obtained at the beginning and end of the track for evidence of rotation 
but we did not find any.  For images with resolution of 75 m x 0.075 Hz, 
this suggests that the the apparent rotation period is at least several days.

The July 27 image shows a pronounced angular, asymmetric distribution
of echo power including a pointed subradar 
region that extends about 400 m toward Earth relative to an adjacent, 
nearly flat region at more positive frequencies (near zero Hz).  
The negative limb appears to have two "steps" as a function of range that
are also the brightest regions in this image, suggesting surfaces with more
facets nearly normal to the line of sight than elsewhere on the target on
this day.  There are no obvious concavities in the July 27 image.
The general weak echo strength may be due, in part, to a dearth of
nearly normal surface facets to reflect the radar, as was seen in end-on
Goldstone images of 1620 Geographos.  

The July 28 image is dramatically different from
the July 27 image.  The distribution of echo power is asymmetric with more power
evident at negative frequencies than at positive frequencies.  The
leading edge has two prominent "hills" with sub-Earth points that are at 
nearly the same time delay.  Between the two hills the LE is about 400 m
back in range, suggesting that the "hill" at negative frequencies may be
the "pointed" feature seen on July 27.    There 
is also an arcuate feature of bright pixels just inside the positive limb
that is similar to other features seen on July 24.  

Between July 31 and August 9 we imaged 1999 JM8 on each day at intervals
that were generally close to or slightly less than 24 hours.  This produced
images in which the rotation of prominent features from day-to-day is 
obvious.  

JULY 31: 
This and the August 1 image are the highest resolution images
obtained at Goldstone.  The image does not obviously repeat features that
were seen on previous days.  The shape of the LE is somewhat angular but
there are no pointed ends or twin peaks visible as there were on July 27
and 28.  New surface features are visible at ranges beyond the LE.  For 
example, at frequencies just positive of zero Hz and beginning about 20
range gates in from the LE there's a large approximately circular feature
that is probabably an impact crater.  Its range extent is about 700 meters 
and its bandwidth is about 0.9 Hz, although the range extent isn't really
obvious due to the low SNR and an adjacent feature that may be more
of the crater.  If so, then then the range extent is close to
880 m.  Adjacent to this crater at slightly
larger range gates is another much smaller, nearly circular feature that
may also be an impact crater that extends about 190 m in range and 0.3 Hz
in Doppler frequency.  At the same range gates as this crater-like feature
but at immediately more positive Doppler frequencies is a small radar-
bright region spanning about 0.2 Hz and about 90 meters.  The resolution
is not high enough to determine definitively what this feature is.

A third possible crater that has range and Doppler extents of about 400 m 
x 0.5 Hz is present adjacent to but at larger time delays than the bright
feature.  There is a weak roughly circular feature near the TE along
the positive limb that may be another crater; it appears to be close to 
1 km in range extent and about 0.9 Hz in Doppler frequency.  

The TE near zero Hz is has a broad distribution of weak pixels that 
suggest a large concavity with a range extent of about 1.2 km.  
The other prominent feature in this image is 
a linear group of bright pixels between the positive limb/LE and the
large crater that starts about 20 range gates behind the LE.

The LE negative of zero Hz is almost linear--that is, it's not parabolic
as would be expected from a spherical target.  

AUGUST 1: 
This is the only day in which we have coverage at both Goldstone
and Arecibo.  The Arecibo image is much stronger, has higher range and
frequency resolution, and shows more detail.  Comparison of the Goldstone
and Arecibo images indicates that there are no features in the Goldstone
image that are not also present in the Arecibo image.  

The two
large crater-like features seen on July 31 are obvious on August 1 and
also correspond to the two tear-shaped features seen on July 24.  One
feature is clearly an impact crater with an apparently radar bright rim
near the LE.  This suggests either elevated topograph, surface roughness,
or both along that rim.  There is a narrow region of bright pixels
extending from the crater rim just negative of zero Hz toward the 
positive LE/limb and in the other direction toward the negative
limb.  Within the large crater just negative of zero Hz there is a 
group of radar bright pixels at ranges just inside (i.e.
closer to the radar) than the far rim.  The really obvious crater
on the negative side of zero Hz has a range extent of about 850 m
in the Arecibo image (using bright pixels along apparent proximal
and distal rims) and about 880 m in the Goldstone image.  

There is a prominent tear-shaped feature along the positive limb that may
be a crater viewed obliquely.  It has a radar-bright rim and there is a 
diffuse group of bright pixels about 10 range gates deep and about 
8 Doppler cells wide adjacent to it on its side toward the LE.  The range
extent is indefinite due to the non-circular shape but it appear to be
either 1.0 or 1.2 km, depending on which group of bright pixels one
chooses to define the distal rim.  

