**RADAR OBSERVATIONS OF ASTEROID 1999 JM8**

LANCE A. M. BENNER^1^\*, STEVEN J. OSTRO^1^, MICHAEL C. NOLAN^2^,
JEAN-LUC MARGOT^3^, JON D. GIORGINI^1^, R. SCOTT HUDSON^4^, RAYMOND F.
JURGENS^1^, MARTIN A. SLADE^1^, ELLEN S. HOWELL^2^, DONALD B.
CAMPBELL^5^, DONALD K. YEOMANS^1^

^1^Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, CA 91109-8099

^2^Arecibo Observatory, National Astronomy and Ionosphere Center,
Arecibo, PR 00612

^3^Division of Geological and Planetary Sciences, California Institute
of Technology, Pasadena, CA 91125

^4^School of Electrical Engineering and Computer Science, Washington
StateUniversity, Pullman, WA 99164-2752

^5^National Astronomy and Ionosphere Center, Space Sciences Building,
Cornell University, Ithaca, NY 14853

Submitted to *Meteoritics and Planetary Science*

November 2001

Revised: January 2002

29 manuscript pages (including cover sheets, tables, and figure
captions)

7 tables

6 figures

\*Correspondence author:

Dr. Lance A. M. Benner email: lance@reason.jpl.nasa.gov

Mail Stop 300-233 phone: 818-354-7412

Jet Propulsion Laboratory fax: 818-354-9476

Pasadena, CA 91109-8099

**ABSTRACT**

**We report results of delay-Doppler observations of 1999 JM8 with the
Goldstone 8560 MHz (3.5 cm) and Arecibo 2380 MHz (13 cm) radars over 18
days in July-August 1999. The images place thousands of pixels on the
asteroid and achieve range resolutions as fine as 15 m/pixel. The images
reveal an asymmetric, irregularly shaped object with a typical overall
dimension within 20% of 7 km. If we assume that 1999 JM8\'s effective
diameter is 7 km, then the absolute magnitude, 15.15, and the average
Goldstone radar cross section, 2.49 km\^2, correspond to optical and
radar albedos of 0.02 and 0.06, establishing that 1999 JM8 is a dark
object at optical and radar wavelengths. The asteroid is in a
non-principal axis spin state that, although not yet well determined,
has a dominant periodicity of about 7 days. However, images obtained
between July 31 and August 9 show apparent regular rotation of features
from day to day, suggesting that the rotation state isn\'t far from
principal axis rotation. 1999 JM8 has regions of pronounced topographic
relief, prominent facets several kilometers in extent, numerous
crater-like features between \~100 m and 1.5 km in diameter, and
features whose structural nature is peculiar. Arecibo images provide the
strongest evidence to date for a circular polarization ratio feature on
any asteroid. Combined optical and radar observations from April
1990-December 2000 permit computation of planetary close approach times
to within** ± **10 days over the interval from 293 to at least 2907, one
of the longest spans for any Potentially Hazardous Asteroid. Integration
of the orbit into the past and future shows close approaches to Earth,
Mars, Ceres, and Vesta, but the probability of the object impacting
Earth is zero for at least the next nine centuries.**

**INTRODUCTION**

1999 JM8 was discovered by LINEAR on May 13, 1999, fortuitously more
than two months prior to an encounter within 0.057 AU (22 lunar
distances) of Earth in July 1999, when it reached visual magnitude 14.
It originally had been discovered at Palomar in April, 1990 by E. F.
Helin and designated 1990 HD1, but was lost. M. Hicks, B. Buratti, and
M. Hanner (pers. comm.) obtained photometric colors, vis-IR
spectroscopy, and thermal infrared radiometry suggesting that 1999 JM8
is a C- or X-type (i.e., E-, M-, or P-type) object; subsequent vis-IR
observations obtained by one of us (E. S. H.) at McDonald Observatory
yielded a spectrum more consistent with an EMP-type object. Photometry
obtained by L. Sarounova, P. Pravec, Y. Krugly, V. Shevchenko, S.
Mottola, F. Lahulla, and M. Hicks (P. Pravec, pers. comm.) between July
3.0 and 21.9 indicated that 1999 JM8 is a very slow rotator. Pravec *et
al.* estimated a synodic rotation period of 5.7 ± 0.2 days. The slow
rotation period indicated that the echoes would be very strong and that
observations on many days would be necessary to obtain thorough coverage
in rotation phase. Consequently, prompt communication of the slow
rotation period was invaluable for planning the radar observations.
Table 1 summarizes the asteroid\'s optically- determined physical
properties.

**OVERVIEW OF THE RADAR EXPERIMENT**

The asteroid\'s close approach, large size, and extremely slow rotation
provided an outstanding radar opportunity and we observed 1999 JM8 at
Goldstone and Arecibo on 18 days between July 18 and August 9, 1999.
Orbit solution JPL #15, used for the initial radar detection at
Goldstone on July 18, was very good due to the 9-year arc of optical
astrometry. Due to problems with the delay-Doppler data acquisition
system, on July 18-19 we obtained only CW (continuous wave; i.e.
Doppler-only) echoes. On July 20 we started with 2 CW transmit-receive
cycles (runs), measured a Doppler correction, and then estimated the
range with coarse- resolution 10 and 11 μs (1500 m and 1650 m
resolution) setups. We completed that 70 minute set of observations
(track) with two imaging runs that resolved the target into about twenty

150-m range cells. We updated the orbit solutions several more times
during the experiment; after July 20 range drift due to the ephemeris
was imperceptible. Table 2 summarizes the Goldstone and Arecibo
observations.

