PLEASE NOTE:
*
CCNet DIGEST, 4 February 1999
------------------------------------------------
(1) NASA: SHOEMAKER NEO SEARCH FUNDED,
BUT YEOMANS GETS NO ADDITIONAL MONEYS
E.P. Grondine <epgrondine@hotmail.com>
(2) UNIVERSITY OF CHICAGO PREPARING INSTRUMENTS FOR ASTEROID
LANDING
Steve Koppes <s-koppes@uchicago.edu>
(3) STARDUST MISSION SET TO BRING BACK A PIECE OF A COMET
Ron Baalke <BAALKE@kelvin.jpl.nasa.gov>
(4) MINOR PLANET WORKSHOP: CALL FOR PAPERS & POSTERS
Richard A Kowalski <bitnik@bitnik.com> wrote:
(5) CRATERING RATES ON THE GALILEAN SATELLITES
Z. Zahnle et al., NASA, AMES RES
CTR
(6) DUST EMISSION FOR COMETS SHOEMAKER-LEVY AND McNAUGHT-RUSSELL
W. Waniak*), S. Zola, JAGIELLONIAN
UNIVERSITY, KRAKOW,POLAND
(7) LEONID METEOR SHOWER
D.M. Hunten et al.,
UNIVERSITY OF ARIZONA
(8) STATISTICAL PROPERTIES OF ENCOUNTERS AMONG ASTEROIDS
A. DellOro and P. Paolicchi,
UNIVERSITY OF PISA
==========================
(1) NASA: SHOEMAKER NEO SEARCH FUNDED,
BUT YEOMANS GETS NO ADDITIONAL MONEYS
From E.P. Grondine <epgrondine@hotmail.com>
Benny -
I attended the NASA Fiscal Year 2000 budget briefing on
Monday. NASA Adminstrator
Dan Goldin's presentation was brief, and he was clearly showing
signs of
exhaustion, which he acknowledged.
While Goldin did not mention the NEO search in his remarks, he
did mention briefly
the need for determining the composition of both asteroids and
comets, in case it
became necessary to stop one.
Afterwards I asked him about the NEO search, and he told me that
the NASA
Comptroller had the numbers on that. The NASA Comptroller
told me that the program
was continuing and that funding had been held at 1999
levels. I asked the Director
of Space Sciences about the NEO search, and recieved the same
reply.
I examined the NASA Budget request hoping to get a more detatiled
breakdown, but
found that the NEO search was not listed as a separate
subhead. I then asked Doug
Isbell, from the NASA Space Sciences Public Affairs Office if he
could provide me
with details, and received today the following reply, which sets
the number at
$3.5 million:
Ed --
Tom Morgan reminded me that NASA FY99 funding for NEO searching
is
approx.$3.5m, and he is not aware of any change to that number
for '00.
-- Doug
Douglas Isbell
NASA HQ Public Affairs Officer
Space Science (Planetary)
202/358-1753 -3093 fax
douglas.isbell@hq.nasa.gov
I know I would find a detailed description by Don of the budget
negotiations quite
interesting, but I have a feeling that it is a lot like hotdotgs:
They're tasty,
but I don't know if you really want to visit the plant.
Best wishes -
EP ,
3 February 1999
=====================
(2) UNIVERSITY OF CHICAGO PREPARING INSTRUMENTS FOR ASTEROID
LANDING
From Steve Koppes <s-koppes@uchicago.edu>
February 2, 1999
For immediate release
Contact: Steve Koppes
(773) 702-8366
s-koppes@uchicago.edu
University of Chicago preparing instruments for first asteroid
landing, two
missions to Mars
The first object that humans will land on the surface of an
asteroid will contain a miniature version of the University of
Chicago
instrument that helped make aerospace history during the Mars
Pathfinder
mission in 1997.
Chicago's alpha proton X-ray spectrometer, or APXS, which was
carried aboard the Sojourner rover, provided the first-ever
chemical
analysis of native Martian rock during the Pathfinder mission.
Now a much
smaller, Chicago-built alpha X-ray spectrometer, AXS, will
provide similar
data during the joint U.S.-Japanese MUSES-C mission scheduled for
launch to
asteroid Nereus in 2002. The AXS may even play a role in
selecting a sample
of the asteroid for return to Earth during the mission in 2005.
"We are now in the final stages of design," said
Thanasis "Tom"
Economou, Senior Scientist at Chicago's Enrico Fermi Institute.
