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Impact Ejecta Exchange Between Planets

Full content for this article includes illustration, table and graph.
                                                                           
  
   Source:  Science, March 8, 1996 v271 n5254 p1387(6).
                                                                           
  
    Title:  The exchange of impact ejecta between terrestrial planets.
   Author:  Brett J. Gladman, Joseph A. Burns, Martin Duncan, Pascal Lee
and 
            Harold F. Levison
                                                                           
  
 Author's Abstract: COPYRIGHT American Association for the Advancement of
Science 1996

Orbital histories of ejecta from the terrestrial planets were numerically
integrated to study their transfer to Earth. The properties of the lunar
and
martian meteorites are consistent with a recurrent ejection of small
meteoroids as a result of impacts on their parent bodies. Long-range
gravitational effects, especially secular resonances, strongly influence
the
orbits of many meteoroids, increasing their collision rates with other
planets
and the sun. These effects and collisional destruction in the asteroid
belt
result in shortened time scales and higher fluxes than previously
believed,
especially for martian meteorites. A small flux of mercurian ejecta
appears
possible; recovery of meteorites from the Earth and Venus is less likely.
                                                                           
  
 Subjects:  Meteorites - Research
            Solar system - Research
                                                                           
  
Electronic Collection:  A18138424
                   RN:  A18138424
                                                                           
  

Full Text COPYRIGHT American Association for the Advancement of Science
1996

The study of meteorites has illuminated the nature of extraterrestrial
environments and astrophysical processes, particularly the conditions at
the
time of our solar system's formation. Most meteorites come from asteroids,
butrecently a number of objects from the moon and Mars have been recognized.

These latter meteorites help to characterize the surfaces of these bodies,
especially the martian meteorites, which are our only samples of that
planet.
To learn more about the parent bodies and the paths that the meteorites
traveled before arriving on Earth, we must understand the orbital dynamics
governing their transfer. In particular, what is the delivery efficiency,
that
is, the fraction of escaping ejecta that reach Earth, from different
sources?

The SNC meteorites (1) have features that suggest they are derived from
Mars (2) and are somehow delivered to Earth. Even though the petrology and
young crystallization ages of the SNCs point to an origin on a large parent
body
with recent geologic activity, Mars was only recently accepted as their
source
because it was thought unlikely that rocks could survive being blasted off
of
a planet (3). Another argument against a martian origin was that if these
objects were launched from Mars, surely there should be many more
meteorites
coming from the moon, which is closer and has a lower escape velocity; yet,
as
of 1992 there were six SNC falls but no lunar meteorites. Then the lunar
meteorite ALHA81005 was recognized among Antarctic meteorites and because
of
our familiarity with the returned Apollo and Luna samples, the origin of
this
meteorite was immediately accepted. With more Antarctic meteorites (5)
being
recovered, we currently have a dozen members of each class, although they
comprise only 0.1% of all meteorites. The SNCs are now generally
acknowledged
to have originated on Mars, after further examination of their
composition,
especially the virtually perfect isotopic match between gases trapped
within
one of them and the martian atmosphere, as determined by the Viking
landers
(6). Thus, we use the term martian meteorites" for the SNCs and ALH84001,
the
latter being distinct from the SNC classification (7).

We can learn about the dynamics of the inner solar system by comparing the
measured transfer ages of such meteorites against orbital histories. Some
of
the ideas presented below are not new, but our dynamical simulations
improve
on previous work that, because of computational limitations of the time,
used
Monte Carlo calculations rather than full orbital integrations. In
principle,
some aspects of the catering process itself can also be constrained (8).

A cosmic ray exposure (CRE) age (9) of a meteorite is the time during
which
the object was bombarded by energetic cosmic rays in space. During this
exposure, measurable radioactive isotopes accumulate, allowing the duration
of
the exposure to be estimated (Table 1). Most lunar meteorites were
delivered
to the Earth in a far shorter time than any martian meteorite, and the
martian
meteorites have an average mass 38 times that of the lunar ones. The issue
of
pairing (10) is unlikely to affect these trends significantly.