After July 20, 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 the finest resolution imaging permitted by the signal-to-noise
ratio. For the final Goldstone tracks on August 7 and 8, the asteroid
was \~50% farther away than at the closest approach, so we used a
coarser resolution of 0.25 μs x 0.075 Hz. However, this still placed
thousands of pixels on the target.

At Arecibo we used two imaging data acquisition systems: the Caltech
Baseband Recorder (CBR), which was designed for observing pulsars and
was made available to us by Stuart Anderson, and a new system (the
Portable Fast Sampler, or PFS) that was then under development. We used
both systems on each day, but the analyses reported here utilize the CBR
data exclusively due to the modestly stronger signal-to-noise ratio
(SNR) and the CBR\'s dual- polarization capability. The range resolution
on all days was 0.1 μs and the frequency resolution varied from 0.010 Hz
to 0.006 Hz depending on the date (Table 2).

**ASTROMETRY & ORBIT REFINEMENT**

Table 3 lists 1999 JM8 radar astrometry and best-fit residuals for a
post-experiment orbit solution and Table 4 lists the estimated orbital
elements and their uncertainties. Combined optical and radar
observations from April 1990-December 2000 permit reliable computation
of the orbit over the interval from 293 to at least 2907, one of the
longest spans for any near-Earth asteroid. Here \"reliable\" means that
the 3-σ uncertainty in the epochs of close approaches is less than 10
days.

Table 5 shows approaches within 0.1 AU of Earth, Mars, Ceres, and Vesta
and within 1.0 AU of Jupiter during that interval. There are multiple
encounters with Earth, Mars, Ceres, Vesta, and Jupiter, but in the next
millennium all the encounters are with Earth, none closer than that in
1999. The impact probability through 2907 is effectively zero.

**DISC-INTEGRATED PROPERTIES**

Our methods of radar data reduction and analysis follow those described
in detail by Ostro e*t al.* (1992, 1996). In Doppler-only observations,
echoes were received simultaneously in the opposite (OC) and same (SC)
senses of circular polarization as the transmission. σ~OC~ is the OC
radar cross section; uncertainties in σ~OC~ are dominated by systematic
pointing and calibration errors that are typically between 20 and 50%.
The circular polarization ratio SC/OC is a gauge of near-surface
roughness at spatial scales near an order of magnitude of the radar
wavelength (12.6 cm at Arecibo and 3.53 cm at Goldstone). For SC/OC,
systematic effects cancel and most remaining statistical errors
propagate from receiver thermal noise.

Table 6 summarizes 1999 JM8\'s 3.5 cm disc-integrated properties and
Fig. 1 shows a collage of CW spectra obtained at Goldstone on each day.
The 3.5 cm cross section varies significantly from day-to-day and we
obtain an average of 2.5 km^2^, to which we assign an uncertainty of
35%. During the course of the experiment the bandwidths increased from
about 1.5 Hz to 3.4 Hz, suggesting a more equatorial view on later dates
and/or an irregular shape. 1999 JM8\'s average SC/OC = 0.19 ± 0.01 is
less than the median of \~0.28 estimated for all radar-detected NEAs, so
the the object\'s near-surface roughness is somewhat less than average.

**DELAY-DOPPLER IMAGES**

Figure 2 shows a chronological sequence of OC delay-Doppler images
obtained between July 20 and August 9. Each frame has the same range and
radial velocity dimensions. Most of the images are sums of all the
highest resolution runs on each day. Due to the well-known north- south
ambiguity inherent with delay-Doppler images, we do not know in which
hemisphere individual features occur.

Table 7 gives the asteroid\'s visible range extents and bandwidths
measured from the images on each day. The maximum extents are 5.3 km on
August 6 and 3.6 Hz (when adjusted to Goldstone\'s frequency of 8560
MHz) on August 5. The Arecibo images generally show larger range extents
than the Goldstone images, perhaps due to the greater sensitivity at
Arecibo and/or due to differences in the asteroid\'s orientation. On
August 1, the only day of overlap between the two observatories, the
visible range extent in the Arecibo image is about 0.3 km deeper. The
images have an average visible range extent of 3.6 km. Based on our
experience with shape inversions of other objects, the visible range
extent typically is about one-half of the true range extent; if so, then
1999 JM8\'s true range extent is about 7 km.

Prominent features in the images appear to rotate by about 50° from
day-to-day between July 31 and August 9, suggesting that 1999 JM8 had an
apparent rotation period of about one week and that the subradar
latitude was within a few tens of degrees of zero during that interval.
Images obtained on July 24, August 1, and August 8 show very similar
surface features, suggesting that the rotation phases were nearly the
same and offering additional support for an apparent rotation period of
about seven days. We searched for evidence of rotation among images
obtained on the same day and found it on several days (e.g., on August 5
and 8, the longest Arecibo and Goldstone tracks; Fig. 3) at rates
consistent with those seen from day to day.

The rotation period evident in the delay-Doppler images is somewhat
longer than the 5.7-d estimate obtained by Pravec *et al.* The
difference could be due to the effects of the large solar phase angles
between 85-120° on dates when the lightcurves were obtained (1999 July
3-21) and the asteroid's irregular shape, sky motion, and the rotation
state (which is discussed below). Given that we can see rotation
directly from in the delay-Doppler images, in the analysis below we
adopt a rotation period of 7 days as our nominal rotation period
estimate. A more precise estimate of the spin state will require
inversion of the delay-Doppler images and lightcurves.