The
prototype is being built, and in a few months, it will be
integrated with
the nanorover "to make sure everything works in
coordination," he said.
The AXS instrument is key to accomplishing mission objectives,
said
Donald Yeomans, a senior research scientist at NASA's Jet
Propulsion
Laboratory and U.S. science team leader for the asteroid lander
mission.
"As the rover wanders around the surface of the
asteroid, we're
counting on Tom's instrument to tell us what the various soils
and rocks
are made of," Yeomans said. "It makes a big difference
as to how the object
formed. Is it a chip off a bigger object or is it an accumulation
of
various bits and pieces of asteroids, sort of a rubble
pile?"
The chemical composition of the asteroid can also be
compared to
that of meteorites found on Earth. "Once we make the link
between a certain
type of asteroid and a certain type of meteorite, we can remotely
observe
asteroids and infer what they're made of," Yeomans said.
This is possible because asteroids, planets and stars have
specific
spectral characteristics -they give off certain types of
electromagnetic
radiation that depend on the object's chemical composition.
"Presumably,
every other asteroid having the same spectral characteristics
will be made
of the same stuff," Yeomans said.
MUSES-C is a cooperative effort between the National
Aeronautics
and Space Administration and Japan's Institute of Space and
Astronautical
Science. The mission is scheduled for launch from Japan in
January 2002.
The spacecraft will arrive at Nereus in early April 2003 and will
land
later that month. Nereus, discovered in 1982, measures less than
a mile in
diameter.
"When the spacecraft is 50 feet above the surface, it
will gently
drop the nanorover. The spacecraft will then land, take some
samples, then
take off and hover nearby for a couple months while we're doing
the surface
analysis and investigations," Economou said. "There
will be an attempt to
do two landings, so it is conceivable that we will tell mission
controllers
where to land for the second time to grab a sample of particular
interest."
The solar-powered nanorover, mounted on four wheels, will
measure
only 6 inches square. It will be equipped with a camera and a
near-infrared
spectrometer as well as the AXS. "The nanorover is a nice
little toy,"
Economou said. "It can go over much larger rocks than
itself. It can also
automatically right itself up after falling on its back."
The APXS that Economou built for Pathfinder's rover
weighed 570
grams (1.2 pounds). But for MUSES-C, Economou had to think on the
Lilliputian scale of Gulliver's Travels. His weight limit for the
nanorover's chemical analyzer is no more than 100 grams (3.5
ounces),
packed into an area measuring less than 3 cubic inches.
Together the AXS's alpha and X-ray detectors can identify
any
chemical element except hydrogen at concentrations as low as a
fraction of
1 percent. The instrument's design saves weight by dispensing
with the
proton detector, which mostly duplicates data collected by the
X-ray
detector, and by sharing capabilities with the nanorover.
In November, Economou was one of 11 Mars Pathfinder team members
and instrument developers to receive special recognition from the
National
Air and Space Museum of the Smithsonian Institution. The
Pathfinder team
received the 1998 National Air and Space Museum Trophy for
Current
Achievement for its demonstration of technologies and concepts
for use in
future Mars missions.
Economou still is analyzing data collected during the
Pathfinder
mission, which officially ended in 1997. He also is designing and
building
two more APXS instruments in collaboration with the
Max Planck Institute in Germany for the rovers of the Mars
Surveyor 2001
and 2003 missions. The rovers of these two missions will visit
more Martian
sites to collect samples, some of which will be returned to Earth
during a
mission set for 2005.
The rover for Mars 2001, called Marie Curie, is similar to
Sojourner.
"For 2003, there will be the Athena rover, a new type of
rover,
capable of traveling farther distances, carrying more instruments
and
carrying a drill bit to collect samples," Economou said.
The Athena rover's robotic arm will pick up a sample and bring it
to the APXS and other instruments. After examination, the robot
arm will
either drop the sample on the surface or place it in a special
container
for return to Earth.
"It will be exciting times," Economou said.
###
Editor's Note: An image of Economou with a prototype of his AXS
instrument
is available upon request.
Radio stations: The University of Chicago has an ISDN line.
Please call
for information.