The CRE studies reveal that most lunar meteorites have been launched from
rather shallow depths (within several meters of the lunar surface),
whereas
all martian meteorites seem to have been shielded by at least several
meters
of rock before acquiring any CRE (11). Presumably this indicates that
larger
impact events were required to produce the martian meteoroids@ because
such
impacts should be rarer, one must explain why roughly equal numbers of
lunar
and martian meteorites have been found. To address this question, we need
to
understand the efficiency of delivery of the meteoroids to the Earth once
they
have been launched from their parent bodies. With the advent of faster
computers and improved numerical algorithms, we have been able to follow
directly the motion of interplanetary particles over the necessary time
scales.

Delivery from the moon. To escape the moon's gravitational field, the
initial
speeds v, of launched ejecta must exceed the lunar escape velocity
([v.sub.esc] [is nearly equal to] 2.38 km/s) For 2.38 < [v.sub.1] < 3.5
km/s,
particles may not have enough energy after leaving the moon to immediately
break free of the Earth's gravitational field and reach heliocentric
orbit;
instead, these may first pass through a phase of geocentric orbit.
Following
the paths of thousands of particles launched at numerous uniformly
distributed
locations on the lunar surface, we find that a large majority of the
escaping
ejecta eventually achieves heliocentric orbit (12). Of the material that
does
not, most hits the Earth within a few decades.

We then followed the particles that escape to heliocentric orbit with
another
numerical integrator (13), accounting for the gravitational effects of the
planets from Mercury through Saturn, until the particles impact a
terrestrial
planet, cross Jupiter's orbit, or have their perihelia lowered to the
sun's
vicinity. Lunar meteoroids that escape to heliocentric orbit periodically
re-approach the Earth and are scattered by its gravitational field to new
orbits, with some striking the Earth after one or more scatterings.
Depending
on the launch speed from the moon, 25 to 50% of the heliocentric material
impacts the Earth in the first million years (1 Myr) the percentage of
returning material dropping monotonically as the initial ejection velocity
rises from 2.4 to 3.2 km/s (Fig. 1). The steep initial decline in the
population is almost entirely the result of collisions with the Earth,
early
in the simulation, Earth's gravitational cross section (14) is large
because
the meteoroids have low relative velocities, having barely escaped Earth's
gravity well. As the evolution proceeds, particles that do not hit the
Earth
are scattered to higher relative velocities, and so the collision rate
drops.
Thus, of the particles that will hit the Earth within [10.sup.7], years,
more
than two-thirds (including those that never escape geocentric orbit) do so
in
less than 50,000 years. After a few hundred thousand years, collisions
occur
with Earth and Venus at about equal frequency. The population's slower
decline
after 1 Myr is due to these collisions, as well as increasing fractions of
particles that cross Jupiter's orbit or are driven into the sun. The swarm
of
lunar meteoroids in heliocentric orbit spreads with time throughout the
inner
solar system because of gravitational scatterings by the planets (Fig.2).
The
initial diffusion along the q = 1 astronomical unit (AU) and Q = 1 AU
lines
(perihelion and aphelion, respectively) is driven by multiple close
approaches
with solely the Earth. After about 1 Myr, the particles no longer have any
special affinity to Earth, having had encounters with more than one planet.
We
have observed the transfer of lunar meteorites to Mars in our simulations.

Our simulations yield an expected delivery spectrum (in time) of the lunar
meteorites (Fig. 3) that can be compared to their 4[pi] CRE ages (Table 1)
(9). The 2.4-km/s simulation matches the data reasonably well. In the
3.2-km/s
simulation, less than one-fifth of the hypothetical meteorites reach Earth
in
less than 20,000 years, whereas roughly half of die actual lunar
meteorites
do. Although the statistics are based on small numbers, this result
suggests
that the velocity spectrum of escaping fragments must be so steep that only
a
small fraction of the lunar meteoroids that escape the moon do so at
speeds
greater than 3 km/s. In view of the diverse geochemistry of the extant
samples
and their relatively young ages, it appears that many lunar meteorites are
launched in frequent cratering events (at least as often as every
[10.sup.4]
years). Because the number of lunar impactors drops off quickly with
increasing impactor size and therefore energy, these common impacts must
be
small ones, resulting in craters with diameters of much less than 10 km
(11).
This frequent liberation of impact ejecta is not found for martian ejecta.