The receding limb is strikingly angular with a sharp bend 
about 3 km beyond the LE at the subradar point.  Between the sub-Earth 
point and the bend, much of the receding limb is approximately linear as
a function of delay and Doppler, and appears to correspond to the
linear LE that was seen at negative frequencies on July 31.  

There is a column of faint but statistically significant pixels at 
the receding limb that extend at least ~1 km deeper in range than the 
rest of the TE.  The column is about 0.2 Hz wide.  

The TE is irregular in shape and it suggests the presence of a large 
concavity; the shape of the concavity is not obvious but it does not 
appear to be not circular.

AUGUST 2:
The perimeter of the August 2 image is strikingly rounded with about 3/4
of a circular perimeter visible.  The most prominent interior feature 
in the echo is a large radar dark region that extends from the TE inward 
to slightly less than 1/2 of the echo's delay
depth.  The large dark feature appears to be a substantial concavity that is
about 2.4 km wide.  

Two prominent tear-shaped features are probably the craters that were 
seen on August 1, but they are rotated by about 45 degrees relative to 
their position on the previous day.  The one near zero Hz has an intriguing
radar bright feature that appears inside it near the distal crater rim.
This feature may be a topographic high, but it is not clear whether it is
actually inside the crater or whether it is a superposition from the 
opposite hemisphere.  The rim of this crater closest to the LE is 
radar bright, as was seen with the rim of the other crater (that is near
the receding limb on Aug 2) that was near zero Hz in the Aug 1 image.
The central crater in this image has an apparent range extent of about 800 m.

The arc of points on the receding limb near the TE has an irregular
distribution of bright and dark pixels suggesting surface structure.

AUGUST 3:
The echo is rounded and modestly asymmetric as a function of Doppler
frequency with points closer to the radar to the negative of zero Hz.

The August 3 image has an angular region at the TE that is devoid of
pixels with significant echo power, suggesting that it is the 
concavity seen in the August 2 image.  

The progression of tear-shaped crater from August 2 is obvious in
the August 3 image. The crater near zero Hz on August 2 is close to 
the receding limb on August 3.  The rim nearest the LE is again radar
bright, particularly at less negative Doppler frequencies.  The 
tear-shaped structure appears to have a maximum range extent of 
about 1.2 km, comparable to its extent on August 1 but about
50% more than its extent on August 2.  

There is another probable impact crater with dimensions of about 
560 m x 0.75 Hz that is evident on the negative side of zero Hz near
the sub-Earth point.  Its proximal rim begins about 150 m into the 
echo from the LE.  

A prominent radar bright, narrow linear feature extends from the 
positive limb toward the LE at zero Hz.  

There are hints of structure on the approaching limb and TE but the
echoes there are not strong enough to distinguish the features.

AUGUST 4:
The August 4 image is distinctly asymmetric with the LE to the negative
of zero Hz.  The delay-Doppler distribution is broadly triangular.
The image has only 5 looks and the SNR relatively weak so that fewer 
surface details are visible than on other days.  The approaching limb
has three distinct linear segments, two of which are approximately
parallel.  There is a short segment between the two parallel
segments.  

The approximately linear radar-bright feature seen on August 3 (between
the approaching limb and the sub-radar point) is more obvious on August
4, although it has rotated by close to 50 degrees.  

There are hints of several circular features but none has sufficient
detail to be confident that it is an impact crater.  The best plausible
crater candidate is just inside the bend in the approaching limb and at
range gates just beyond the linear radar bright feature mentioned above.

AUGUST 5:
The LE of this echo is the most nearly uniform in time delay of any 
day that we observed 1999 JM8.  The LE is not remotely parabolic, as 
would be expected of a spheroidal target, but is approximately flat.
The image is very strong and shows the most detail of any Arecibo 
image of this object.  Numerous approximately circular patches of
pixels dot the surface and are probably impact craters.  The two largest
craters are just past the LE near zero Hz and about half-way between
zero Hz and the receding limb.  They have dimensions of about 470 m x 0.14 Hz
and 450 m x 0.17 Hz.  There is another smaller crater-like feature
near the positive limb about half way between the LE and the TE
that has dimensions of about 420 m x 0.11 Hz. 
A fourth comparably-sized feature exists slightly closer to the TE
and near the receding limb.  

The August 5 image gives the impression that the portion of the surface
illuminated is heavily cratered.  Clearly more features that appear to
be impact craters are visible.  

The linear feature seen on the previous two days is evident close to the
receding limb but it isn't as prominent as it was on August 4.  

