CCNet DIGEST, 5 July 1999



Formed deep inside some broken protoplanet
where iron had differentiated  out to form a core,
then fired like a nickel-jacketed bullet at target Earth,
its sixty thousand tons punched through the atmosphere.
Bright plasma of trapped compressed air in front of it
blazed at a solar temperature and melted the surface
of its leading face before the final impact came.
Hypervelocity impact allows no energy to escape
by compression waves or sound, there isn't time.
All that kinetic energy must break the bonds
of molecules and atoms; nickel-iron and limestone
flashed in a microsecond from the solid state
under the pressure of that shock,  jetting out
a hellish spray of white-hot fluid from the impact point.
Only a fraction of the trailing side resisted melting
its larger fragments scattered round the site,
while the melted mass froze to a billion tiny spheres,
a short-lived plume that settled to the desert sand,
to puzzle those who sought the cosmic bullet
inside the crater's depths so  many years ago.

Malcolm Miller 4.7.99


    Brian G. Marsden <>

    Luigi Foschini <>

    Andrew Yee <>

    Harvey Leifert <>

    S. Knowles et al., USN, RES LAB


    V.L. Teplitz et al., SO METHODIST UNIVERSITY

    A. Morbidelli, NICE OBSERVATORY

    M. A. Barucci et al., PARIS OBSERVATORY



From Brian G. Marsden <>

I am sorry if Andrea Milani and Steve Chesley were upset by my
"criticism" last Thursday, but my criticism was only of the rather
curious statement by Chesley in the Minor Planet Mailing List, not of
the manner in which they actually carry out their calculations. His
remarks, with regard to 1999 AN10, that the "collision risks increased
by a factor of about 1.6 since a few weeks ago" and "unhappily, the
nominal orbit actually moved closer to the 2044 collision" actually
seem to have alarmed a few people, and that is why I tried to put the
situation into perspective with regard to the current observations. I
think we are all well aware, and have been since March 11 last year,
that the REAL problem of the public's perception of asteroidal near
misses and possible collisions stems from the way things are stated,
not from any mistakes in the calculations. I think that most CCNet
readers are now well aware that "there is no such thing as a unique
impact probability" and that "the nominal solution is not important for
this kind of computations." The fact is that the MPML note specifically
alluded ("unhappily") to the nominal orbit and an impact probability of
1 in 100,000, the latter having become a popular barrier at which
people sit up and take notice.    

But there was a deeper point in my message last Thursday, and that was
to question whether there is really a NEED to recompute (and publicize
in the WWW) the various 1999 AN10 impact probabilities with the arrival
of every new observation. Too many people rather peripherally involved
with the NEO effort have become quite obsessed with the idea that the
impact probability is a useful quantity, uniquely defined, in relation
to other orbital parameters that actually provide more definitive
information about whether an NEO threat should be taken seriously. It
is INEVITABLE that 1999 AN10's more significant impact probabilities
(defined in some manner that is at least consistent) will increase over
the course of the next few months. It is indeed very likely that, when
the present observing season ends toward the end of this year, the 2044
impact probability will be roughly TWICE its current value. Should that
be cause for concern? Certainly not. The point is that it cannot then
be more than a few times what it currently is. If I can assert this to
be the case, some may ask, why did I say that "further observations
over the next several months are very much to be encouraged"? The point
is that the object is faint, we do want SOME observations (data on two
nights each month, say, for as many months as possible), and if nothing
is said, nothing gets done. 

At some stage, we can hope (and that is really the only verb we can
use) that the 2044 impact probability will drop dramatically, rather
quickly going down to "essentially zero" when, depending on the
circumstances of the 2027 approach to the earth, the possibility that
the "dangerous" post-2027 revolution period is 1.70 years can be
eliminated. It is very likely that this hope will not be met this
year. Even if some authorities feel that it is, there is enough
flexibility in the assessment of the maximum permissible errors that
others will argue that it isn't. This situation is quite different
from that in May, when the recovery observations rather unexpectedly
showed the inevitability of the 2027 close pass, the uncertainty in
the resulting perturbations being the sole root of the current
problem. We may in fact have to wait until 2004 before we can resolve
the problem, hopefully in a favorable manner...  On the other hand,
with access to a suitably large telescope at the far-north opposition
in October 2001, we may definitively purge the 2044 danger--or,
alternatively, quadruple the impact probability, which could then be
significantly above (though still not worryingly above) the
background impact probability for 1-km objects. (Of course, as
Andrea Milani and Steve Chesley have stated before, we should not be
out of the woods as regards other impact opportunities for 1999 AN10
during the next several centuries.)