[TABULAR DATA OMITTED]

Delivery from Mars. The recovered martian meteorites have taken much longer
to
reach the Earth than the lunar ones (Table 1), simply because the orbits
of
most ejected martian meteoroids do not initially cross that of the Earth.
However, because of the eccentric orbit of Mars, the [v.sup.infinity] (15)
of
escaping particles need only be about 2.3 km/s corresponding to an
ejection
speed of 5.5 km/s, merely 10% greater than the escape speed) for some
ejecta
to be on orbits that immediately cross Earth's. Thus, fast transfers are
occasionally possible, and the short 4[pi] CRE age of 0.7 Myr for EET79001
is
not especially surprising. In fact, transfers as rapid as 16,000 years
were
observed in our simulations.

The ground-breaking work of Wetherill (16), who a decade ago addressed the
delivery efficiency of martian meteorites using Monte Carlo simulations,
presents, in hindsight, a puzzle given what we now know of the 4[pi] CRE
ages
of these meteorites. Even though collisional destruction was included in
those
simulations, the majority of martian objects arrived at the Earth having
taken
longer in their journeys than the recovered meteorites with the greatest
CRE
age (15 Myr), unless the mean ejection velocities are very large (>6.4
km/s).
Because the lunar results appear to indicate that proportionally little
material is launched at speeds greater than 125% of the escape speed, we
expect that most martian meteoroids should be launched at less than 6 km/s.
Of
course, it may be that the regolithic structure of the lunar surface is
responsible for the sharp drop-off with velocity and that this result does
not
apply to Mars (17).

We simulated the gravitational evolution of 2100 particles escaping from
Mars
at various speeds. These simulations included the gravitational effects of
Venus through Neptune. The initial conditions correspond to uniform
cratering,
and previous work (16) has shown that the delivery efficiency is
insensitive
to the orbital phase and current orbital elements of Mars. The depletion
rate
of the ejected particles (Fig. 1) is different from the lunar and
mercurian
cases because, even at this low ejection speed, re-collision with Mars is
not
a significant removal mechanism. Of the few Mars reimpacts that do occur,
more
than 90% take place in the first few million years; once the relative
velocities increase above the escape velocity (14), collisions with Mars
remove an insignificant fraction. For higher ejection speeds, typically
less
than 2% of the particles re-collide.

The delivery efficiency of martian meteoroids to Earth for [v.sub.infinity]
=
1 km/s is 7.5%, with about one-third of these occurring in the first 10
Myr
(Table 2). Raising the ejection velocity causes a small increase in the
delivery efficiency (Table 3). Our yields are about an order of magnitude
larger than those seen in Monte Carlo simulations (16). The discrepancy can
be
understood by examining Fig. 4, which shows how the orbits of the escaped
ejecta evolve after launch. The particles remain in the vicinity of Mars
(whose orbital semimajor axis is a = 1.5 AU) only for the first 0.1 Myr. By
1
Myr, several interesting phenomena have occurred: a few particles have
diffused down the Q = 1.5 AU line, and some of these have had their orbits
drastically modified by the Earth (having crossed the q = 1.5 AU line. The
diffusion up the q = 1.5 AU line is halted by the presence of two
nonlinear,
second-order secular resonances near a [approximate] 1.6 to 1.7 AU (18).
These
resonances cause oscillations with periods of [10.sup.5] years in the
eccentricities of particles in this region up to Earth-crossing values (e
[approximated] 0.4), thereby raising the efficiency of delivery for
martian
meteoroids. Because these resonances were not incorporated into earlier
Monte
Carlo simulations, it is not surprising that our results differ.
Furthermore,
delivery of particles to the q = 1 AU curve allows their semi-major axes to
be
raised to the inner edge of the asteroid belt (a [approximate] 2.1 AU),
where
the powerful secular resonances [v.sub.6], [v.sub.5], and [v.sub.16],
operate;
these resonances are capable of driving the eccentricities of test
particles
to unity, at which point the particles strike the sun (19).

