From: Amara Graps (amara@amara.com)
Date: Wed Feb 12 2003 - 01:37:59 MST
EvMick@aol.com:
>I'd like to know more about this...where might I look?
Current work is by Canup and Ward and Agnor and Levison and Cameron and others.
Here is one:
Title: Evolution of a Terrestrial Multiple-Moon System
Authors: Canup, Robin M.; Levison, Harold F.; Stewart, Glen R.
Affiliation: AA(Southwest Research Institute, 1050 Walnut Street,
Suite 426, Boulder, CO 80302), AB(Southwest Research
Institute, 1050 Walnut Street, Suite 426, Boulder, CO
80302), AC(Laboratory for Atmospheric and Space
Physics, University of Colorado, Campus Box 392,
Boulder, CO 80309-0392)
Journal: The Astronomical Journal, Volume 117, Issue 1, pp.
603-620. (AJ Homepage)
Publication Date: 01/1999
Origin: AJ
AJ Keywords: MOON, PLANETS AND SATELLITES: GENERAL, SOLAR SYSTEM:
FORMATION
Abstract Copyright: (c) 1999: The American Astronomical Society
Bibliographic Code: 1999AJ....117..603C
Abstract
The currently favored theory of lunar origin is the giant-impact hypothesis.
Recent work that has modeled accretional growth in impact-generated disks
has found that systems with one or two large moons and external debris are
common outcomes. In this paper we investigate the evolution of terrestrial
multiple-moon systems as they evolve due to mutual interactions (including
mean motion resonances) and tidal interaction with Earth, using both
analytical techniques and numerical integrations. We find that multiple-moon
configurations that form from impact-generated disks are typically unstable:
these systems will likely evolve into a single-moon state as the moons
mutually collide or as the inner moonlet crashes into Earth.
===============
another
Title: On the Character and Consequences of Large Impacts in
the Late Stage of Terrestrial Planet Formation
Authors: Agnor, Craig B.; Canup, Robin M.; Levison, Harold F.
Affiliation: AA(Space Studies Department, Southwest Research
Institute, Boulder, Colorado), AB(Space Studies
Department, Southwest Research Institute, Boulder,
Colorado), AC(Space Studies Department, Southwest
Research Institute, Boulder, Colorado)
Journal: Icarus, Volume 142, Issue Icarus, pp. 219-237. (Icarus
Homepage)
Publication Date: 11/1999
Origin: ICAR
Abstract Copyright: (c) 1999: Academic Press
Bibliographic Code: 1999Icar..142..219A
Abstract
We perform three-dimensional N-body integrations of the final stages of
terrestrial planet formation. We report the results of 10 simulations
beginning with 22-50 initial planetary embryos spanning the range 0.5-1.5
AU, each with an initial mass of 0.04-0.13M⊕. Collisions are treated
as inelastic mergers. We follow the evolution of each system for 2x108 years
at which time a few terrestrial type planets remain. On average, our
simulations produced two planets larger than 0.5M⊕ in the terrestrial
region (1 simulation with one m>=0.5M⊕ planet, 8 simulations with two
m>=0.5M⊕ planets, and 1 simulation with three m>=0.5M⊕ planets).
These Earth-like planets have eccentricities and orbital spacing
considerably larger than the terrestrial planets of comparable mass (e.g.,
Earth and Venus). We also examine the angular momentum contributions of each
collision to the final spin angular momentum of a planet, with an emphasis
on the type of impact which is believed to have triggered the formation of
the Earth's Moon. There was an average of two impacts per simulation that
contributed more angular momentum to a planet than is currently present in
the Earth/Moon system. We determine the spin angular momentum states of the
growing planets by summing the contributions from each collisional
encounter. Our results show that the spin angular momentum states of the
final planets are generally the result of contributions made by the last few
large impacts. Our results suggest that the current angular momentum of the
Earth/Moon system may be the result of more than one large impact rather
than a single impact. Further, upon suffering their first collision, the
planetary embryos in our simulations are spinning rapidly throughout the
final accretion of the planets, suggesting the proto-Earth may have been
rotating rapidly prior to the Moon-forming impact event.
===================
Title: Accretion of the Moon from an Impact-Generated Disk
Authors: Canup, Robin M.; Esposito, Larry W.