Earlier last week, the CCNet drew attention to the recent paper by
the same Pisa team on 1998 OX4, where four impact possibilities have
been identified during the next half century, but the extreme orbital
uncertainty (and intrinsic faintness) effectively dooms any
deliberate recovery attempt to failure. Rather understandably, they
propose to eliminate (hopefully) the possibility of earth impact by
restricting search activities to the sky positions (at the
appropriate times) corresponding to where 1998 OX4 would have to be
if it were on the impact trajectories (and praying not to find it
there). The idea of considering "virtual impactors" in order to cut
down on the need for an extensive search is a good one, although it
is not particularly new. For example, I made use of the concept (in
reverse) in my paper, in the September 1973 issue of The Astronomical
Journal, showing the most likely regions and times to search for
comet 109P/Swift-Tuttle, on the assumption that it was not observed
with the naked eye at perihelion passages in the centuries prior to
its 1862 discovery because it was unfavorably placed for detection. 
Although non-zero impact probabilities, on the order of 1 in 10
million, are specified for 1998 OX4 (on the basis of the 9-day arc),
the point should perhaps not be lost that these probabilities are
several orders of magnitude smaller than those of unknown objects of
comparable size. As it happens, this point IS lost, because the whole
emphasis of the paper is to encourage the making of
"non-observations" of the object. Of course, if and when those
non-observations are made, the relevant impact probability
immediately drops to essentially zero--unless the non-observation
turns out not to be a non-observation of the object, in which case
the 1-in-10-million chance would spectacularly increase.  I mention
this as yet another illustration that the actual calculation of
impact probabilities is largely irrelevant. What counts is that the
error ellipsoid (or other measure of the orbital uncertainty) does,
at some specific and calculable moment or moments in the
not-too-distant future, intersect the earth. And so it is with 1999
AN10.  And so it was with 1997 XF11 (even if nobody was fully aware
of this at the time), prior to the discovery of the 1990 observations.

In their "virtual impactors" paper the authors pay some attention,
appropriately, to how a non-observing campaign might be undertaken. 
Yes, it is fine to know that there are many observers, particularly
amateur astronomers, ready to make follow-up observations of NEOs
immediately after discovery. Observers like to make positive
observations, because there is something, including a publication, to
show for it. Observations one expects to be negative are another
matter, however, and there are only so many wild-goose chases many
observers are willing to entertain. In instances where the object, if
present, would be very faint, the only recourse is to some large
telescope somewhere--as for the proposed positive observations
discussed above for 1999 AN10 in 2001.

But, in large measure, the virtual-impactors scenario applies to
objects seen and lost in the past. In the future, there is every
likelihood that the Pisa group will perform its impact analysis as
soon as an NEO is announced. There would thus be incentive to try not
to lose a troublesome object, and although that is certainly not
always possible, the best tool to mitigate against possible loss is,
again, that proverbial large telescope. Yes, nowadays even more than
new search programs, that is what we need - at least one in each

So, given that, at least from the point of view of the working NEO
astronomers, it is impact POSSIBILITIES that are important, what,
indeed, is the value of calculating (or estimating) impact
PROBABILITIES? The answer is, of course, that they are for the
consumption of others: non-working NEO astronomers, the press and the
general public. And therein lies the problem. We astronomers are
expected to get together in a concerted manner to advise the press on
what is newsworthy. We can, ourselves, appreciate that we can solve
(and probably to our satisfaction) the most immediate problems
involving 1999 AN10 by October 2001 and those involving 1998 OX4 by
February 2003. But, conceivably, we may not be satisfied with the
outcome. Most of us thought that 1999 AN10 would "go away" (at least
for a longer while) when it was recovered in May. It is really not
easy to convince the press that we are completely omniscient.


From Luigi Foschini <>

The departure of the Tunguska99 Scientific Expedition is planned for
the 14 July 1999 from the Forli' airport. An Iljuschin Il-20 will land
off from Moscow to Forli on 13 July to load the expedition equipement
in the second half of the day. The departure for Moscow-Krasnoyarsk is
fixed for the 14 July at 10 AM (local time).

The Iljuschin Il-20 will be used also to carry out the aerial survey of
the Tunguska meteorite site using two aerial cameras A-87P (focal
length  120 cm, frame  30x30 cm). In addition to this, there are
interchangeable (2 from 7) aerial cameras on gyro-stabilized pods
GUT-3, GUT-8, AFUS for down-looking topographic and multi-spectral
photo survey.