For more news from the University of Chicago, visit our Web site
at
http://www-news.uchicago.edu
===========================
(3) STARDUST MISSION SET TO BRING BACK A PIECE OF A COMET
From Ron Baalke <BAALKE@kelvin.jpl.nasa.gov>
MEDIA RELATIONS OFFICE
JET PROPULSION LABORATORY
CALIFORNIA INSTITUTE OF TECHNOLOGY
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
PASADENA, CALIF. 91109. TELEPHONE (818) 354-5011
http://www.jpl.nasa.gov
Contact: Franklin O'Donnell
FOR IMMEDIATE
RELEASE
February 3, 1999
STARDUST MISSION SET TO BRING BACK A PIECE OF A COMET
NASA's Stardust mission, scheduled for launch
Saturday, February 6, from Cape
Canaveral, FL, will send a spacecraft flying through the
cloud of dust that
surrounds the nucleus of a comet - and, for the first time ever,
bring cometary
material back to Earth.
Launch is scheduled at 4:06 p.m. Eastern
time, with live coverage on NASA
Television beginning at 2:30 p.m. Eastern. A post-launch
briefing is planned to be
broadcast on NASA Television at 6 p.m. Eastern.
Comets, which periodically grace our sky
like celestial bottle rockets, are
thought to hold many of the original ingredients of the recipe
that created the
planets and brought plentiful water to Earth. They are also
rich in organic
material, which provided our planet with many of the ready-to-mix
molecules that
could give rise to life. They may be the oldest, most
primitive bodies in the
solar system, a preserved record of the original nebula
that formed the Sun and
the planets.
"Scientists have long sought a
sample directly from a known comet because of
the unique chemical and physical information these bodies contain
about the
earliest history of the solar system," said Dr. Edward
Weiler, NASA's associate
administrator for space science. "Locked within comet
molecules and atoms could
be the record of the formation of the planets and the materials
from which they
were made."
Stardust is the first U.S. mission
dedicated solely to a comet and will be the
first to return extraterrestrial material from outside the orbit
of the Moon.
Stardust's main objective is to capture a sample from a
well-preserved comet called
Wild-2 (pronounced "Vilt-2").
The spacecraft will also collect
interstellar dust from a recently discovered
flow of particles that passes through our solar system from
interstellar space. As
in the proverbial "from dust to dust," this
interstellar dust represents the
ultimate in recycled material; it is the stuff from which all
solid objects in the
universe are made, and the state to which everything eventually
returns.
Scientists want to discover the composition of this
"stardust" to determine the
history, chemistry, physics and mineralogy of nature's most
fundamental building
blocks.
Because it would be virtually impossible
to equip a spacecraft with the most
sophisticated lab instrumentation needed to analyze such material
in space, the
Stardust spacecraft is more of a robotic lab assistant whose job
it is pick up and
deliver a sample to scientists back on Earth. The
spacecraft will, however, radio
some on-the-spot analytical observations of the comet and
interstellar dust.
"The samples we will collect are
extremely small, less than a micron, or
1/25,000th of an inch, in size, and can only be adequately
studied in laboratories
with sophisticated analytical instruments," said Dr. Donald
C. Brownlee of the
University of Washington, principal investigator for the Stardust
mission.
"Even if a ton of sample were
returned, the main information in the solids
would still be recorded at the micron level, and the analyses
would still be done a
single grain at a time."
Stardust will meet up with Comet Wild-2
on January 2, 2004. A gravity assist
flyby of Earth will put Stardust on a trajectory that will allow
it to capture
cometary dust intact at a low relative speed of 6.1 kilometers
per second (about
13,600 miles per hour). An onboard camera will aid in
navigating the spacecraft as
close as about 150 kilometers (100 miles) from the comet's
nucleus, permitting the
capture of the freshest samples from the heart of the comet.
Dressed for survival behind
armored shields, Stardust will document its
10-hour passage through the hailstorm of comet debris with
scientific instruments
and the navigation camera. On approach to the dust cloud,
or "coma," the
spacecraft will flip open a tennis-racket-shaped particle catcher
filled with a
smoke-colored glass foam called aerogel to capture the comet
particles. Aerogel,
the lowest-density material in the world, has enough
"give" in it to slow and stop
particles without altering them too much. After the sample
has been collected, the
aerogel capturing device will fold down into a return capsule,
which closes like a
clamshell to enclose the sample for its safe delivery to Earth.
In addition, a particle impact mass
spectrometer will obtain in-flight data on
the composition of both cometary and interstellar dust,
especially very fine
particles. The optical navigation camera should provide excellent
images of the
dark mass of the comet's nucleus. Other equipment will reveal the
distribution in
both time and space of coma dust, and could give an estimate of
the comet's mass.