[TABULAR DATA OMITTED]

Sun-grazing is the dominant loss mechanism after 10 Myr. Within 100 Myr
about
40% of the particles have been driven into the sun, more than twice the
number
removed from the system by crossing Jupiter's orbit. These two effects
ultimately deplete the swarm and yield an almost linear decline in the
number
of surviving meteoroids (Fig. 1); this partly explains why no martian
meteorites have 4[pi] ages older than 15 Myr. The expected CRE age
spectrum
for our purely gravitational N-body simulation (Fig. 5) does not agree as
well
with the SNC data as in the lunar case; only a little more than half of
the
meteorites delivered in the simulation arrive within the 15-Myr upper bound
of
the recovered meteorites. This disagreement is not surprising because many
orbits extend out to the asteroid belt (Q> 2.1 AU), and so the meteoroids
are
prone to catastrophic collisional disruption, with a half-life of 1 to 10
Myr
(20) the mean time spent in the main belt as a function of transit time
was
computed from the simulations and convolved into the delivery spectrum
(Fig.
5). With such a collisional model, the N-body simulation matches the CRE
data
quite well; however, the collisions lower the delivery efficiency for the
[v.sub.infinity] 1 km/s case from 7.5 to 44%.

Thus, the age distribution of the martian meteorites is consistent with a
model in which all fragments are launched at speeds modestly above the
escape
velocity as small bodies and are delivered independently to Earth. The
simulated meteorites delivered in the first 15 Myr all have entry
velocities
into Earth's atmosphere in the range of 11 to 17 km/s, in agreement with
the
ablation data for the SNCs (21). However, our results do not explain the
apparent clustering of the 4[pi] CREs into at least three groups: 0.7 Myr
(one
object), 3 Myr (four objects), and 13 [+ or -] Myr (five objects). Are
these
groups a result of source-crater pairing (10, 22) or, alternatively, a
result
of separate collisional fragmentations of large meteoroids in space (23)?
The
martian meteorites share much closer petrologic affinities than the lunar
meteorites (7): the 3-Myr group, contains only shergottites, and three of
the
13-Myr group are the only three nakhlites. In our view, these age clusters
likely represent individual impact events into distinct source terrains
(23).

A previously considered hypothesis (24) - that all the martian meteorites
are
derived from recent catastrophic fragmentations of large bodies that were
launched 200 Myr ago and then stored in space - is rendered very unlikely
because our simulations demonstrate that few parent bodies can dynamically
survive for this time owing to the efficiency of meteoroid destruction by
sun-grazing. This model would also have to explain why (i) there are no
meteorites from the upper few meters of the parent meteoroids, (ii) no
impacts
more recent than 200 Myr have been sampled, and (iii) only shergottite
parent
meteoroids have been disrupted in the last 3 Myr, and none before. Our
results
show that the simpler model, which produces exclusively small meteoroids,
explains all of the CRE evidence, although source-crater pairings and
relative
surface properties of the moon compared with Mars may be important. The
issues
of whether the groupings represent distinct impact events, why such
groupings
occur for Mars but not for the moon, and why there are equal numbers of
lunar
and martian meteorites (16) remain.

Delivery from Mercury, Venus, and Earth. Numerical simulations indicate
that
particles d@ readily throughout the inner solar system, and so we now
consider
the likelihood that pieces of other terrestrial planets might also have
come
to Earth. It should be possible to liberate meteoroids from the surface of
Mercury, as its escape velocity is lower than that of Mars (14). However,
the
dynamical transfer of this ejecta to Earth is substantially more difficult
because Mercury lies deep within the sun's gravitational well. Ignoring
resonance effects, a series of properly timed Mercury scatterings are
needed
for the meteoroids to be pushed across Venus's orbit and then to Earth.
Monte
Carlo calculations (16, 25) have found the total delivery efficiency to
Earth
to be on the order of [10.sup.-4] in [10.sup.7] years.