Because the July 31-August 9 image sequence is strikingly similar to
what we\'d expect for a normal rotator viewed close to its equatorial
plane, we adjusted the images to the same delay and Doppler scales and
aligned them by hand to construct an estimate of 1999 JM8\'s pole-on
silhouette (Fig. 4). The silhouette\'s elongation is about 1.15, a value
that ranks near the lower end of the distribution of radar-derived NEA
elongations, which have a mean and rms dispersion of 1.6 ± 0.4 (Ostro
*et al.* 2001).

**SPIN STATE**

Is 1999 JM8\'s rotation principal axis (PA) or non-principal axis (NPA)?
Let us pretend that it is principal axis and then examine the images to
see if this assumption is valid. The apparent rotation vector **W**~app~
is the vector sum of the intrinsic rotation **W**~int~ and the
contribution due to sky motion **W**~sky~. Figure 5 shows that the
angular rate of motion varied from a minimum of about 2° per day to a
maximum of about 7° per day. Between July 20-28, the appearance of the
asteroid changed substantially from day to day (it is difficult to
identify the same features on adjacent days), indicating considerable
apparent daily rotation. Between July 31 and August 9 we observe about
50° of rotation per day, so *W*~int~ dominates over *W*~sky~ and
*W*~app~ \~ *W*~int~.

Delay-Doppler images obtained on July 24 and August 1, days in which the
sky motion was about 4° and 7°, have very similar orientations but their
bandwidths differ by about a factor of two:

*B*~jul24~/*B*~aug1~ = *B*~1~/*B*~2~ = (1.7 ± 0.15 Hz)/(3.3 ± 0.15 Hz) =
0.52 ± 0.05.

If the spin is PA, this bandwidth change was due to the change in
subradar latitude δ from July 24 to August 1. Expressing the apparent
rotation period *P* in hours and the diameter *D* in km gives the 8560
MHz bandwidth *B* in Hz: *B* = 100 *D* cosδ/*P*, so the ratio of the
bandwidths

*B*~1~/*B*~2~ = cosδ~1~/cosδ~2~ = 0.52 could be caused by a change in
cosδ due to about 50° of sky motion between the two days. Furthermore,
\|δ~2~\| 8 0° and \|cosδ~2~\| 8 1, so \|cosδ~1~\| 8 0.52 and \|δ~1~\| 8
59°.

However, visual inspection of features in the July 24 and August 1
images suggests that the orientations of 1999 JM8 on those days differ
by less than 10° of latitude. To quantify the latitude difference
\|δ~1~ - δ~2~\|, we measured the locations in range relative to the
leading edge of several features that are visible in images on both July
24 and August 1. The features differ in range by \~0.5 μs to \~1 μs,
which is 1-2 range pixels at the July 24 resolution, indicating that the
displacement in latitude is small. We quantified the displacement
further by computing the latitude difference that is implied by 0.15 km
(1 μs) of displacement on a sphere \~7 km in diameter. We are convinced
that 10° is a conservative number unless the subradar latitude on July
24 was within a few degrees of the pole, which is impossible because
that would imply an object larger by a factor of several than the one
observed.

Let us adopt the upper limit on the change in \|δ~1~ - δ~2~\| of 10° and
explore its implications:

First cosδ~1~ = (0.52) cosδ~2~

Then cos(δ~2~ + 10°) = (0.52) cosδ~2~

After applying a trigonometry identity and some algebra we obtain:

sinδ~2~/cosδ~2~ = tanδ~2~ = (cos10° - 0.52)/sin10°

So δ~2~ = 69.5°

Therefore: δ~1~ = δ~2~ + 10° = 79.5°

That is, principal axis rotation requires that the subradar latitude had
an absolute value of at least 79.5° on July 24. If \|δ~1~\| 9 79.5° on
July 24, then the \~7 d rotation period evident in the images and the
bandwidth of 1.7 Hz constrains the diameter:

*D* 9 (1.7 Hz)(\~7 d)(24 h/d)/(100 cos79.5°)

*D* 9 15.7 km

However, the visible range extents, which presumably show about one-half
of the true range extent, average only 3.6 km (Table 7), which is
inconsistent with *D* 10 15.7 km. Thus, the assumption of principal axis
rotation leads to a contradiction and we are forced to conclude that
1999 JM8 is a non-principal axis rotator.

We also conducted a search for principal axis spin states in which sky
motion was explicitly included. We searched for spin state/diameter
combinations that match the observed bandwidths and produce similar
longitudes on July 24, August 1, and August 8, days when the orientation
of 1999 JM8 is very similar. The search covered the entire sky at 5°
intervals, rotation periods between 5.0 and 18.0 days at intervals of
0.1 days, diameters between 3.5-10.0 km in 0.1 km increments, and the
search assumed that 1999 JM8 is spherical.

We found that principal axis spin states fit the observations only if
the absolute values of the subradar latitudes are about 55-63° on July
24, about 15-25° on August 1, and 5-15° (and on the opposite side of the
equator relative to the other two days) on August 8. That is, in order
for principal axis rotation to fit the observations, the subradar
latitudes on July 24 and August 1 must differ by 30-40°. However, that
contradicts the striking similarities seen in the images, which indicate
a latitude difference on those days of much less than 30°.

Stated more succinctly, the July 24 and August 1 images clearly show the
same side of 1999 JM8 but have bandwidths that differ by nearly a factor
of two. Given that *W*~int~ dominates over *W*~sky~, the position of the
spin vector in the asteroid had to be different on the two days; that
is, the spin must be NPA. On the other hand, the apparent regular
rotation of features in images between July 31-August 1 suggests that
*W*~int~ has a period of about one week and that the rotation state
isn\'t far from principal axis rotation. PA rotation would be admissible
if the latitude difference between July 24 and August 1 was 30-40°, so
the upper bound of 10° on the difference in latitudes suggests that the
spin axis moved by at least 20° in seven days. Refined estimates of the
spin state will require shape inversion, which is beyond the scope of
this paper.