There is an indentation in Doppler frequency on the approaching limb.  
Pixels on the trailing edge at this feature are radar bright, suggesting
that surface facets have more projected area oriented normal to the line
of sight than is present on adjacent regions.  

The brightest pixels are on the positive side of the approaching LE.

AUGUST 6:
The nearly flat surface that formed the LE in the August 5 image forms
the receding limb on August 6.  The echo is asymmetric and angular and
there are more pixels at positive frequencies than at negative frequencies.
The brightest pixels are on an approximately flat region positive of
zero Hz. Numerous dark circular features 
 are present and are probably impact craters.  Fewer are visible
in the August 6 image, which has only about 1/3 the number of looks
relative to the August 5 image.  The craters appear to be up to several
hundred meters in diameter. 

AUGUST 7:
We resumed observing at Goldstone for two days.  The echoes have an
asymmetric delay-Doppler distribution.  The echo is more rounded than
on the previous three days. There is a radar-bright "step" on the 
negative limb that is the rotated "indentation" that was seen on the approaching
limb on August 5.  The image does not show any obvious detail inside
the echo other than an arcuate collection of pixels at the positive
limb.  
 

AUGUST 8:
The delay-Doppler distribution of echo power illustrates that this side
of 1999 JM8 is approximately spheroidal, in stark contrast with the 
distribution seen between August 4 and 6.
The August 8 images span more than 7 hours and show the most compelling
evidence of rotation among any of the 1999 JM8 images.  However, the 
rotation is subtle.  In general the image is similar to the August 1 image:
the two prominent craters close to 1 km in diameter are both obvious, with
what appears to be a smaller crater between them, although there is some
rotation between the Aug 1 and 8 images.

This is the best example of a nearly circular delay-Doppler distribution
for the tear-shaped feature that was seen on August 1, 2, and 3.  That 
feature on August 8 has a visible range extent of about 0.9 km, which is
substantially less than suggested by the August 1 and 3 images but is
closer to the extent from the August 2 image. 

The large concavity seen previously seems to have more of its interior 
illuminated on August 8.  The concavity appears to be somewhat angular 
and it is about 1.5 km across and close to 1.4 Hz wide.  The distal 
arc of points at the negative limb is on the negative limb and is now 
seen to be the rotated "indentation" that was prominent on the approaching 
limb on August 5.  

AUGUST 9:
This is the highest resolution view of 1999 JM8.  The delay-Doppler 
distribution is parabolic and indicates that the portion of the asteroid 
that was imaged is rounded.  Nevertheless, the image is asymmetric: there
are more distal points at negative frequencies than at positive frequencies.
One of the two prominent craters that is evident in the August 8 images is
located just negative of zero Hz on August 9.  The crater has dimensions of
1.1 km x 0.22 Hz.  The big concavity seen on August 8 is largely in 
radar shadow on August 9.  As was the case on August 2, the crater has
a distinct group of bright pixels inside it near the distal rim.  The pixels
look like a topographic high.  There is another large region just positive
of zero Hz that looks like another large concavity.  It has dimensions of
1.4 km x 0.21 Hz.   

SIZE, ALBEDOS, and COMPOSITION
==============================

The visible range extents listed in Table DELAY-DOPPLER DISPERSIONS
have a mean of 3.3 km for the Goldstone data and 4.2 km for the Arecibo data,
a difference that is probably due to the greater sensitivity at Arecibo.  
The variation in the range extents and the asymmetric
distribution of delay-Doppler echo power indicate that 
JM8 has an irregular shape, but since the Arecibo observations cover
close to one full rotation, let us assume that the mean range extent of
4.2 km (which is effectively rotationally-averaged) equals the 
effective diameter of JM8 and explore the implications.  

If JM8 has an effective diameter of 4.2 km, then the absolute magnitude
of 15.2 (Table OPTICAL PROPERTIES) corresponds to an optical geometric
albedo pv = 0.08 that establishes that JM8 is an optically dark object.
This is probably a conservative upper bound given that
experience with modeling other asteroid echoes (Hudson and Ostro 1994, 
1995) indicates that the true effective diameter is about a factor 
of two larger than the visible range extent.  The nominal optical albedo 
of 0.08 is consistent with C- and BFGP-type taxonomies.  If JM8 has an 
effective diameter of 8.4 km, then the optical albedo is pv = 0.02, 
which is among the lowest optical albedo estimates ever obtained for
any near-Earth or main-belt asteroid.