We tracked 200 particles launched from Mercury in random directions having
[v.sub.infinity] = 1 km/s after escaping from the planet (15). The
re-accretion rate is initially very high (Fig. 1), again because of the
low
relative velocity of the particles with respect to Mercury (14). The lunar
and
mercurian cases are similar because, compared to the planetary orbital
speed,
the initial random velocity is very small. For Mercury, about
three-quarters
of all of the launched particles were re-accreted during the 30-Myr
simulation
(Table 2).
Table 2. The fates of meteoroids after a [v.sub.infinity] = 1
km/s launch from Mars and Mercury. The simulation
for Mars included 900 particles and ran for
100 Myr; the simulation for Mercury included 200
particles over 30 Myr. No collisional effects were
included. The position of Mercury was not tracked
in the martian simulation, so collisions with it were
not possible.
 
                             Particles (% of total)
                                from parent body
 
Meteoroid fate
                            Mars            Mercury
 
Impact Mercury              N.A.              76
Impact Venus                 7.5               6.5
Impact Earth                 7.5               0.5
Impact Mars                  9.0               0
Sun-grazing                 38                 4
Reach Jupiter               15                 2
Survivors                   23                11

Just one of the 200 particles was found to hit the Earth, after 23 Myr.
This
0.5% delivery efficiency is 50 times higher than previously suggested (16)
but
is based on poor statistics@ it is about an order of magnitude smaller
than
the efficiency for Mars. If we accept this efficiency and if the mercurian
impactor flux is comparable to that of Mars (26) the existence of 12
martian
meteorites should lead us to expect a few mercurian meteorites. However, a
purely gravitational model may not be sufficient to accurately simulate
the
transfer of material from Mercury to Earth. Radiation forces in the inner
solar system cause significant orbital evolution over tens of millions of
years, times like that required for our single meteoroid to reach Earth.
Orbital collapse as a result of Poynting-Robertson (P-R) drag at Mercury's
heliocentric distance takes only 5 Myr (27) for a meteoroid 1 cm in radius
with a density of 5 g/[cm.sub.3]. On the other hand, the Yarkovsky effect,
which dominates P-R effects for particles of this size with spin periods
longer than 1 s (27), may induce some mercurian meteoroids to spiral
outward
to Earth (28) However, mercurian meteoroids may be catastrophically
fragmented
by dust-sized impactors, which, because of gravitational focusing,
increase
significantly as the sun is approached. Collisional lifetimes of 100-g
bodies
at Mercury's distance are estimated to be less than [10.sup.5] years (29).
Because of these complications, the likelihood of finding mercurian
meteorites
is difficult to quantify.

The identification of meteorites from the moon and Mars has allowed
scientists
to consider more seriously the possibility of finding meteorites from Venus
or
Earth (hereafter, venusian and terrene meteorites, respectively). The
larger
escape velocities of these planets will only be overcome by a tiny fraction
of
the ejecta, and then only in the larger and rarer impact events. The
difficulty of successful ejections is heightened by the presence of the
massive atmospheres of Earth and Venus, because such atrmospheres
effectively
screen out all crater-producing impactors below a certain threshold size
(30),
and launched fragments have to plow back through the atmosphere (31). On
the
basis of our simulations, we expect that the reaccretion efficiency by the
Earth of its own ejecta would be several times higher than Earth's
accretion
of venusian ejecta (25). Given the much more massive atmosphere of Venus,
if
venusian meteorites are possible, then certainly terrene meteorites should
be
much more abundant. Thus we restrict our attention to the latter.

It may be problematic to distinguish terrene meteorites from untraveled
material. Presumably only falls, or finds with preserved fusion crusts,
would
be readily accepted as bona fide terrene meteorites; anomalous Earth rocks
found on the Antartic arctic ice sheet are probably our best hope. Because
only massive rare impacts are capable of launching such objects, the Earth
likely has not recently experienced an event capable of ejecting Earth
rocks
at greater than the escape velocity. Thus, terrene meteorites should be
comparitively rare in the relatively young (<1 Myr old) Antarctic ice
sheet.