Several other slowly rotating asteroids are suspected of being NPA
rotators. 4179 Toutatis is in a well-defined NPA state (Hudson and Ostro
1995) and NPA rotation is strongly suspected for 253 Mathilde (Mottola
*et al.* 1995), 288 Glauke (Harris *et al.* 1999), 3288 Seleucus (Harris
*et al.* 1999), 4486 Mithra (Ostro *et al.* 2000), and 1999 GU3 (Pravec
*et al.* 2000).

**SURFACE FEATURES**

The sequence of daily images from July 31-August 9 show a clear
progression of familiar prominent features. 1999 JM8 has an irregular,
asymmetric shape characterized by regions of pronounced topographic
relief, prominent facets several kilometers in extent, at least one
large concavity, and numerous smaller concavities. On July 23, 24,
August 1, 2, 8, and 9, the leading edge is rounded, suggesting a
spheroidal shape at those aspects. In contrast, on July 20, 27, 28,
August 5, and 6, the leading edge is more angular and the July 20 image
is almost triangular.

On several days the leading edges show relative topographic relief of up
to several hundreds of meters. For example, the July 27 leading edge
shows a pronounced \"peak\" extending \~400 m toward the radar. The July
28 leading edge has a \"valley\" that is 100-300 m more distant in range
than the two adjacent \"hills.\"

There is a large, nearly flat feature evident on the leading edges of
the July 31 and August 1 images. On July 31 the feature extends across
the middle of the leading edge and on August 1 it is on the right
(receding side), with a range extent of at least 2 km. The August 4-6
images show a prominent, nearly flat region on the leading edge that, as
seen in the August 6 image, has a range extent of at least 5 km.

A prominent relatively dark feature, apparently a 2-km-diameter
concavity, is near the center of the trailing edge on July 24, August 1,
2, 8, and 9. It is the largest concavity evident in the images.

Other circular to ellipsoidal and relatively dark features are probably
impact craters; they have diameters ranging from about 100 meters to
about 1 km. One of the smallest, near the center of the July 28 image,
is surrounded by a relatively bright annulus that is reminiscent of the
relatively bright ejecta deposits seen near impact craters in Arecibo
delay-Doppler images of the Moon (Thompson *et al.* 1981) and Venus
(Campbell *et al.* 1990). Two large, kilometer-sized crater-like
structures are particularly prominent on July 24, 31, Aug. 1, 2, and 8.

**POLARIZATION SIGNATURE**

Figure 6 shows daily sums of SC, OC, and SC/OC images obtained at
Arecibo. The images show only those pixels in which the echo power in
both polarizations exceeds 3-standard deviations. Each ratio image shows
a region of relatively low SC/OC \~ 0.1 at the echo\'s leading edge and
a general pattern of increasing SC/OC (to 12 0.5) as a function of
increasing range toward the trailing edge. This pattern is similar to
that seen in SC/OC images from Toutatis (Ostro *et al.* 1999). Low SC/OC
at the leading edge reveals a smooth, specularly reflecting surface that
preferentially returns OC echo near normal incidence. We also
investigated thresholds of 5 and 10 standard deviations and found that
although the number of points decreases with each increase in the
threshold, the patterns in the distribution of SC/OC do not change
significantly.

Near the trailing edge of the August 2 image is an ellipsoidal region of
about 200 pixels with lower SC/OC than its surroundings. We filtered the
image with a 10 x 10 pixel boxcar and found that SC/OC = 0.08 ± 0.01
within the region and 0.24 ± 0.01 at more positive and negative Doppler
frequencies in the same span of range gates. The ellipsoidal structure
is within an oval region that is relatively bright in both the SC and OC
images. Its origin is not clear, and due to the north-south ambiguity,
it is possible that there are contributions to the SC/OC difference from
both hemispheres. One plausible explanation is that this may be a crater
wall oriented at a low incidence angle that gives more specular
reflections than adjacent regions. This may be evidence for a
polarization ratio feature, which, if true, would be the first observed
on an asteroid. There are also suggestions of narrow regions of lower
SC/OC on August 1, 2, 3, and 5 adjacent to arcuate features that may be
crater rims.

**DISCUSSION**

If, as we suspect, 1999 JM8\'s effective diameter is \~7 km, then the
absolute magnitude of 15.15 (Table 1) corresponds to a very low optical
geometric albedo *p*~v~ = 0.02. This albedo and the optical spectrum
strongly suggests that 1999 JM8 is a P-class object. The average
Goldstone radar cross section, 2.49 km^2^, corresponds to a radar albedo
of 0.06, an estimate that overlaps the radar albedos for C-, S-, and
BFGP-type main-belt and near-Earth asteroids.

How did the NPA rotation originate? Perhaps 1999 JM8 is a collisional
fragment that was excited into NPA rotation during its dispersal from a
larger progenitor, either directly into an NPA rotation state (Giblin
and Farinella 1997, Asphaug and Scheeres 1999) or due to gravitational
interactions with other fragments and/or the parent body (Scheeres *et
al.* 2000). Alternatively, perhaps the NPA rotation was caused by an
impact into the asteroid or by gravitational torques during one or more
very close passes by Earth or another planet (Scheeres *et al.* 2000).
The presence of at least three kilometer-sized concavities that appear
to be impact craters is consistent with the hypothesis that the NPA
rotation was induced by impacts, but the concavities do not rule out the
other mechanisms. Perhaps a combination of these mechanisms is
responsible.