For further details see:

The transportation of the expedition from Krasnoyarsk to the Ceko lake
will be carried out by means of a helicopter Mi-26, that is designed
for carrying large-size cargoes weighing up to 20 tons. It has a crew
of 4-5 men and can reach a speed of 295 km/h.

For further details see:

The return from the lake Ceko is planned for the 29 July, with arrival
in Forli' on 30 July.

For more information see the web page:

For the Tunguska99 Press Office:
Luigi Foschini (


From Andrew Yee <>

Scientists Will Meet in Vienna to Discuss Increasing Man-Made
Environmental Problems for the Oldest Science

International Astronomical Union

IAU Press Release 02/99


Astronomy, a science that has been a leading engine of human progress
since ancient times, now finds itself increasingly at risk from a new
type of environmental degradation -- that of space itself.
Astronomers from around the world will gather in Vienna (Austria) on
July 12 - 16 to discuss the threats of light pollution, radio
interference and space debris to their research.

"The rapidly-accelerating exploitation of space is quickly degrading
an environment that has been declared 'the common heritage of all
mankind,'" says Dr. Johannes Andersen, General Secretary of the
International Astronomical Union (IAU), and adds: "Because
astronomers must use extremely sensitive instruments to study very
faint and distant objects in the universe, they are the first to feel
the effects of this degradation. However, they will not be alone for

The Vienna meeting, an IAU-COSPAR-UN (International Astronomical
Union - COmmittee on SPAce Research - United Nations) Special
Environmental Symposium (IAU Symposium 196), will focus on three
major threats to astronomical research.

In space, interference at radio frequencies from telecommunications
satellites and their ever-increasing demand for new wavebands cloud
the future of radio astronomy and the communication with scientific
satellites. Space debris is a growing threat to scientific satellites
and also interferes with ground-based observations.

There also are projects to launch highly luminous objects into space
for various purposes such as earth illumination and artistic,
celebratory, or advertising goals. Depending on the size,
reflectivity and orbital charateristics, they could be devastating to
all of observational astronomy.

On the ground, man-made light pollution has already made large areas
of the world unsuitable for astronomical observations. Radio
astronomers are now concerned about growing levels of radio pollution
and its effect on existing and planned radio observatories.

Several causes of these problems are global in extent and
irreversible in time, so it is urgent to address them now.

Specialists from all over the world will attend the IAU Symposium at
the UN facilities in Vienna (Austria). The theme is "Preserving the
Astronomical Sky" and the meeting is part of the Technical Forum of
the Third United Nations Global Conference on the Exploration and
Peaceful Uses of Outer Space (UNISPACE III). The theme of this
conference is "Space Benefits for Humanity in the Twenty-first
Century." It is convened as a special session of the Committee on the
Peaceful Uses of Outer Space (COPUOS) and is open to all member
states of the United Nations, international organizations and space

The threats to astronomy jeopardize a science that has contributed to
human progress for thousands of years. From producing the calendar
that made agriculture possible to making modern medical imaging and
telecommunications more effective, astronomy has changed life for the
better in innumerable ways. Today, astronomical research is the only
way for scientists to use the "cosmic laboratory" of the universe,
containing extreme conditions of temperatures, pressures, densities,
etc., from which new insights about fundamental physics -- and
possibly entire new technologies -- will emerge.

In addition, understanding the nature of the Universe is one of
mankind's oldest and strongest fascinations. Observations of the sky
above us have been made at all ages, our knowledge about the Universe
and its mysteries has gradually improved and with great intellectual
and technological efforts, we have come to better understand our
distant cosmic origins and amazingly small niche in space and time.
The intellectual adventure of this quest inspires people of all ages,
and is a particularly powerful tool for attracting young people to
the scientific and technical career fields that build economic

Observations at all wavelengths of the electromagnetic spectrum, from
the ground and from space, have been vital in the phenomenal progress
in all areas of astronomy in the 20th century. They range from the
exploration of the solar system to discoveries of the echo of the Big
Bang and the beginnings of structure in the Universe. Most recently,
new and powerful research facilities have found planets around other
stars and many scientists are convinced that we may one day discover
distant Earth-like abodes that could also harbour life.

Nevertheless, continued scientific studies by all nations of the
origin and evolution of the Universe are now being jeopardized by
man-made environmental problems of rapidly growing severity.