On January 15, 2006, a parachute will
set the capsule gently onto the salt
flats of the Utah desert for retrieval. The scientifically
precious samples can be
studied for decades into the future with ever-improving
techniques and analysis
technologies, limited only by the number of atoms and molecules
of the sample
material available. Many types of analyses now performed on
lunar samples, for
example, were not even conceived at the time of the Apollo
missions to the Moon.
Comets are small, irregularly shaped
bodies composed of a mixture of grains of
rock, organic molecules and frozen gases. Most comets are
about 50 percent water
ice. Typically ranging in size up to about 10 kilometers (6
miles) in diameter,
comets have highly elliptical orbits that bring them close to the
Sun and then
swing them back out into deep space. They spend most of
their existences in a deep
freeze beyond the orbit of Pluto - far beyond the Sun's dwindling
influence, which
is why so much of their original material is well-preserved.
When a comet approaches within
about 700 million kilometers (half billion
miles) of the Sun, the surface of the nucleus begins to warm, and
material on the
comet's nucleus heats and begins to vaporize. This process,
along with the loss of
rocky debris or other particles that fly off the surface, creates
the cloud around
the nucleus called the coma. It is the glowing, fuzzy coma
that appears as the
head of a comet when one is observed from Earth. A tail of
luminous debris and
another, less apparent, tail of gases flow millions of miles
beyond the head in
the direction away from the Sun.
Comet Wild-2 is considered an ideal
target for study because, until recently,
it was a long-period comet that rarely ventured close to the
Sun. A fateful pass
near Jupiter and its enormous gravity field in 1974 pulled Comet
Wild-2 off-course,
diverting it onto a tighter orbit that brings it past the Sun
more frequently and
also closer to Earth's neighborhood. Because Wild-2 has only
recently changed its
orbit, it has lost little of its original material when compared
with other
short-period comets, so it offers some of the best-preserved
comet samples
that can be obtained.
Stardust was competitively selected in
the fall of 1995 under NASA's Discovery
Program of low-cost, highly focused science missions. As a
Discovery mission,
Stardust has met a fast development schedule, uses a small Delta
launch vehicle, is
cost-capped at less than $200 million, and is the product of a
partnership
involving NASA, academia and industry.
Principal investigator Brownlee is
well-known for his discovery of cosmic
particles in Earth's stratosphere known as Brownlee
particles. Dr. Peter Tsou of
NASA's Jet Propulsion Laboratory, Pasadena, CA, an innovator in
aerogel technology
and maker of aerogel, serves as deputy investigator. JPL, a
division of the
California Institute of Technology, manages the Stardust mission
for NASA's Office
of Space Science, Washington, DC. Dr. Kenneth L. Atkins of
JPL is project manager.
The spacecraft is designed, built and operated by Lockheed Martin
Astronautics,
Denver, CO. JPL provided the spacecraft's optical
navigation camera, and the Max
Planck Institute of Germany provided the real-time dust
composition analyzer.
NASA Television is broadcast on the
satellite GE-2, transponder 9C, C band, 85
degrees west longitude, frequency 3880.0 MHz, vertical
polarization, audio monaural
at 6.8 MHz.
==========================
(4) MINOR PLANET WORKSHOP: CALL FOR PAPERS & POSTERS
From Richard A Kowalski <bitnik@bitnik.com>
wrote:
Ladies and gentlemen.
As you have read on the (MPML) mailing list, we are planning a
workshop for the
minor planet researcher. This workshop will be held on April 23rd
and 24th, 1999
at Lowell Observatory in Flagstaff, Arizona, USA. There will be a
reception held
on the evening of April 22.
The intent of this meeting is to provide an outlet for discussion
and
collaboration between the amateur and professional communities.
It is hoped that
this workshop will strengthen the ties between these related
groups and result
in better understanding of this field of research.
The general plan is as follows. The first day will be devoted
entirely to
questions of astrometry, including: the scope of the follow-up
problem,
follow-up strategies, astrometry techniques, and how best to
organize the
amateur efforts, plus a review of on-line resources available to
amateurs, and
how amateurs can obtain grants. The second day will cover mainly
questions of
photometry and photometric techniques.