Earth impacts have ejected tektites (impact glasses), some of which may
have
been launched along suborbital trajectories arching above Earth's
atmosphere
before re-entry (32). With slightly higher speeds, other tektites might
have
escaped the Earth's gravitational field. Such objects would have a high
probability ([is nearly equal to]30 to 50%) of rapidly re-impacting the
Earth.
Isolated tektite finds (that is, not part of a strewn field) would be
worth
examining for evidence of a brief (<<1 Myr) CRE (33). A proviso in this
picture is that tektites are not strictly analogous to the relatively
lightly
shocked lunar and martian meteorites.

The orbital histories of terrene meteoroids, if any exist, are also of
interest in view of the enormous efforts expended to sterilize spacecraft
to
prevent the contamination of Mars by terrestrial organisms. This
sterilization
would make little sense if terrestrial microorganisms have already been
carried to Mars aboard terrene meteorites (31).

REFERENCES AND NOTES

[1.] Named for the three large meteorite falls Shergotty, Nakhla, and
Chassigny. H. Y. McSween Jr., Meteorites and Their Parent Parent Planets
(Cambridge Univ. Press, Cambridge, 1987). [2.] D. D. Bogard, P. Johnson, L.
E.
Nyquist, Lunar Planet. Sci. XV, 68 (1984). [3.] L. E. Nyquist, J. Geophys.
Res. 88, 785 (1983). The SNC meteorites record only very mild shock
histories
(< 1 to 50 GPa), whereas escape from Mars was thought to require >100 GPa,
which argued further against their being ejected in a cratering event. A.
M.
Vickery and H. J. Melosh, Icarus 56, 299 (1983). [4.] See D. D. Bogard and
P.
Johnson, Geophys. Res. Lett. 10, 801 (1983) for references. [5.] W. A.
Cassidy
and L. A. Rancitelli [Am. Sci. 70, 156 (1982) have reviewed Antarctic
meteorites, and O. Eugster [Science 245, 1197 (1989) has focused on some
early
lunar Antarctic finds. [6.] D. D. Bogard and P. Johnson, Science 221, 651
(1983). [7.] H. Y. McSween Jr., Meteoritics 29,757 (1994). The possibility
of
meteorites, like ALH84001, falling outside of the SNC categorization
argues
further for ceasing to use "SNCs" as a synonym for "martian meteorites."
See
also D. W. Mittlefehldt, Meteoritics 29, 214 (1994). [8.] High-speed,
lightly
shocked eM may be launched by shock wave interference [H. J. Melosh,
Icarus
59, 234 (1984)] or by vapor-plume entrainment [J. D. O'Keefe and T. J.
Ahrens,
Science 234, 346 (1986)!. The cratering physics that launches ejecta at
speeds
above the escape velocity may differ greatly from the physics of the
excavation flow that creates the impact crater. [9.] Objects that are
shielded
by several meters of rock, or even by Earth's atmosphere, do not
accumulate
radioactivity, and the radioisotopes HO are present begin to decay. Because
of
this, with enough measurements of a variety of isotopes, it is possible to
calculate (i) the length of time that the object spent in the upper few
meters
of the parent body before launch (2[pi] age), (ii) the depth at which d
was
burried, (iii) the duration of its transit to the Earth (4[pi] age), and
(iv)
the terrestrial age or Earth residence time ([t.sub.direct sum]) [R.C.
Reedy,
J. R. Arnold, D. Lal, Science 219, 127 (1983).! [10.] Paired meteorites
are
different pieces of the same meteoroid that fragmented during atmospheric
entry or was broken apart by subsequent erosional processes. Such pairs
should
be counted as a single meteorite fall (for example, MAC88104/5 in Table
1).
"Source-crater pairing" is also possible, in which two meteorites launched
during a single cratering event may travel on independent paths to the
Earth,
spending different times in space and landing at different locations on
the
Earth. Nevertheless, CRE and petrologic data may link the two samples as
being
from the same source crater. It seems unlikely that any lunar meteorites
are
source-crater paired except for Asuka-881757 and Y-793169 (11). The case
is
less dear for the Martian meteorites. [11.] P. Warren, Icarus 111, 338
(1994).
[12.] For details about the lunar simulations, see B. J. Gladman, J. A.
Bums,
M. Duncan, H. Levison, ibid. 118, 302 (1995). [13.] H. Levison and M.
Duncan,
ibid. 108, 18 (1994). This integration method is based on the
mixed-variable
symplectic integrator developed by J. Wisdom and M. Holman [Astron. J.
102,
1528 (1991)]. [14.] The gravitational cross section [pi][b.sup.2] (the area
at
[infinity] through which passing particles will impact the body) for a body
of
radius R and escape speed [v.sub.esc] is [pi][b.sup.2] = [pi][R.sup.2][1 +