In Vienna, the Symposium participants will hear reports of
astronomers and other scientists from many different disciplines and
geographical areas about the increasing problems; this will include a
number of audio-visual demonstrations. The participants will attempt
to establish a global overview of the current status. They will
evaluate the severity of the various threats and their progression.
Where possible, constructive measures of alleviation will be
proposed. They will discuss means to call attention to the
increasingly dramatic situation. They will pass on their findings and
formal recommendations to the participants in UNISPACE III, for
consideration during the impending review and update of the UN Space
Treaties that will be carried out by the Legal Subcommittee of the UN
Committee on the Peaceful Uses of Outer Space (COPUOS) on this

Arrangements for the Media

All media representatives are welcome to be present at IAU Symposium
196 ("Preserving the Astronomical Sky"), and will have the
opportunity to interact with the participating scientists. Please
note that you must preregister with the UN Information Service (UNIS)
in Vienna to get access to the site (Ms. Veronica Mayerhofer, UNIS
Accreditation Service, Tel.: +43-1-26060-2242).

A Press Conference will be held on the UN premises in Vienna on
Friday, July 16, 1999, at 12:30 local time (CEST) during which the
outcome of the meeting will be summed up by key participants in this

Media representatives who wish to report on this meeting are invited
to contact soonest one of the Press and Media Officers:

  David Finley (NRAO)
  National Radio Astronomy Observatories, Socorro, NM, USA
  Tel: +1-(505) 835-7302
  Fax: +1-(505) 835-7027

  Richard West (ESO)
  European Southern Observatory, Garching, Germany
  Tel: +4989-32006276
  Fax: +4989-32-2362

Information about IAU Symposium 196

More information about IAU Symposium 196 and the detailed scientific
programme is available at the dedicated website:

The symposium is sponsored by the International Astronomical Union
and organized by Commission 50 of (Protection of Existing and
Potential Observatory Sites), with the support of Commissions 9
(Instrumentation), 21 (Light of the Night Sky), 25 (Photometry), 40
(Radio Astronomy), 46 (Education), and 51 (Bioastronomy: Search for
Extraterrestrial Life).

The International Co-sponsors are COSPAR, the UN Office for Outer Space
Affairs, International Commission on Illumination (CIE), URSI, IAF, ICSU,
UNESCO, IUCAF, International Dark-Sky Association (IDA), and others.

IAU website:


For more information, contact the Secretariat or the Press and Media
Officers, indicated above.

The International Astronomical Union (IAU), founded in 1919, is the
international non-governmental organization uniting professional
astronomers all over the world. It currently has 61 Member States and
over 8,300 Individual Members in 83 countries. Its scientific
activities are coordinated by 11 Divisions and 40 Commissions
spanning the entire field of astronomy. The IAU is integrated in the
international scientific community through its membership of the
International Council for Science (ICSU) and represents astronomy in
committees of the UN and other international organizations. The
permanent IAU Secretariat is located in Paris, France. (see below).
IAU/UAI Secretariat
Institut d'Astrophysique  Tel: +33 1 4325 8358
98bis, Bld. Arago         Fax: +33 1 4325 2616
F - 75014 Paris           E-Mail:
France                    WWW:


From Harvey Leifert <>

Geophysical Research Letters
Highlights of this issue - July 1, 1999

A dusty source for meteoric water vapor

The presence of a narrow H2O layer centered near 70 km altitude and
restricted to latitudes within 30 degrees of the equator cannot be
explained by conventional chemical or dynamical processes. An
extraterrestrial source (influx of small comets) has been suggested
as a possibility (see GRL, 1 Oct. 1997). Summers and Siskind
["Surface recombination of O and H2 on meteoric dust as a source of
mesospheric water vapor"] propose a terrestrial mechanism for the
production of the observed mesospheric H2O layer: the reaction O + H2
--> H2O on the surface of meteoric dust. Noting that depleted H2 must
coincide with the observed layer of mesospheric water vapor, they
suggest that coincident observations of H2 and H2O in the mesosphere
will help answer whether the observed water vapor layer has a
terrestrial or extraterrestrial source.

Michael E. Summers, David E. Suskind, E.O. Hulburt Center for Space
Research, Naval Research Laboratory, Washington, DC.

Journalists and public information officers of educational and
scientific institutions (only) may receive one or more of the papers
cited in the Highlights; send a message to Daryl Tate
[], indicating which one(s). Include your fax number. If
you did not receive this message directly from AGU, please provide
your full name, title, organization, address, and phone as well.