Radar albedo
------------

The mean X-band radar cross section is 1.89 km^2 from observations between July
18-August 1.  Those observations appear to sample more than one full
rotation, so although there is considerable variation in the radar cross sections
that may be real due to the target's irregular shape, let us adopt 
the mean of 1.9 km^2 and explore its implications.

If JM8 has an effective diameter of 4.2 km, then the mean X-band radar 
cross section corresponds to a radar albedo of ~0.14, which overlaps the 
radar albedos for C-, S-, and BFGP-type main-belt and near-Earth
asteroids.  If the effective diameter is much larger, say 8.4 km, then 
the radar albedo decreases to 0.034, which is among the lowest asteroid 
radar albedos ever obtained.  However, systematic errors 
in the radar cross section indicate that the true radar albedo of JM8 could 
be a factor of two-three larger than this estimate, but even so, it is 
clear that JM8 is not a radar bright object, so we can rule out E- and
M-class taxonomies.  

SC/OC images
------------

Figure "RATIO IMAGES" shows Arecibo SC, OC, and SC/OC images from 
Aug 1, 2, 3, and 5. The images cover days with the 
strongest echo strengths and for which there are at least 25 looks, so
that the noise statistics are approximately Gaussian.  The images
show only those pixels in which the echo power in both polarizations exceeds 
a threshold of 3-standard deviations.  We also explored thresholds of 5 and 10 
standard deviations and found that although the number of points decreases
with each increase in the threshold, the overall patterns in the 
distribution of SC/OC did not change.  

The OC and SC images look very similar except for features
that are present in the OC images but are not evident in SC 
due to differences in the SNR.  

In each ratio image there is a region of low SC/OC (~0.1) at the LE 
and a general pattern of increasing SC/OC as a function 
of increasing range toward the TE.  Many points near the TE are
characterized by SC/OC > 0.5.  This pattern is similar to that seen
with the 1996 Toutatis data, except that the variation 
in SC/OC for Toutatis is more subtle and the ratio for Toutatis along
the LE is close to 0.2.  

The low SC/OC at the LE probably
indicates that the subradar point of 1999 JM8 has smooth facets that 
are oriented orthogonal to the radar line of sight, in direct analogy
with the specular reflections seen from the sub-Earth points in radar
echoes from Mercury, Venus, the Moon, and Mars.  Ultimately the shape 
model will clarify the situation.

Regions of low SC/OC appear at the LE on each day, generally at the
sub-Earth region.  A notable exception is the image from August 5:
lowest SC/OC occurs in two regions on either side of zero Hz.  

The August 2 image has an ellipsoidal region with low SC/OC near zero Hz 
and close to the apparent TE.  We filtered the
image with a 10 x 10 pixel boxcar and found that SC/OC = 0.08+/-0.002
within the "feature" region and SC/OC = 0.24+/-0.01 in the adjacent 
region at more positive Doppler frequencies (but covering the same 
span of range gates).  This constitutes the first significant circular 
polarization ratio feature observed on an asteroid.

The low SC/OC region appears inside a concavity that is probably an impact crater,
but whether the feature is physically in the 
crater or whether it is superposed from the opposite
hemisphere is not yet clear.  Careful inspection of OC images on Aug 1, 2, 
and 9 shows the feature on all three days and suggests that it is a 
topographic high, but a pronounced region of low SC/OC is present only 
on August 2.  There could be a lack of small-scale structure in the 
low-SC/OC region, causing a deficit of SC power, which seems plausible, or 
perhaps the radar scattering law there could be different from other parts 
of the surface.

The August 2 image also has a narrow, arcuate low SC/OC feature between
the ellipsoidal region described above and the echo's LE.  This feature
is only a few range gates deep and it appears to follow, at least in
part, the contours on the apparent rim of the crater that encloses the
larger ellipsoidal low SC/OC feature described above.  The arcuate feature
also seems to extends toward the negative limb along what may be the rim 
of another crater.  There are also hints of similar structures adjacent
to apparent crater rims on August 1.

SHAPE INVERSION
===============

DISCUSSION
==========

1. Surface bulk density
--------------------
The X-band circular polarization ratio of JM8 indicates that most of the
echo power comes from single back reflections.  Consequently, we can relate
the OC radar albedo to the normalized reflection coefficient and thus
back out constraints on the surface bulk density (refs).  In the absence of 
a 3-D shape model we do not know the gain g, but from previous shape 
reconstructions we have found that g does not usually differ from unity by
more than several tens of percent, which is less than the adopted systematic
uncertainty in the radar cross section, so, to first order, let us assume
that g = 1.  Then R = the radar albedo (+/- 100%) and the bulk density 

d (R) = 3.2 ln[(1 + sqrt(R))/(1 - sqrt(R))].

d (R = 0.034) = 1.2 g/cm^3  ...similar to Mathilde...
d (R = 0.14)  = 2.5 g/cm^3  ...similar to Phobos...