Affiliation: AA(Laboratory for Atmospheric and Space Physics,
University of Colorado, Boulder, Colorado),
AB(Laboratory for Atmospheric and Space Physics,
University of Colorado, Boulder, Colorado)
Journal: Icarus, Volume 119, Issue 2, pp. 427-446. (Icarus
Homepage)
Publication Date: 02/1996
Origin: ICAR
Abstract Copyright: (c) 1996: Academic Press
Bibliographic Code: 1996Icar..119..427C
Abstract
We present the first published numerical calculations of accretion of an
impact-generated protolunar disk into a single large Moon. Our calculations
are based on the model developed by R. M. Canup and L. W. Esposito (Icarus
113, 331-352, 1995) to describe accretion in the Roche zones around the
giant planets. Previous numerical simulations of a large impact event
predict the formation of a disk of material centered near or within the
Roche limit (~2.9R_⊕). A natural expectation based on our previous
results and comparison with the satellite systems of the outer planets would
be for multiple small moons to arise from such a protolunar disk. Multiple
moonlets could accrete to form a single Moon if they evolved into crossing
orbits due to tidal interaction with the Earth. This would occur if the
innermost moonlet in the disk were also the most massive, so that it evolved
outward at the relatively fastest rate and swept up all exterior material.
Our calculations, which include both moonlet accretion and orbital
evolution, demonstrate that forming massive moonlets in the inner disk near
the Roche limit is extremely difficult. We conclude that an Earth system
with multiple moons is the final result unless some particularly severe
constraints on initial conditions in the disk are met. A disk with a lunar
mass of material exterior to a ~ 3.5-4R_⊕ or an extremely steep radial
surface density profile at the onset of collisional growth is required for a
single, lunar-sized body to result from accretion of silicate density
material in a protolunar disk. The former corresponds most closely to disks
produced by impactors with nearly twice the mass of Mars and about twice the
angular momentum of the current Earth/Moon system. Other processes, such as
gravitational instability or primary accretion of an iron core in the inner
disk, might be able to ``seed'' accretional growth and allow for the
formation of a single Moon if disk temperature and compositional
requirements are met. Our analysis demonstrates the need for more detailed,
higher resolution impact simulations.
===================
another
Title: From interstellar gas to the Earth-Moon system
Authors: Cameron, A. G. W.
Affiliation: Lunar and Planetary Laboratory, University of Arizona,
Tucson, Arizona, 85721 USA; acameron@lpl.arizona.edu
Journal: Meteoritics & Planetary Science, vol. 36, no. 1, p.
9-22 (2001).
Publication Date: 01/2001
Origin: M&PS
Bibliographic Code: 2001M&PS...36....9C
Abstract
This paper reports the current status of my SPH simulations of the formation
of the Moon. Since the Moon has recently been found to have been formed
approximately 50 million years after the solar nebula itself was formed, I
have placed the lunar formation problem in the entire context of the
formation and early evolution of the solar nebula. This set of processes
remains controversial, and I have outlined what I believe to be the
essential physical processes involved. These start with the formation of
short-lived (now extinct) radioactive nuclides in a massive supernova. Then
follows the probable role of the supernova ejecta in triggering the collapse
of a core in a molecular cloud to form the solar nebula, and the injection
of the radioactivities into the collapsing cloud core. Most of the solar
nebula dissipates to form the Sun, and what remains becomes relatively
quiescent. Gas drag acting on interstellar grains and the dustballs formed
from them, due both to vertical descent to midplane and inward spiralling in
midplane, quickly causes growth of the solid materials to form
planetesimals. When these bodies reach the kilometer size range and beyond,
gravitational forces dominate the accumulation process. The accumulation of
the Earth requires of the order of 10(8) years. About half-way through that
process the giant impact occurs with the next largest accumulating body near
the protoearth. I have been simulating the giant impact using smoothed
particle hydrodynamics (SPH) with 100,000 particles. The simulations of
three of these runs are depicted in detail with a series of color images. It
is shown that conventional accumulation simulations that assume Keplerian
orbits and that merge bodies upon collision are misleading because they
cannot take account of tidal stripping nor of loss and gain of particles
during the accumulation. In addition, the large rotational flattening of the
protoearth renders the orbital motions nonkeplerian. The simulations that
are shown in detail have been followed for just over a week of real time,
and in that time the largest accumulating clump has reached about half or
more of the mass of the Moon and additional clumps have accumulated into
bodies in the range of 1 to 20 percent of a lunar mass. It is important to
note that although these runs have given very promising results, the
parameter space that could plausibly be associated with the giant impact is
not yet adequately explored.