Another viable explanation is that the NPA rotation could be the result
of (or was modified by) outgassing if 1999 JM8 was once a comet. There
is a precedent for this conjecture: comet Halley, which is known to be
an NPA rotator (Belton 1990; Belton *et al.* 1991). 1999 JM8\'s
timescale for damping to principal axis rotation (Harris 1994) exceeds
the age of the solar system, so if the NPA rotation was caused by
cometary outgassing, it could still be in that state after cometary
activity ceased. 1999 JM8\'s optical albedo is also consistent with the
value of \~0.04 estimated for comet Halley (Delamere *et al.* 1986,
Sagdeev *et al.* 1986), although some comets have albedos as large as
\~0.1.

However, no cometary activity was seen during the 1999 apparition
despite extensive spectrophotometric observing campaigns. The most
reliable cometary radar albedo available is the estimate of \~0.04 for
IRAS-Araki-Alcock (Harmon *et al.* 1989), a result that is comparable to
our estimate for 1999 JM8. However, the nominal radar albedo of 1999 JM8
is also consistent with those estimated for primitive B-, F-, G-, and
P-type main-belt asteroids (Magri *et al.* 1999). The orbit of 1999 JM8
(*a* = 2.72 AU, *e* = 0.644, *i* = 13.7°) has a Tisserand criterion =
2.988 that is consistent with an origin as a Jupiter-family comet.
Still, many asteroids have comparable Tisserand values, so the Tisserand
criterion is not compelling evidence for a cometary origin (Valsecchi
*et al.* 1995). Applying the Bottke *et al.* (2001) dynamical analysis
to 1999 JM8, W. F. Bottke (pers. comm.) estimated a probability of about
8% that 1999 JM8 is a Jupiter-family comet. Thus, although the evidence
favors an origin as a primitive, outer main-belt asteroid, an origin as
a comet nucleus cannot be excluded.

Given our images, it seems likely that inversion of the delay-Doppler
images can improve constraints on the asteroid\'s shape significantly
and define its spin state, following the example of 4179 Toutatis
(Hudson and Ostro 1995). The next radar opportunity is in 2008 when 1999
JM8 will approach within 0.315 AU of Earth. Estimated SNRs during that
apparition could approach a few hundred per day and be adequate to
refine the spin state.

**ACKNOWLEDGMENTS**

Part of this research was conducted at the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the National
Aeronautics and Space Administration (NASA). Work at Washington State
University was supported, in part, by a grant from NASA. Some of the
observations reported here were obtained with the Caltech Baseband
Recorder (CBR), whose development was funded by the National Science
Foundation. The Arecibo Observatory is part of the National Astronomy
and Ionosphere Center, which is operated by Cornell University under a
cooperative agreement with the National Science Foundation and with
support from NASA.

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Shapiro, E. M. Standish, R. Winkler, D. K. Yeomans, R. Velez, and R. M.
Goldstein 1992.

Europa, Ganymede, and Callisto: New radar results from Arecibo and
Goldstone. *J.*

*Geophys. Res.* **97**, 18227-18244.

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.
Littlefair, L. A. M.

Benner, M. L. Thomas, and M. A. Slade 1999. Asteroid 4179 Toutatis: 1996
radar

observations. *Icarus* **137**, 122-139.

Ostro S. J., R. S. Hudson, L. A. M. Benner, M. C. Nolan, J.-L. Margot,
J. D. Giorgini, R. F.

Jurgens, R. Rose, and D. K. Yeomans 2000. Radar observations of 4486
Mithra (abstract).

*Bull. Am. Astron. Soc.* **32**, 1003.

Ostro S. J., R. S. Hudson, L. A. M. Benner, M. C. Nolan, J. D. Giorgini,
D. J. Scheeres, R. F.

Jurgens, and R. Rose 2001. Radar observations of asteorid 1998 ML14.
*Meteorit. Planet.*

*Sci.* **36**, 1225-1236.

Pravec P., L. Sarounova, L. A. M. Benner, S. J. Ostro, M. D. Hicks, R.
F. Jurgens, J. D.

Giorgini, M. A. Slade, and D. K. Yeomans 2000. Slowly rotating asteroid
1999 GU3.

*Icarus* **148**, 589-593.

Sagdeev R. Z., G. A. Avanesov, Ya. L. Ziman, B. Smith, I. Toth, V. I.
Moroz, V. I.

Tarnopolsky, B. S. Zhukov, and V. A. Shamis 1986. TV experiment of the
Vega mission:

Photometry of the nucleus and inner coma. In *20th ESLAB Symposium on
the Exploration*

*of Halley\'s Comet* (eds. B. Battrick, E. J. Rolfe, and R. Reinhard),
Vol. 2, pp. 317-326,

ESA SP-250.

Scheeres D. J., S. J. Ostro, R. A. Werner, E. Asphaug, and R. S. Hudson
2000. Effects of

gravitational interactions on asteroid spin states. *Icarus* **147**,
106-118.

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.

TABLE 1. Optically-derived physical properties

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Property Value Reference

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

*H* (mag) 15.15 ± 0.10 3

*G* -0.09 ± 0.02 3

Period (d) 5.7 ± 0.2 3

∆m (mag) 0.7 3

Taxonomy C or EMP 1

EMP 2

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

References:

1\. M. Hicks et al., pers. comm.

2\. E. S. Howell, pers. comm.

3\. P. Pravec et al., pers. comm.