==> We need the shape model <==

2. Compare the radar properties of JM8 with those of other radar-dark asteroids
----------------------------------------------------------------------------
1998 KY26, 1986 JK, 1580 Betulia, 2100 Ra-Shalom (?), main belt asteroids

It's clear now that JM8 is an optically and radar dark object.  It's the best
look with radar that we've ever had at such an object, but there are still
others with which we can compare it: Mathilde, Phobos, Deimos, and possibly
Ra-Shalom, 1986 JK, Betulia, and 1998 KY26.  

KY26 is so drastically different
due to its small size, rapid rotation, and weak gravity that a comparison
may not be very meaningful.  For KY26 SC/OC ~ 0.5 and the radar albedo is
between 0.012 and 0.11.  The radar albedo estimates overlap very preliminary
estimates for JM8.  

We don't know the radar albedo, effective diameter, or rotation period of 
1986 JK.  SC/OC = 0.26+/-0.02.  That's close to estimates for JM8, but it's
also close to the mean for ALL radar-detected NEAs, so it doesn't say much
(yet).  Correction: Steve estimated the radar albedo by adopting the best
available estimates of the effective diameter from optical observations of
H and the taxonomy, suggesting that the radar albedo is between 0.0053 and
0.067.  The upper limit is consistent with that of JM8.

1580 Betulia was observed at both 3.5 cm and 13 cm in 1989.  SC/OC is 0.18+/-0.03
at 3.5 cm and 0.16+/-0.01 at 13 cm.  In the 1986 DA paper Steve reported that
the radar albedo of Betulia is about 0.09, which is also consistent with
the preliminary estimates.

How well does the radar albedo of JM8 compare with the mean and rms 
dispersion observed among radar-detected main-belt targets?  Chris Magri found
that the main-belt C- and S-class radar albedos are indistinguishable.  The
lowest is 0.11 (Daphne) and a few others are about 0.13.  Some, however,
are as large as 0.23.  Perhaps it would be more appropriate to compare 
the radar albedo of JM8 with the BFGP objects.   Most of their radar albedos
cluster at less than 0.1, although one (554 Peraga, type FC) is about 0.2.

Conclusion: radar albedo of JM8 is consistent with other radar-dark C- and 
BFGP-type objects.  SC/OC is less diagnostic due to the substantial observed
range of values.  

What about Phobos?  
Steve mentioned that he's almost sure that the radar cross section and radar
albedos that he published for Phobos are too small: he didn't trust the Goldstone
calibration, which he later discovered were reliable.  Steve's nominal estimated
albedo is 0.093+/-0.035, which is consistent with results for JM8, although the
consistency isn't as good if Steve's estimate is too small by ~20%.  
SC/OC = 0.09+/-0.10, so the decimeter-scale surface is smooth.  This is all based
on a ~9 sigma detection.  SC/OC is about a factor of two smaller for Phobos 
than it is for JM8.  Again, I don't think that SC/OC has reliable correlations
with composition.

Mathilde
Mathilde is about an order of magnitude larger, but like JM8, is is optically
dark (a C-type) and it has several very large craters relative to its diameter.
Mathilde actually has *more* craters large compared with its diameter than
JM8 does.  Perhaps a better analogy with large craters would be Ida... 

Is 1999 JM8 a rubble pile?
--------------------------
Rotation period is extremely slow and is consistent with a rubble pile, 
but does not prove it.  Irregular shape will probably provide the best evidence.  

Abundance of large impact craters isn't necessarily 
an indicator: we don't know the shape yet or Deff.  However, if the four
concavities close to or greater than 1 km in diameter are impact craters,
then that suggests that a significant portion of JM8's interior is 
fractured.

Comparison of relative crater sizes on Ida seems to show more that are relatively larger,
but Ida has a density of 2.6+/-0.5 g/cm^3 that does not strongly suggest
a porous object, plus grooves on Ida are more consistent with an object
that is structurally intact, at least in part.  Surface bulk density 
may or may not be consistent with a rubble pile...as that is sensitive
to the upper few decimeters.  

Comet nucleus?
--------------
Is JM8 an inactive comet nucleus?   JM8's orbit is similar to those of 
some Jupiter family comets.  1999 JM8's Tisserand parameter (def), which is 
< 3 for ~90% of numbered
Jupiter family comets and > 3 for nearly 100% of numbered asteroids with 
a < 3.3 AU, has a value of 2.988.  However, out of ~890 NEAs discovered
through the end of January, 2000, 49 have T less than that of 1999 JM8.
Furthermore, it is known that the orbits of NEAs and 
Jupiter-family comets can intermingle (Valsecchi et al. 1995), so by itself
the orbit of 1999 JM8 does not constitute compelling evidence either 
for or against a cometary origin.