Harvey Leifert
Public Information Manager
American Geophysical Union
2000 Florida Avenue, N.W.
Washington, DC 20009

Phone (direct): +1 (202) 777-7507
Phone (toll-free in North America): (800) 966-2481 x507
Fax: +1 (202) 328-0566


S. Knowles*), R.R. Meier, B.A.S. Gustafson, F.J. Giovane: A search for
small comets with the Naval Space Command radar


We have searched for the hypothetical small comets proposed by Frank et
al. [1986a, b] and Frank and Sigwarth [1993] using the world's most
powerful radar in terms of gain-aperture product. The Naval Space
Surveillance System can detect most space objects in low Earth orbit
with radar cross sections (RCSs) of 0.1 m(2) or larger; at higher
altitudes of the order of 10,000-20,000 km the radar can detect objects
with RCSs of 1 m(2). We carried out detailed first-principle
calculations of the RCS of spherical comet using the properties
proposed by Frank and Sigwarth [1993]. We find that 8-12 m diameter
comets have an average cross section of 0.4 m(2) at the radar frequency
(217 MHz), with peaks reaching 1 m. Therefore the Naval radar system
has sufficient sensitivity to detect many small comets, especially as
they approach low Earth orbit. We estimate that at least 800-5000 small
comets should have been detected by the radar during the 37 day search
period during fall 1997. None of the more than 12,000 unidentified
detections can be explained by small comets. The lack of detection of
small comets by the radar can be explained only if small comets have
RCSs <0.1% of their assumed physical size,(which is unrealistic, given
that human technology can match this value only by tailoring a design
for a specific radar) or if their impact rate with Earth is some 4
orders of magnitude less than proposed by Frank et al. [1986a] and
Frank and Sigwarth [1993]. Copyright 1999, Institute for Scientific
Information Inc.


D. Jewitt: Kuiper belt objects. ANNUAL REVIEW OF EARTH AND PLANETARY
SCIENCES, 1999, Vol.27, pp.287-312


The region of the solar system immediately beyond Neptune's orbit is
densely populated with small bodies. This region, known as the Kuiper
Belt, consists of objects that may predate Neptune, the orbits of which
provide a fossil record of processes operative in the young solar
system. The Kuiper Belt contains some of the Solar System's most
primitive, least thermally processed matter. It is probably the source
of the short-period comets and Centaurs, and may also supply
collisionally generated interplanetary dust. I discuss the properties
of the Kuiper Belt and provide an overview of the outstanding
scientific issues. Copyright 1999, Institute for Scientific Information


V.L. Teplitz*), S.A. Stern, J.D. Anderson, D. Rosenbaum, R.J. Scalise,
P. Wentzler: Infrared Kuiper belt constraints. ASTROPHYSICAL JOURNAL,
1999, Vol.516, No.1 Pt1, pp.425-435


We compute the temperature and IR signal of particles of radius a and
albedo a at heliocentric distance R, taking into account the emissivity
effect, and give are interpolating formula for the result. We compare
with analyses of COBE DIRBE data by others (including recent detection
of the cosmic IR background) for various values of heliocentric
distance R, particle radius a, and particle albedo a. We then apply
these results to a recently developed picture of the Kuiper belt as a
two-sector disk with a nearby, low-density sector (40 < R < 50-90 AU)
and a more distant sector with a, higher density. We consider the case
in which passage through a molecular cloud essentially cleans the solar
system of dust. We apply a simple model of dust production by comet
collisions and removal by the Poynting-Robertson effect to find limits
on total and dust masses in the near and far sectors as a function of
time since such a passage. Finally, we compare Kuiper belt IR spectra
for various parameter values. Results of this work include: (1)
numerical limits on Kuiper belt dust as a function of (R, a, alpha) on
the basis of four alternative sets of constraints, including those
following from recent discovery of the cosmic IR background by Hauser
et al.; (2) application to the two-sector Kuiper belt model, finding
mass limits and spectrum shape for different values of relevant
parameters including dependence on time elapsed since last passage
through a molecular cloud cleared the outer solar system of dust; and
(3) potential use of spectral information to determine time since last
passage of the Sun through a giant molecular cloud. Copyright 1999,
Institute for Scientific Information Inc.


