Icarus 155, 94?103 (2002)
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All rights re6/icar.2001.6751, available online at http://www.idealibrary.com on
Estimate of Eros?s Porosity and Imp
Sarah L. Wilkison and Mark
Department of Geological Sciences, Northwestern Un
E-mail: sarah@earth.nwu
Peter C. Thomas and Josep
Department of Astronomy, Cornell University,
Timothy J. McCoy
Department of Mineral Sciences, National Museum of Natural History, Sm
Scott L. Murchie and Louise M
Applied Physics Laboratory, Laurel, M
and
Donald K. Yeoman
Jet Propulsion Laboratory, California Institute of Techno
Received December 14, 2000; revised
based spectral measurements and NEAR Shoemaker mag-
r, X-ray, and near-infrared spectrometer data are all con-
ith Eros having a bulk composition and mineralogy similar
ry chondrite meteorites (OC). By comparing the bulk den-
3 Eros (2.67? 0.03 g/cm3) with that of OCs (3.40 g/cm3), we
the total porosity of the asteroid to be 21?33%. Macro (or
l) porosity, best estimated to be ?20%, is constrained to be
6 and 33%. We conclude that Eros is a heavily fractured
we find no evidence that it was ever catastrophically disrup-
eaccumulated into a rubble pile. c? 2002 Elsevier Science (USA)
ords: Eros; meteorites; surfaces, asteroids; interiors.
INTRODUCTION AND BACKGROUND
ear Earth Asteroid Rendezvous (NEAR) Shoemaker
ft orbited 433 Eros from February 14, 2000 to February
, collecting positional, image, altimetry, and spectral
ough remote sensing experiments. Although NEAR
ker has no instrumentation that allows for a direct mea-
t of the asteroid?s interior structure, the density and
of an asteroid can give first-order information regard-
structural makeup of an asteroid. Utilizing the avail-
sity and porosity data for meteorites (Consolmagno and
98, Flynn et al. 1999, Wilkison and Robinson 2000)
bulk density of Eros obtained from NEAR Shoemaker
measure
estimate
review
might st
tempt to
ally alte
ison of t
porosity
to infer
Sever
have be
asteroid
impacts
viously
shell mo
phosed p
column
The u
posed o
such wo
either in
Chapma
large as
diffusiv
94
02 $35.00
evier Science (USA)
served.ications for Internal Structure
. Robinson
ersity, Evanston, Illinois 60208
du
Veverka
Ithaca, New York 14853
ithsonian Institution, Washington, DC 20560?0119
. Prockter
aryland 20723
s
logy, Pasadena, California 91109July 25, 2001
ments (Veverka et al. 2000, Yeomans et al. 2000), we
a range of porosity for Eros. Additionally, we briefly
relevant asteroid formation models and how asteroids
ructurally evolve over time due to impacts, and we at-
clarify terms previously used to describe the collision-
red parent bodies (i.e., ?rubble pile?). Finally, a compar-
he formational and structural models with the estimated
and morphologic observations of the surface allows us
the gross internal structure of 433 Eros.
PARENT BODY FORMATION MODELS
al models of applicable (for 433 Eros) parent bodies
en proposed that describe the internal structure of an
before any significant structural modification (due to
) has occurred. In this section we briefly review these pre-
proposed models: the undifferentiated model, the onion
del, the heterogeneously heated model, the metamor-
lanetesimal model, and the differentiated model (Fig. 1,
1).
ndifferentiated model proposes that an asteroid is com-
f primitive undifferentiated chondritic material and as
uld have a solid coherent interior lacking any layering,
composition or in alteration state (e.g., Wetherill and
n 1988). The classic onion shell model proposes that
teroids (perhaps >50 km radius depending on thermal
ity) are accreted cold and heated by either external
FIG.