TABLE 2. Observations.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Resolution RA DEC ∆ motion OSOD runs start stop

μs x Hz (°) (°) (AU) (°) HHMMSS-HHMMSS

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

**GOLDSTONE JULY 18**

CW 0.977 187.6 59.7 0.100 0.04 15 1 211432-211609

CW 0.244 15 6 212119-213931

**GOLDSTONE JULY 19**

CW 0.061 186.5 60.0 0.098 0.54 15 10 014044-021542

CW 0.122 15 3 070604-071410

**GOLDSTONE JULY 20**

CW 0.244 182.5 63.5 0.093 0.12 17 2 023155-023633

10 x 6.15 17 3 025009-025802

11 x 2.24 17 1 030858-031029

1 x 0.1 17 2 033703-034149

**GOLDSTONE JULY 21**

CW 0.244 173.4 63.5 0.084 0.14 19 1 174136-174257

1 x 0.1 19 2 175851-180305

1 x 0.1 19 14 180541-184433

**GOLDSTONE JULY 23**

CW 0.244 163.5 64.9 0.077 0.17 21 1 003648-003803

0.5 x 0.075 21 4 005306-010223

0.5 x 0.075 21 13 010410-013854 **GOLDSTONE JULY 24**

CW 0.244 146.0 65.5 0.070 0.60 21 2 165825-170154

10 x 2.46 21 2 172513-172850

11 x 2.24 21 2 174329-174659

0.5 x 0.075 21 49 180151-195954

**GOLDSTONE JULY 27**

CW 0.244 118.4 62.0 0.062 0.35 21 2 013115-013422

0.25 x 0.05 21 30 014947-025407

**GOLDSTONE JULY 28**

CW 0.244 101.4 55.6 0.058 0.51 23 1 171425-171514

0.25 x 0.05 23 18 173023-180552

0.25 x 0.05 23 25 181013-190102

**GOLDSTONE JULY 31**

CW 0.244 81.7 38.7 0.058 0.85 23 2 170111-170404

0.125 x 0.05 23 48 172454-190134

0.125 x 0.05 23 24 190739-195539

**GOLDSTONE AUGUST 1**

CW 0.244 78.3 33.9 0.059 1.10 23 2 120321-120617

0.125 x 0.05 23 2 122101-122405

0.125 x 0.05 23 3 122647-123152

0.125 x 0.05 23 45 123337-140627

0.125 x 0.05 23 52 141225-155925

**GOLDSTONE AUGUST 7**

0.25 x 0.075 64.1 6.2 0.082 0.11 26 2 171958-172405

0.25 x 0.075 26 14 172616-180409 **GOLDSTONE AUGUST 8**

0.25 x 0.075 63.0 3.5 0.087 0.93 26 50 115342-142242

0.25 x 0.075 26 53 142939-170807

0.25 x 0.075 26 6 171246-172906

0.25 x 0.075 26 36 173238-191931

**ARECIBO AUGUST 1**

4.0 78.4 34.1 0.059 0.34 21 2 123730-124051

0.1 x 0.0098 21 26 125104-135333

**ARECIBO AUGUST 2**

CW 74.9 28.4 0.061 0.34 23 1 123810-123903

0.1 x 0.0094 23 28 130204-135658

**ARECIBO AUGUST 3**

CW 72.0 23.2 0.064 0.36 23 2 121929-122235

0.1 x 0.0089 23 31 124312-134900

**ARECIBO AUGUST 4**

0.1 x 0.0083 69.5 18.3 0.068 0.04 23 5 132600-133504

**ARECIBO AUGUST 5**

CW 67.6 14.1 0.072 0.26 26 1 115436-115540

0.1 x 0.0078 26 35 115814-131950

**ARECIBO AUGUST 6**

0.1 x 0.0074 65.9 10.2 0.076 0.08 26 13 123350-130414

**ARECIBO AUGUST 9**

0.1 x 0.0060 62.1 1.3 0.091 0.14 26 25 104635-115923

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Right ascension, declination, and delta are given at the mid- epoch of
each day\'s observations. Motion indicates the plane-of- sky motion
during each track. OSOD refers to the orbit solution

computed using the JPL On-Site Orbit Determination software. Runs are
the numberof transmit-receive cycles with each setup. Start and stop
refer to the UTC epochs at the beginning and end of reception of echoes.

TABLE 3. Radar astrometry.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

OSOD

UTC Epoch Soln Correction Measurement +/- resid.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

1999 07 18 21:30:00 15 +1.7 Hz 580912.4 Hz 0.4 Hz 0.175

1999 07 20 02:40:00 17 -0.5 Hz 547278.4 Hz 0.3 Hz 0.125

1999 07 20 03:00:00 17 -3132.5 μs 92.6270694 s 10.0 μs -2.215

1999 07 21 17:40:00 19 +0.8 Hz 528308.3 Hz 0.4 Hz 0.439

1999 07 24 17:00:00 21 +0.5 Hz 420950.7 Hz 0.3 Hz 0.163

1999 07 24 19:00:00 21 -4 μs 69.426792 s 5.0 μs 2.538

1999 07 27 01:30:00 21 +0.5 Hz 264385.7 Hz 0.3 Hz -0.272

1999 07 27 02:30:00 21 -20 μs 61.40113 s 5.0 μs -1.574

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Astrometry corresponds to echoes from 1999 JM8\'s estimated

center of mass. The reference point for Goldstone is the

intersection of the altitude and azimuth axes of the 70-meter

antenna, DSS-14. Residuals are the remaining difference when the\
best-fit prediction of solution #34 is subtracted from the actual
measurements. The range equivalent of 1 usec is 150 meters and the
radial velocity equivalents of 1 Hz are 17.6 mm/s at Goldstone\'s
transmitter frequency of 8560 MHz.