1999 JM8's low optical and radar albedos are consistent with those estimated 
optically for comet Halley (value; ref) and by radar for comet IAA (0.04; 
Harmon et al. 1989), but they are also consistent with estimates
for radar and optically dark near-Earth (Ostro et al. 1991) and main-belt 
asteroids (Magri et al. 1999).  Nor is there evidence of a coma or tail 
from the very close encounter in 1999.

Comet Halley is strongly suspected of being an NPA rotator (Belton et al.), but 
the abundance of NPA rotators among short-period comets is not known, and NPA
rotation has been confirmed with one NEA (Toutatis, Hudson and Ostro 1995) 
and is strongly suspected for several others (Harris 1994),  so it is unclear 
whether NPA rotation can be regarded as diagnostic of a comet.

Is 1999 JM8 a small version of Mathilde? 
---------------------------------------- 
composition is similar: optically dark and primitive object
rotation states are both very slow and apparently NPA
abundance of large craters, although really large craters are more common on Mathilde
irregular shapes...but we could say that about other objects too.
Surface bulk density compared with Mathilde's density.

What are plausible explanations for JM8's shape?
------------------------------------------------

Non-principal axis rotation
---------------------------
Is 1999 JM8 a non-principal axis rotator?  Pravec et al. obtained
a best-fit rotation period of 6.76 days, but they note that the lightcurves
do not appear to be strictly periodic.  A rotation period of close to 7
days is also consistent with delay-Doppler images obtained on July 24
and August 1.  Impact simulations by Asphaug and Scheeres (1999) suggest 
that excitation of NPA rotation may be common among fragments of 
catastrophic disruptions; if so, then the question is whether enough time 
has elapsed for damping into a principal axis rotation state.  A simple 
expression for estimating the damping timescale from non-principal to 
principal axis rotation is 

tau ~ (P/C)^3/(Deff^2), 

where tau is in 10^9 y, P is the rotation period in h, Deff is the effective
diameter in km, and C is a constant that depends on the material properties
of the asteroid.  Using Deff = 8.4 km, P = 6.76 d (162.2 h), and C = 17+25-10,
we obtain tau ~ 1.2 +16.4 -1.2 x 10^10 y, an estimate so long that unless
1999 JM8 originated in uniform rotation, then it probably is a non-principal
axis rotator.  
Several other asteroids, notably 288 Glauke, 887 Alinda, 1220 Crocus, 1689
Floris-Jan, 3102 Krok, and 3288 Seleucus are strongly suspected of being NPA 
rotators (Harris 1994).  The only confirmed NPA rotator among the NEA population, 
4179 Toutatis (Hudson and Ostro 1995), has an estimated damping time of 
~6 E 10 y.  

How did 1999 JM8 acquire its spin state?
----------------------------------------
The nominal ~7-day rotation period of 1999 JM8 exceeds more than 99% of all 
reported asteroid rotation periods (Pravec and Harris 1999). How did the 
slow, non-principal axis rotation state of 1999 JM8 originate?  Among plausible
explanations are that the rotation resulted from the disruption of a larger 
progenitor, of which 1999 JM8 is a fragment, either as a direct consequence 
of the disruption or due to gravitational interactions during dispersal
(Asphaug and Scheeres 1999); from tidal interactions during one or more very 
close terrestrial planetary flybys (Richardson et al. 1998, Scheeres et al. 
1999); from secular effects of Yarkovsky thermal forces (Rubincam 1999); from 
a sequence of large impacts; or from a combination of these mechanisms.  
Simulations may elucidate the efficacy of these mechanisms.

REFERENCES
==========
Asphaug, E., J. M. Moore, D. Morrison, W. Benz, M. C. Nolan, and R. J. Sullivan 1996.
     Mechanical and geological effects of impact cratering on Ida.  Icarus 120, 158-184.

Benner, L. A. M., S. J. Ostro, J. D. Giorgini, R. F. Jurgens, D. L. Mitchell, R. Rose,
     K. D. Rosema, M. A. Slade, R. Winkler, D. K. Yeomans, D. B. Campbell, J. F.
     Chandler, and I. I. Shapiro 1997.  Radar detection of near-Earth asteroids
     2062 Aten, 2101 Adonis, 3103 Eger, 4544 Xanthus, and 1992 QN.  Icarus 130,
     296-312.