([v.sub.esc]/[([v.sub.infinity].sup.2], where [v.sub.infinity] is the
relative
encounter speed at infinity. For Mercury, Venus, Earth, and Mars,
[v.sub.esc]
= 4.2, 10.3, 11.2, and 5.0 km/s, respectively. [15.] The relative
planetocentric velocity at infinity, after being ejected at speed
[v.sub.ej]
from a planet with escape speed [v.sub.esc], is approximately
[v.sub.infinity]
[approximate] [Mathematical Expressions Omitted]. This [v.sub.infinity] is
generally much less than the heliocentric orbital velocity of the planet
and
therefore produces a slightly eccentric and inclined orbit with respect to
the
planet's orbit. [16.] G. W. Wetherill, Meteoritics 19, 1 (1984). [17.] A.
M.
Vickery [Geophys. Res. Lett. 14, 726 (1987)] studied secondary crater
fields
around martian, lunar, and mercurian impact craters and found power-law
decreases in the fragment size with increasing ejection speed. [18.] The
resonances are 2g = [g.sub.5] + [g.sub.6] and g - s = [g.sub.5] -
[s.sub.6],
with the former the more dynamically effective of the two. Here g and s
denote
the precession rates of the perihelion and ascending node of the particle,
and
[g.sub.i] and [s.sub.i] are the ith fundamental secular eigen-frequencies
of
the solar system. The resonances are nonlinear because they involve more
than
one fundamental frequency, and second order because they do not appear in
the
expansion of the secular disturbing function until quadratic terms in the
planetary masses are considered. See Ch. Froeschle and A. Morbidelli, in
Asteroids, Comets, and Meteors, 1993, A. Milani, M. Di Martino, A.
Cellino,
Eds. (Kluwer, Boston, 1994), pp. 189-204. [19.] Sun-grazing is discussed
for
near-Earth asteroids by P. Farinella et al. [Nature 371, 314 (1994)], for
the
short-period comets by M. E. Bailey, J. E. Chambers, and G. Hahn [Astron.
Astrophys. 257, 315 (1992)!, and for the Jupiter-family comets by Levison
and
Duncan (13). [20.] In rough agreement with the observed CRE ages of the
ordinary chondrites (1)). G. W. Wetherill [Icarus 76, 1 (1988)] used a
collisional haft-life of [1.2r.sup.1/2] Myr for a meteoroid of radius r
(in
centimeters) when Q > 2.1 AU. Thus, a meteoroid with r [approximate] 3 cm
(pre-atmospheric mass, ^300 g) and aphelion in the main belt would have a
collisional lifetime of 2 Myr. In our model collisional fragments of
martian
meteoroids are not large enough to engender recoverable meteorites. [21.]
N.
Bhandari et al., Geochim, Cosmochim. Acta 50, 1023 (1988). [22.] D. D.
Bogard,
Lunar Planet. Sci. XXVI, 143 (1995). The cumulative spectrum (Fig. 5) is
unchanged by source-crater pairing. If the interval between martian
launches
is 2 Myr, then the impactors are [approximate] 1 km in diameter [W. F.
Bottke,
M. C. Nolan, R. Greenberg, R. A. Kolvoord, in Hazards Due to Comets and
Asteroids, T. Gehrels, Ed. (Univ. of Arizona Press, Tucson, 1994), pp.
337-358!. [23.] Treiman and co-workers [A. H. Treiman, J. Geophys. Res.
100,
5329 (1995); A. H. Treiman et al., Meteoritics 29, 581 (1994)! argue for
one-stage exposures as small bodies but allow for source-crater pairing of
the
shergottites or nahklites-Chassigny. An additional constraint that must be
satisfied is the puzzling prevalence of martian meteorites from young
source
terrains. This constraint has been used to argue in favor of large martian
impact craters [see R. A. Kerr, Science 237, 721 (1987)!. [24.] A. M.
Vickery
and H. J. Melosh, Science 237, 738 (1987). [25.] H. J. Melosh and W. B.
Tonks,
Meteoritics 28, 398 (1993). [26.] The current formation rate of craters
with
diameters larger than 10 km is a factor of 2 larger on Mercury than on
Mars
(although most of the crater-producing projectiles on Mercury are
cometary)
[G. W. Wetherill, ibid. 24, 15 (1989)!. Mercury's smaller escape velocity
should result in a larger meteoroid generation rate. A comparison based on
the
moon's supply (because the present cratering rate for Mercury is at least
an
order of magnitude larger than the moon's, but the delivery efficiency is
100
times smaller) also yields a few expected mercurian meteorites. [27.] J.
A.
Burns, P. L. Lamy, S. Soter, Icarus 40, 1 (1979). [28.] S. G. Love and K.
Keil
[Meteoritics 30, 1 (1995)] discuss the Yarkovsky effect and the problems
of
identifying mercurian meteorites. [29.] E. Grun, H. A. Zook, H. Fechtig, R.
H.
Giese, Icarus 62, 244 (1985). [30.] The Earth's atmosphere prevents stony
object with diameters <50 from reaching the ground and creating
hypervelocity
impact craters [C.