A number of well known individuals in this field will be in
attendance and will
be presenting papers. To allow for a greater range of
participation and ideas,
the Organizing Committee (OC) is now requesting the submission of
abstracts for
contributed talks for possible inclusion in the workshop.
Contributed talks will be limited to 15 minutes. All abstracts
for contributed
speakers MUST be submitted no later than February 28th, 1999 to
be considered
for inclusion in the workshop.
The OC is also requesting submission of poster presentations. The
idea of poster
presentations is so that participants who do not wish to speak or
can not fill
15 minutes worth of time can make presentations. These posters
may be elaborate
or can simply be a description of your observing program,
techniques and
instrumentation.
We have set a deadline for submission of poster requests of April
1st, 1999.
Please advise Paul Comba that you will be a poster presenter and
the approximate
amount of space your posted information will require. This will
then allow the
OC to insure that there will be sufficient space for all
presentations.
Commercial presentations of any sort will not be permitted.
However, attendees
with items and products of a commercial nature will be permitted
to bring along
handouts for placement on tables held in reserve for handouts,
flyers and the
like.
All abstracts and requests for poster presentations should be
sent to:
Paul
G. Comba
1411
Galaxy Lane
Prescott, AZ 86303
e-mail: comba@northlink.com
Richard Kowalski bitnik@bitnik.com
http://www.bitnik.com/QHO
Quail Hollow Observatory 761 Zephyrhills
=====================
(5) CRATERING RATES ON THE GALILEAN SATELLITES
Z. Zahnle*), L. Dones, H.F. Levison: Cratering rates on the
Galilean
satellites. ICARUS, 1998, Vol.136, No.2, pp.202-222
*) NASA, AMES RES CTR, MS 245-3, MOFFETT FIELD,CA,94035
We exploit recent theoretical advances toward the origin and
orbital
evolution of comets and asteroids to obtain revised estimates for
cratering rates in the jovian system. We find that most, probably
more
than 90%, of the craters on the Galilean satellites are caused by
the
impact of Jupiter-family comets (JFCs). These are comets with
short
periods, in generally low-inclination orbits, whose dynamics are
dominated by Jupiter. Nearly isotropic comets (long period and
Halley-
type) contribute at the 1-10% level. Trojan asteroids might also
be
important at the 1-10% level; if they are important, they would
be
especially important for smaller craters. Main belt asteroids are
currently unimportant, as each 20-km crater made on Ganymede
implies
the disruption of a 200-km diameter parental asteroid, a
destruction
rate far beyond the resources of today's asteroid belt,
Twenty-kilometer diameter craters are made by kilometer-size
impacters; such events occur on a Galilean satellite about once
in a million years. The paucity of 20-km craters on Europa
indicates
that its surface is of order 10 Ma. Lightly cratered surfaces on
Ganymede are nominally of order 0.5-1.0 Ga. The uncertainty in
these
estimates is about a factor of five. Callisto is old, probably
more
than 4 Ga. It is too heavily cratered to be accounted for by the
current flux of JFCs. The lack of pronounced apex-antapex
asymmetries
on Ganymede may be compatible with crater equilibrium, but it is
more
easily understood as evidence for nonsynchronous rotation of an
icy
carapace. (C) 1998 Academic Press.
===============
(6) DUST EMISSION FOR COMETS SHOEMAKER-LEVY AND McNAUGHT-RUSSELL
W. Waniak*), S. Zola: Dust emission for Comets Shoemaker-Levy
1991a1
and McNaught-Russell 1993v. ICARUS, 1998, Vol.136, No.2,
pp.280-297
*) JAGIELLONIAN UNIVERSITY,ASTRON OBSERV,PL-30244 KRAKOW,POLAND
We present CCD photometric results for the dust comae of the
dynamically new Comet Shoemaker-Levy 1991a1, carried out at
heliocentric distances from 1.2 to 0.8 AU pre-perihelion, and
the high-eccentricity, long-period Comet McNaught-Russell 1993v
obtained at a heliocentric distance close to 1.0 AU
post-perihelion.