===================
another
Title: In search of lost planets - the paleocosmochemistry of
the inner solar system
Authors: Halliday, A. N.; Porcelli, D.
Affiliation: AA(Department of Earth Sciences, ETH Zentrum,
Sonneggstrasse 5, CH-8092, Zurich, Switzerland),
AB(Department of Earth Sciences, ETH Zentrum,
Sonneggstrasse 5, CH-8092, Zurich, Switzerland)
Journal: Earth and Planetary Science Letters, Volume 192, Issue
4, p. 545-559. (E&PSL Homepage)
Publication Date: 11/2001
Origin: ELSEVIER
Abstract Copyright: (c) 2001 Elsevier Science B.V.
Bibliographic Code: 2001E&PSL.192..545H
Abstract
The depletion of moderately volatile elements in planetesimals and planets
is generally considered to be a result of removal of hot nebula gases. This
theory can be tested with Sr isotopes. The calculated initial 87Sr/86Sr of
the angrite parent body (APB), eucrite parent body (EPB), the Moon and the
Earth are significantly higher than the initial Sr isotopic composition of
the solar system despite the volatile-depleted nature of all of these
objects. Calculated time-scales required to accomplish these increases in
87Sr/86Sr with a solar Rb/Sr in a nebula environment are >2 Myr for the APB,
>3 Myr for the EPB and >10 Myr for the Moon. These times are more than an
order of magnitude longer than that expected for cooling the nebula in the
terrestrial planet-forming region and correspond to the period during which
most of the mass already should have been accreted into sizeable
planetesimals and even planets. Therefore, incomplete condensation of the
nebula does not provide an adequate explanation for the depletion in
moderately volatile elements. The data are better explained by a protracted
history of depletion via more than one mechanism, including processes
completely divorced from the earliest cooling of the circumstellar disk. The
Sr model ages are maximum formation ages of the APB and EPB and indicate
that these are most probably secondary objects. With independent estimates
of their minimum age, a time-integrated Rb/Sr can be calculated for the
precursor materials from which they formed. These are consistent with
accretion of the APB and EPB from objects that at one stage may have
resembled carbonaceous chondrite parent bodies in terms of volatile budgets.
At some late stage there were large losses of volatiles, the most likely
mechanism for which is very energetic collisions between planetesimals and
proto-planets that, in the case of the Asteroid Belt, have since been lost.
The same applies to the Moon, which presently has Rb/Sr=0.006 even though
the material from which it formed had a time-integrated Rb/Sr ratio of
~0.07, consistent with a precursor planet (Theia) that was even less
volatile element-depleted than the present Earth (Rb/Sr=0.03). The
time-integrated Rb/Sr of Theia is similar to the present Rb/Sr of Mars
(0.07). There is suggestive evidence of a similar time-integrated value for
the proto-Earth (~0.09). Therefore, prior to the later stages of planet
formation involving giant impacts between large objects, the inner solar
system may have had relatively uniform concentrations of moderately volatile
elements broadly similar to those found in volatile-depleted chondrites.
Correlations of the present Rb/Sr ratios in planets and planetesimals with
ratios of other volatile elements to Sr can be used to infer the
time-integrated composition of precursor materials. The time-integrated
inferred K/U ratios of the proto-Earth, as well as Theia, were ~20000, so
that early radioactive heat production may have been ~40% greater than that
calculated by extrapolating back from the Earth's present K/U. Higher C and
S bulk concentrations may have led to concentrations in proto-cores of
0.6-1.5% C and 4-10% S. These are significantly higher than those
anticipated from the degree of volatile depletion of the present silicate
Earth (~0.12% C, ~1.3% S). If the late history of accretion did not involve
large-scale re-equilibration of silicates and metal, the present core may
have inherited such high C and S concentrations. In this case, S would be
the dominant light element in the present core.
===================
and more
http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?return_req=no_params&db_key=AST&text=We%20perform%20three-dimensional%20N-body%20integrations%20of%20the%20final%20stages%20of%20terrestrial%20planet%20formation%20We%20report%20the%20results%20of%2010%20simulatiginning%20with%2022-50%20initial%20planetary%20embr
NASA ADS is your friend.
-- Amara Graps, PhD Istituto di Fisica delle Spazio Interplanetario (IFSI) Consiglio Nazionale delle Ricerche (CNR), Roma, ITALIA Amara.Graps@ifsi.rm.cnr.it
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