 Chyba, Nature 363, 701 (1993)!. [31.] It is conceivable that ejecta could
escape out through the atmospheric "tunnel" left by the impactor's entry
[H.
J. Melosh, ibid. 332, 687 (1988)]. [32.] See C. Koeberl, Annu. Rev. Earth
Planet Sci. l4, 323 (1986), and references therein. [33.] Searches for
radionuclides induced by cosmic rays in tektites have produced only upper
limits on their time in space, varying from goo to 90,000 years. Relevant
papers are reviewed in J. A. O'Keefe, Tektites and Their Origin (Elsevier,
New
York, 1976), pp. 160-165. Because the tektites examined were from strewn
fields, which implies that they never escaped to helio-centric orbit,
these
results do not necessarily constrain theories of objects that escape from
the
Earth. [34.] Calcalong Creek and QUE93069 have large CRE age uncertainties
because of incomplete analyses; we have used the lower ages given in Table
1
in analogy with the other lunar meteorites. Warren (11) argued that the
remaining meteorites may be from seven different source craters. We accept
the
proposed source-crater pairing of Asuka-881757 and Y-793169 and go further
to
assert conventional pairing because the odds of having two lunar
meteoroids
from the same source Grater arrive at the Earth at the same time after
spending l Myr in space and landing close to each other is so small. [35.]
T.
D. Swindle, M. K. Burkland, J. E. Grier, Meteoritics 30, 584 (1995). [36.]
K.
Nishiizumi, Lunar Planet. Sci. XXVI, 1051 (1995). [37.] P. H. Benoit, D.
Sears, S. Symes, ibid., in press. [38.] We thank H. J. Melosh, P.
Farinella,
P. Warren, and G. Wetherill for constructive input to this study, and
three
referees for valuable comments. This work was supported in part by
National
Aeronautics and Space Administration grant NAGW-310.
                                                                           
  
                                -- End --


LOUIS VARRICCHIO
 Environmental Information Specialist &
 Producer/Writer, "Our Changing Planet"
  (Visit OCP-TV on the Web at: www.umac.org/ocp)
  Upper Midwest Aerospace Consortium
  Odegard School of Aerospace Sciences
  University of North Dakota
  Grand Forks, N.D. 58202-9007
    Phone: 701-777-2482
    Fax: 701-777-2940
    E-mail: varricch@umac.org (in N.D.); morbius@together.net (in Vt.)

"Behind every man alive stand thirty ghosts, for that is the ratio by
which the dead outnumber the living. Since the dawn of time, a hundred
billion human beings have walked the planet Earth." -- Arthur C. Clarke

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