Maps of the directional distribution of the dust emission rate
from
these cometary nuclei were obtained using the directional
deconvolution
method (Waniak 1994, Icarus 111, 237-245). For Comet
Shoemaker-Levy the
prominent region of enhanced dust production was situated
between the
solar terminator and the nucleocentric meridian opposite the
subsolar
point. Activity in this region on the night side of the nucleus
may be
explained both by the heating of the nucleus' surface by
scattered
visible and reemitted infrared radiation, which is produced by
the dust
coma, or by non-solar radiation sources of energy, such as
chemical
reactions or phase transitions. During the period of observations
the
dust emission rate for this region decreased in comparison with
that of
another region of enhanced dust production situated on the
subsolar
hemisphere. For Comet McNaught-Russell tno active regions were
also
visible, although the subsolar region was much more active than
that on
the night side of the nucleus. For both comets, dust was emitted
from
the entire surface of the nucleus at a level no lower than 30% of
the
maximum value for the active regions. The total (integrated over
a 4 pi
solid angle) dust emission rate for Comet Shoemaker-Levy changed
as
r(h)(-2.3) for the observed range of heliocentric distance r(h).
For
both comets, the ejection velocity of submicron dust particles
was of
the order of 0.1 km sec(-1) and the power-law size distribution
of dust
particles (a(-n)) had a mean value of exponent n equal to 2.9.
The
power-law dependence of the ejection velocity upon the beta
parameter
(nu similar to beta(k)) was specified by a mean value of k close
to
0.18. (C) 1998 Academic Press.
==========================
(7) LEONID METEOR SHOWER
D.M. Hunten*), G. Cremonese, A.L. Sprague, R.E. Hill, S. Verani,
R.W.H.
Kozlowski: The Leonid meteor shower and the Lunar sodium
atmosphere.
ICARUS, 1998, Vol.136, No.2, pp.298-303
*) UNIVERSITY OF ARIZONA,LUNAR & PLANETARY
LAB,TUCSON,AZ,85721
Observations of lunar sodium were made on November 16-18, 1997,
at
Asiago and Mount Lemmon Observatories. A small enhancement
was
observed, and me suggest that it was related to the Leonid
shower.
Visual observations by members of the Association of Lunar and
Planetary Observers and the North American Meteor Network show a
peak,
a few hours wide, at about 12:50 UT on the 17th. The possible
enhancement of the lunar Na appears to last at least 3 days, and
must
be associated with a considerably more extended cloud of
particles than
that responsible for the bright visual meteors. The circumstances
of
the 1997, 1998, and 1999 events are discussed. Large showers may
occur
in 1998 and 1999; the 1998 shower occurs too close to new moon
for good
atmospheric observations, but if the extended, faint shower is
also
enhanced the corresponding lunar Na should be observable for a
considerably longer period. (C) 1998 Academic Press.
======================
(8) STATISTICAL PROPERTIES OF ENCOUNTERS AMONG ASTEROIDS
A. DellOro and P. Paolicchi: Statistical properties of
encounters
among asteroids: A new, general purpose, formalism. ICARUS, 1998,
Vol.136, No.2, pp.328-339
UNIVERSITY OF PISA, DIPARTIMENTO FIS,PIAZZA TORRICELLI 2,I-56127
PISA, ITALY
The statistical properties of asteroid mutual encounters have
been
studied by several authors, with the main purpose of estimating
collisional rates (and thus mean collisional lifetimes) and the
distribution of encounter velocities. In this paper we present a
new
approach, conceptually not really different with respect to the
classical ones, but implemented with a rather different
mathematical
formalism and consequently more flexible. When a comparison is
possible
our results are very similar to those obtained by means of other
techniques. We exploited the peculiar flexible features of the
present
formalism to study-in a quantitative way-what happens when
special
dynamical conditions occur, such as a clustering of longitudes of
perihelia (as in the so-called Kresak effect) or of the
longitudes of
the sample around the longitude (variable in time) of Jupiter, as
in
the case of Trojans. These dynamical situations have never been
explored in the past using statistical approaches, and the
development
of the present one can avoid the use of heavy N-body
integrations.
Concerning the Trojan asteroids, the results of our analysis,
although
discussed here in a simplified version, are satisfactorily
compared
with those emerging from a detailed numerical integration of the
orbits
(Marzari et al., 1996, Icarus 119, 192-201). Finally, we used our
approach to analyze the statistical properties of impacts among
very
large samples of objects with a moderate amount of computer time,
thanks to the numerical algorithm, based on a Monte Carlo
technique of
integration. We have tested this numerical procedure by comparing
our
results with previous ones published in the literature; we find
an
amazing agreement with the more standard and refined numerical
methods. (C) 1998 Academic Press.
----------------------------------------
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