Benner, L. A. M., S. J. Ostro, K. D. Rosema, J. D. Giorgini, D. Choate, R. F. Jurgens,
     R. Rose, M. A. Slade, M. L. Thomas, R. Winkler, and D. K. Yeomans 1999a.  Radar
     observations of asteroid 7822 (1991 CS).  Icarus 137, 247-259.

Benner, L. A. M., R. S. Hudson, S. J. Ostro, K. D. Rosema, J. D. Giorgini, D. K. 
     Yeomans, R. F. Jurgens, D. L. Mitchell, R. Winkler, R. Rose, M. A. Slade, M. L.
     Thomas, and P. Pravec. 1999b. Radar observations of asteroid 2063 Bacchus.  
     Icarus 139, 309-327.

Burns, B. A., and D. B. Campbell 1985.  Radar evidence for cratering on Venus.  J. 
     Geophys. Res. 90, 3037-3047.

Campbell, D. B., N. J. S. Stacy, and A. A. Hine 1990.  Venus: Crater distributions
     at low northern latitudes and in the southern hemisphere from new Arecibo 
     observations.  Geophys. Res. Lett. 17, 1389-1392.

Chapman, C. R., W. J. Merline, and P. Thomas 1999.  Cratering on Mathilde.  Icarus
     140, 28-33.

Harmon, J. K., D. B. Campbell, A. A. Hine, I. I. Shapiro, and B. G. Marsden 1989. 
     Radar observations of comet IRAS-Araki-Alcock 1983 d.  Astrophys. J. 338, 
     1071-1093.

Harris, A. W. 1994.  Tumbling asteroids.  Icarus 107, 209-211.

Hudson, S. 1993.  Three-dimensional reconstruction of asteroids from radar
     observations.  Remote Sens. Rev. 8, 195-203.

Hudson, R. S., and S. J. Ostro 1994. Shape of asteroid 4769 Castalia (1989 PB) from 
     inversion of radar images.  Science 263, 940-943.

Hudson, R. S., and S. J. Ostro 1995.  Shape and non-principal axis spin state of asteroid
     4179 Toutatis.  Science 270, 84-86.

Hudson, R. S., and S. J. Ostro 1999.  Physical model of asteroid 1620 Geographos from radar
     and optical data.  Icarus 140, 369-378.

Hudson, R. S., S. J. Ostro, et al. 2000.  Radar observations and physical modeling of
     asteroid 6489 Golevka.  In preparation.

Jurgens, R. F., M. A. Slade, and R. S. Saunders 1988.  Evidence for highly reflecting
     materials on the surface and subsurface of Venus.  Science 240, 1021-1023.

Magri, C., S. J. Ostro, K. D. Rosema, M. L. Thomas, D. L. Mitchell, D. B. Campbell,
     J. F. Chandler, I. I. Shapiro, J. D. Giorgini, and D. K. Yeomans 1999.  Mainbelt
     asteroids: Results of Arecibo and Goldstone radar observations of 37 objects 
     during 1980-1995.  Icarus 140, 379-407.

Melosh, H. J. 1989.  Impact Cratering: A Geologic Process. Oxford University Press,
     New York. 

Mitchell, D. L., R. S. Hudson, S. J. Ostro, and K. D. Rosema 1998. Shape of asteroid 
     433 Eros from inversion of Goldstone radar Doppler spectra.  Icarus 131, 4-14.

Ostro, S. J. 1987.  Physical properties of asteroids from radar observations.  In
     Evolution of the Small Bodies of the Solar System.  pp. 131-146, XCVII Corso,
     Soc. Italiana di Fisica, Bologna, Italy.

Ostro, S. J., D. B. Campbell, J. F. Chandler, A. A. Hine, R. S. Hudson, K. D. Rosema, 
     and I. I. Shapiro 1991.  Asteroid 1986 DA: Radar evidence for a metallic composition.
     Science 252, 1399-1404.

Ostro, S. J., R. S. Hudson, R. F. Jurgens, K. D. Rosema, D. B. Campbell, D. K. Yeomans,
     J. F. Chandler, J. D. Giorgini, R. Winkler, R. Rose, S. D. Howard, M. A. Slade,
     P. Perillat, and I. I. Shapiro 1995.  Radar images of asteroid 4179 Toutatis.
     Science 270, 80-83.

Ostro, S. J., R. F. Jurgens, K. D. Rosema, R. S. Hudson, J. D. Giorgini, R. Winkler, 
     D. K. Yeomans, D. Choate, R. Rose, M. A. Slade, S. D. Howard, D. J. Scheeres, 
     and D. L. Mitchell 1996.  Radar observations of asteroid 1620 Geographos.  Icarus
     121, 46-66.