TABLE 4. Orbit.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Quantity Value Uncertainty

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Epoch 2451911.5 JD (= 2001 Jan 02.0)

Eccentricity (*e*) 0.64440537378 ± 0.0000000086

Perihelion distance (*q*) 0.96733323427 AU ± 0.0000000156 AU

Perihelion date (*T*~p~) 2451383.7257358508 JD ± 0.0000052119 d

(1999 Jul 24.22574)

Long. asc. node (Ω) 134.00962375234° ± 0.0000052995°

Arg. of perihelion (ω) 165.98932252768° ± 0.0000095614°

Inclination (*i*) 13.7134598550° ± 0.0000029247°

Semimajor axis (*a*) 2.72032579502 AU ± 0.0000000472 AU

Period 1638.81453203005 d ± 0.00004263 d

(4.48675103853089 y)

Mean anomaly 115.93669166356° ± 0.0000030143°

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

1999 JM8\'s heliocentric orbital elements (OSOD solution #34) and

formal 1-standard deviation uncertainties, estimated using our
delay-Doppler radar astrometry (Table 3) and currently available optical
astrometry (403 angular measurements from April 29, 1990 to December 31,
2000). The mean post-fit radar residuals are: time-delay -0.417 μs ±
2.57 μs, and Doppler frequency, +0.125 Hz ± .255 Hz. Mean post-fit
optical residuals are RA, -0.02\" ± 0.54\", and declination, -0.03\"±
0.63\". The r.m.s. of residuals normalized by the assigned measurement
uncertainty are (0.368, 0.732, 0.589) for delay data, Doppler data, and
total data set (including optical), respectively. Elements are in the
coordinate frame of the JPL planetary ephemeris DE405 (ICRF93/ J2000, a
quasar-based radio frame, generally within 0.01 arcseconds of the
optical FK5/J2000 frame). Angular elements are referred to the ecliptic
and mean equinox of J2000.

TABLE 5. Close approaches.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Close-Approach Distance

Date Body nominal min max *V*~rel~ ∆*T* Nsigs

AU AU AU km/s min

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

293 Sep 19.76 Jupiter 0.9235 0.9009 0.9460 5.7 5079 3.4E6

412 May 24.48 Jupiter 0.9636 0.9523 0.9748 6.0 3783 1.5E6

507 May 4.44 Jupiter 0.9576 0.9370 0.9779 5.6 4290 7.4E5

584 May 11.34 Earth 0.0599 0.0437 0.0812 13.3 6516 5.9E4

625 Dec 22.81 Jupiter 0.9933 0.9837 0.0029 6.0 2621 1.7E6

756 Aug 1.34 Jupiter 0.9963 0.9788 0.0136 5.7 2641 5.9E5

811 May 11.51 Earth 0.0591 0.0340 0.0881 13.1 6987 2.2E5

1024 Nov 22.16 Mars 0.0591 0.0591 0.0621 15.1 2211 3.3E5

1060 May 10.83 Earth 0.0867 0.0864 0.0887 13.9 2974 9.2E5

1078 Jun 7.22 Mars 0.0510 0.0384 0.0641 14.4 1507 6.0E4

1091 Aug 18.89 Earth 0.0794 0.0759 0.0833 14.4 1039 3.5E5

1105 Aug 28.53 Ceres 0.0883 0.0881 0.0885 14.1 58 3.2E4

1123 Jul 1.11 Vesta 0.0814 0.0770 0.0857 12.6 353 5.9E4

1194 Aug 24.21 Earth 0.0462 0.0454 0.0470 15.0 214 1.7E5

1256 Mar 23.79 Mars 0.0692 0.0658 0.0728 16.1 462 1.6E5

1261 Jun 18.77 Vesta 0.0771 0.0757 0.0785 13.7 275 1.7E5

1269 Jun 4.02 Mars 0.0701 0.0690 0.0712 14.5 319 2.0E5

1318 May 3.59 Mars 0.0919 0.0914 0.0926 14.4 565 4.4E5

1412 Aug 25.85 Earth 0.0459 0.0455 0.0463 15.1 54 1.3E4

1474 Aug 21.81 Earth 0.0546 0.0545 0.0547 14.0 22 1.9E5

1692 Aug 9.95 Earth 0.0963 0.0963 0.0964 13.4 15 7.6E5

1981 Aug 20.29 Earth 0.0665 0.0665 0.0665 13.8 6 5.6E5

1990 Aug 8.41 Earth 0.0335 0.0335 0.0335 12.7 2 6.5E5

**1999 Jul 30.40 Earth 0.0568 0.0568 0.0568 12.3 0 5.4E6**

2137 Aug 1.53 Earth 0.0764 0.0764 0.0764 13.3 6 1.5E6

2573 Aug 11.86 Earth 0.0852 0.0852 0.0852 14.0 5 8.6E5

2791 Aug 15.18 Earth 0.0947 0.0947 0.0947 14.0 15 4.3E5

2831 Jul 26.37 Earth 0.0715 0.0715 0.0715 14.0 12 2.4E5

2907 Jul 20.53 Earth 0.0911 0.0911 0.0911 14.2 3 6.9E4

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Note: Close approaches within 0.1 AU of the given body except

for Jupiter, which is indicated for approaches less than 1.0 AU,

are listed along with nominal, 3-sigma minimum and maximum

distances. *V*~rel~ is the relative velocity at the nominal close

approach, ∆*T* is the 3-sigma uncertainty in the epoch of close

approach, and Nsigs is the number of standard deviations required

for the uncertainty ellipse to intersect the close-approach body.