A. Morbidelli: An overview on the Kuiper belt and on the origin of
Vol.72, No.1-2, pp.129-156


The present paper reviews our current understanding of the dynamical
structure of the Kuiper belt and of the origin of Jupiter-family
comets. It also discusses the evolutionary scenarios that have been
proposed so far to explain the observed structure of the Kuiper belt
population. Copyright 1999, Institute for Scientific Information

M. A. Barucci*), M. Lazzarin, G.P. Tozzi: Compositional surface variety
among the Centaurs. ASTRONOMICAL JOURNAL, 1999, Vol.117, No.4,


The Centaurs are a particular family of objects with orbits whose
semimajor axes fall between those of Jupiter and Neptune. They are
likely the transition objects between the Kuiper belt population and
short-period comets. To investigate the nature of these particular
objects, we have performed optical spectroscopic observations of five
Centaurs. The results show a great diversity among the reflectances of
the five Centaurs. The colors do not seem to be related to the
perihelion distance of the objects. We looked for weak cometary
emission features, in particular the CN-band emission at 3880 Angstrom,
but no CN emission feature has been detected within 3 sigma in any of
the investigated spectra. Copyright 1999, Institute for Scientific
Information Inc.


M.G. Parisi*) & A. Brunini: Dynamical constraints to the masses of
large planetesimals. PLANETARY AND SPACE SCIENCE, 1999, Vol.47, No.5,


The mean square momentum accumulated by a planet as a result of
collisions and encounters with planetesimals during the accretionary
epoch was computed. It is assumed that the present mean square
eccentricity and inclination of the planetary orbits were determined by
this process. The encounters resulted the dominant effect, especially
for Saturn, Uranus and Neptune, where using the current upper limit of
the mass distribution of planetesimals m(1)/M inferred from the
obliquities and spin periods of the planets (Safronov, 1969. Evolution
of the Protoplanetary Cloud and Formation of the Earth and the Planets.
NASA TTF-677, Nauka, Moscow; Lissauer and Safronov, 1991. Icarus 93,
288), the resulting orbital parameters would be higher than their
present values. For this reason, a new upper limit to the power law
mass distribution of planetesimals in the outer solar system,
consistent with the present orbital parameters is obtained, which is
one or two orders lower than the previous estimates cited above. In the
case of the Earth and Venus we obtain a high upper limit of the mass
distribution, since the present eccentricity and inclination of their
orbits are probably determined mainly by the gravitational
perturbations and not by the process of accumulation. Our results of
m(1)/M in the inner and outer solar system are in good agreement with
those obtained by Harris and Ward (1982. Annu. Rev. Earth Planet. Sci.
10, 61). They carried out a somewhat different calculation of the
random impulses than the one presented in this work, obtaining that the
present eccentricity and inclination of the giant planets' orbits
demand a very small mass ratio. On one hand we have calculated m(1)/M
considering that the total mass of the planets is due to the accretion
of planetesimals. On the other hand, in the case of the giant planets,
we considered the accretion of planetesimals to form a core of solid
material which accreted prior to gas accumulation. The inclusion of the
gas component leads to a higher value of the mass ratio for Jupiter and
Saturn, while for Uranus and Neptune the results remain the same
neglecting the gas component. Even when the gas is taken into account,
the present eccentricity and inclination of the planetary orbits in the
outer solar system demand much smaller values of m(1)/M than most of
the previous estimates. This is consistent with the runaway accretion
scenario, where the largest planetesimals rapidly grow becoming
detached from the distribution while the rest of the mass remains in
smaller bodies. We also constrain the masses of the largest
planetesimals which are probably out of the continuous mass
distribution, studying the increase in the eccentricity of the
planetary orbits caused by a single close encounter and a single impact
with these large bodies. Previous estimates of the largest planetesimal
masses at the end of the accretionary epoch have been obtained assuming
that the inclination of the spin axes of the planets were caused by
off-center impacts (Safronov, 1969. Evolution of the Protoplanetary
Cloud and Formation of the Earth and Planets. NASA TTF-677, Nauka,
Moscow; Lissauer and Safronov, 1991. Icarus 93, 288; Parisi and
Brunini, 1996a. Muzzio, J.C., Ferraz-Mello, S., Henrard, J. (Eds.),
Proceedings of the Workshop: Chaos in Gravitational N-Body Systems, p.
291; Parisi and Brunini, 1997. Planet. Space Sci. 45, 181). In the case
of the giant planets our results of the maximum allowed masses of the
largest bodies are, generally speaking, in good agreement with those
previous estimates, although we obtain masses for the Earth and Venus
which are much higher. (C) 1999 Elsevier Science Ltd. All rights

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