Ostro, S. J., R. S. Hudson, K. D. Rosema, J. D. Giorgini, R. F. Jurgens, D. K. Yeomans,
     P. W. Chodas, R. Winkler, R. Rose, D. Choate, R. A. Cormier, D. Kelley, R. Little-
     fair, L. A. M. Benner, M. L. Thomas, and M. A. Slade 1999a.  Asteroid 4179 Toutatis:
     1996 radar observations.  Icarus 137, 122-139.

Ostro, S. J., P. Pravec, L. A. M. Benner, R. S. Hudson, L. Sarounova, M. D. Hicks,
     D. L. Rabinowitz, J. V. Scotti, D. J. Tholen, M. Wolf, R. F. Jurgens, M. L.
     Thomas, J. D. Giorgini, P. W. Chodas, D. K. Yeomans, R. Rose, R. Frye, K. D.
     Rosema, R. Winkler, and M. A. Slade 1999b.  Radar and optical observations of
     asteroid 1998 KY26.  Science 285, 557-559.

Phillips, R. J., R. E. Arvidson, J. M. Boyce, D. B. Campbell, J. E. Guest, G. G.
     Schaber, and L. A. Soderblom 1991.  Impact craters on Venus: Initial analysis
     from Magellan.  Science 252, 288-297.

Pravec, P., and A. W. Harris 2000. Fast and slowly rotating asteroids. Submitted to
     Icarus. 

Pravec, P., et al. Optical and radar observations of 1999 GU3, in preparation.

Rubincam, D. P. 2000.  Radiative spin-up and spin-down of asteroids.  Submitted to
     Icarus.

Scheeres, D. J., S. J. Ostro, E. I. Asphaug, and R. S. Hudson 1999.  Alteration
     of asteroid spin states during close planetary encounters.  Bull. Am. Astron.
     Soc. 31, 1112. [Abstract]

Shepard, M. K., S. J. Ostro, L. A. M. Benner, A. W. Harris, K. D. Rosema, I. I.
     Shapiro, J. F. Chandler, and D. B. Campbell 2000.  Radar observations of
     2100 Ra-Shalom.  In preparation. 

Stacy, N. J. S., D. B. Campbell, and P. G. Ford 1997.  Arecibo radar mapping of the
     lunar poles: A search for ice deposits.  Science 276, 1527-1530.

Sullivan, R., R. Greeley, R. Pappalardo, E. Asphaug, J. M. Moore, D. Morrison, 
     M. J. S. Belton, M. Carr, C. R. Chapman, P. Geissler, R. Greenberg, J. Granahan,
     J. W. Head III, R. Kirk, A. McEwen, P. Lee, P. C. Thomas, and J. Veverka 1996.
     Geology of 243 Ida.  Icarus 120, 119-139.

Thomas, P. C., J. Veverka, J. F. Bell III, B. E. Clark, B. Carcich, J. Joseph,
     M. Robinson, L. A. McFadden, M. C. Malin, C. R. Chapman, W. Merline, and 
     S. Murchie 1999.  Mathilde: Size, shape and geology.  Icarus 140, 17-27.

Thompson, T. W., S. H. Zisk, R. W. Shorthill, P. H. Schultz, and J. A. Cutts 1981.
     Lunar craters with radar bright ejecta.  Icarus 46, 201-225.

Valsecchi, G. B., A. Morbidelli, R. Gonczi, P. Farinella, Ch. Froeschle, and Cl.
     Froeschle 1995.  The dynamics of objects in orbits resembling that of P/Encke.
     Icarus 118, 169-180.

Veverka, J. P. Thomas, D. Simonelli, M. J. S. Belton, M. Carr, C. Chapman, M. E.
     Davies, R. Greeley, R. Greenberg, J. Head, K. Klaasen, T. V. Johnson, D.
     Morrison, and G. Neukum 1994.  Discovery of grooves on Gaspra.  Icarus 107,
     72-83.  

Veverka, J. P. C. Thomas, J. F. Bell III, M. Bell, B. Carcich, B. Clark, A. Harch,
     J. Joseph, P. Martin, M. Robinson, S. Murchie, N. Izenberg, E. Hawkins, J. 
     Warren, R. Farquhar, A. Cheng, D. Dunham, C. Chapman, W. J. Merline, L. 
     McFadden, D. Wellnitz, M. Malin, W. M. Owen Jr., J. K. Miller, B. G. Williams,
     and D. K. Yeomans 1999.  Imaging of asteroid 433 Eros during NEAR's flyby
     reconnaissance.  Science 285, 562-564.