TABLE 6. Disc-Integrated 3.5-cm Radar Properties.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Date runs FFTs OC SNR *B* σ~OC~ SC/OC

(Hz) (km^2^) (+/-0.01)

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Jul 18 7 1270 940 1.5 2.96 0.19

Jul 19 10 1576 540 1.3 2.46 0.21

Jul 20 2 154 500 2.0 2.97 0.19

Jul 21 1 140 830 1.7 3.54 0.22

Jul 23 1 132 580 1.6 2.26 0.16

Jul 24 2 162 1100 2.3 2.85 0.15

Jul 27 2 216 520 2.6 1.08 0.18

Jul 28 1 80 5700 2.9 3.02 0.17

Jul 31 2 180 1400 3.3 1.94 0.22

Aug 1 2 192 880 3.4 1.81 0.23

Experiment average 2.49 0.19

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

The bandwidths were estimated using CW spectra with

a resolution of 0.122 Hz. *B* is the echo bandwdith.

The cross sections and SC/OC were estimated using

a frequency resolution of 1.95 Hz in order to have

enough fast-Fourier transform (FFTs) to approach

Gaussian noise statistics.

TABLE 7. Delay-Doppler dispersions.

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

RESOLUTION DELAY BANDWIDTH

Date μs x Hz EXTENT (km) (Hz)

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

GOLDSTONE (3.5 cm)

Jul 19 CW 0.061 no data 1.3

Jul 20 1.0 x 0.1 2.85 1.8

Jul 21 1.0 x 0.1 2.70 1.6

Jul 23 0.5 x 0.075 2.55 1.43

Jul 24 0.5 x 0.075 4.28 1.65

Jul 27 0.25 x 0.05 3.26 2.40

Jul 28 0.25 x 0.05 3.90 2.65

Jul 31 0.125 x 0.05 3.45 3.35

Aug 1 0.125 x 0.05 4.16 3.05

Aug 7 0.25 x 0.075 2.66 3.15

Aug 8 0.25 x 0.075 3.30 3.38

ARECIBO (12.6 cm)

Aug 1 0.1 x 0.0098 4.50 3.31

Aug 2 0.1 x 0.0094 4.13 3.17

Aug 3 0.1 x 0.0089 3.71 3.17

Aug 4 0.1 x 0.0083 3.47 3.24

Aug 5 0.1 x 0.0078 4.32 3.63

Aug 6 0.1 x 0.0074 5.27 3.20

Aug 9 0.1 x 0.0060 3.96 3.34

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

Estimated dispersions include pixels with echo power above

the 2-sigma level, except on July 27, 28, and 31, when contiguous

pixels with SNRs \> 1.0 were used. July 24 and August 1

estimates include the distant arc of pixels at the trailing

edge that Arecibo images indicate are real. Arecibo

bandwidths have been multiplied by 8560/2380 (the ratio of

the Goldstone and Arecibo transmitter frequencies) to facilitate

comparison with 3.5 cm results.

**FIGURE CAPTIONS**

**Fig. 1.** Weighted sums of Goldstone echo power spectra grouped by
observation date between July 18 (top left) to August 1 (bottom right).
The spectra have been smoothed to a resolution of 0.5 Hz.

**Fig. 2.** Sequence of OC delay-Doppler images obtained at Goldstone
and Arecibo. In each image range increases from top to bottom and
Doppler frequency increases from right to left, so rotation is
clockwise. The height in each frame is 6.0 km (40 usec). The images are
shown with a Doppler extent of 3.7 Hz when adjusted to a frequency of
8560 MHz in order to facilitate direct comparison between Goldstone and
Arecibo images. The images have logarithmic contrast stretches in order
to take advantage of the dynamic range. The collage shows one image per
day, where each frame is the sum of all the highest resolution images on
a given day. On August 1 we imaged 1999 JM8 at both telescopes; the
image shown was obtained at Arecibo.

**Fig. 3.** Difference images obtained on August 5 (left) and 8 (right),
the longest tracks at Arecibo and Goldstone. Range increases from top to
bottom and Doppler frequency increases from right to left, so rotation
is clockwise. The August 5 (Arecibo) image shows the difference between
the first (white) and last (black) runs on that day, which were obtained
1.3 hours apart. The August 8 (Goldstone) image shows the difference
between the first 17 runs (white) and the last 14 runs (black), which
were obtained 7.5 hours apart. Several degrees of rotation are evident
in the August 8 image.

**Fig. 4.** Silhouette of 1999 JM8 using delay-Doppler images obtained
between August 1-9 assuming principal axis rotation. Images were cut out
from hardcopies and aligned by eye.

**Fig. 5.** Top: Right ascension and declination of 1999 JM8 at the mid
epoch of each track. Observations at Goldstone and Arecibo are indicated
with circles and crosses. Middle: Angular rate of sky motion as a
function of day-of-year (DOY). Bottom: Angular separation of 1999 JM8 as
a function of DOY relative to the first Goldstone track on DOY 199 (July
18).

**Fig. 6.** Arecibo SC (left), OC (middle), and SC/OC (right) images.
The delay-Doppler extents and orientations are the same as in Fig. 2.
SC/OC is plotted by adopting a detection threshold per pixel of three
standard deviations in both SC and OC images. All other pixels are
mapped to white. The color stretch is saturated at SC/OC = 0.5 (black)
in order to emphasize the most interesting regions of the dynamical
range. An arrow points to a region with relatively low

SC/OC on August 2