represen
into the t
this is a
material
layers of
heating t
Rajan (1
(e.g., e
clides 2
Minste
and Fu
centric
cores o
cooling
ing rap
(1990)
of heat
dicts th
parent
would
this mo
mals (r
a larger
tures fo1. Potential parent body models for 433 Eros. Colors represent different ordinary chondrite petrologic types (yellow represents petrologic type 3, red
ts petrologic type 4, blue represents type 5, and green represents type 6). The five modeled asteroids could evolve with collisional modification/disruption
hree structural models (fractured but coherent body, heavily fractured, and rubble pile). Shapes and sizes of fragments are not meant to be taken literally;
schematic representation. (A) The undifferentiated model, after Wetherill and Chapman (1988). The asteroid is composed of undifferentiated chondritic
(in this example the material is petrologic type 3). (B) The onion shell model, after Miyamoto et al. (1981). The chondritic parent body exhibits successive
petrologic types 3 through 6. (C) The heterogeneously heated model, as described in McCoy et al. (1990). The chondritic body experiences heterogeneous
hroughout that results in petrologic types being dispersed randomly through the parent body. (D) The metamorphosed planetesimal model, after Scott and
981). Small, unconsolidated chondrite planetesimals accrete into a larger parent body. (E) The differentiated model, after Wetherill and Chapman (1988).
arly luminous Sun) or internal (e.g., short-lived radionu-
6Al and/or 60Fe) sources (Herndon and Herndon 1977,
r and Allegre 1979, Pellas and Storzer 1981, Miyamoto
jii 1980, Miyamoto et al. 1981). Heating results in a con-
?onion shell? structure: internally heated bodies have
f strongly metamorphosed type 6 material in the slowly
center with weakly metamorphosed type 3 material cool-
idly near the surface (Miyamoto et al. 1981). McCoy et al.
suggested a heterogeneously heated model (with a source
such as electromagnetic induction). Such a model pre-
at petrologic types are randomly distributed through the
body. A similar random distribution of petrologic types
also occur in the metamorphosed planetesimal model. In
1982; Grimm 1985). Finally, the differentiated coherent model
proposes that the asteroid is composed of material that differen-
tiated into a core, mantle, and crust (e.g., Wetherill and Chapman
1988). We include the differentiated model because one inter-
pretation of Earth-based spectral data indicates that Eros may
have distinct compositional units (Murchie and Pieters 1996).
COLLISIONAL EVENTS AND
DISRUPTION/MODIFICATION MODELS
Collisional events are generally classified into three groups:
1. cratering, 2. fracturing or fragmentation, and 3. catastrophic
fragmentation and dispersal (Davis et al. 1979). Cratering isd
a
rEROS?S POROSITY AND IMPLICATIONS FORel, petrologic grades are established in small planetesi-
dii less than 10 km) that are subsequently accreted into
body (100-km radius) near peak metamorphic tempera-
each planetesimal (Scott and Rajan 1981, Taylor et al.
defined
high vel
define fr
part orINTERNAL STRUCTURE 95as the excavation of debris on a large body due to a
ocity impact (Gault et al. 1963). Davis et al. (1979)
agmentation or fracturing as the process of crushing
all of the body. They further define disruption as the
96
process o
define ca
largest re
mass. N
propose
are high
et al. 19
1997).
What Is
The te
ferent sta
evolution
compose
gravitati
of Phobo
expande
Davis et
?rubble p
Chapm
gies in th
during s
just frag
no intern
ate the id
tured bu
They als
(strong v
each from
two deca
their orig
gesting t
be suffic
waves, th
Hartm
sized bo
bodies in
of the p
50 km in
bly into
cess of c
conditio
and the r
body. Ot
from the
complete
Size and
Farine
ters betw
fragmen
rubble p
hydrody
m
s
t
o
s
n
d
z
o
g
s
o
p
o
h
n
e
a
m
n
w
g
i
S
r
r
m
H
a
-
l
i
(
e
aWILKISON ET AL.
f fragmenting and dispersing a body. Davis et al. (1989)
tastrophic fragmentation as a collision in which the
sulting piece contains 50% or less of the initial target
umerical hydrocode simulations of asteroid collisions
that most collisionally evolved bodies larger than?1 km
ly fragmented (Asphaug and Melosh 1993, Greenberg
94, 1996, Love and Ahrens 1996, Melosh and Ryan
a ?Rubble Pile? Asteroid?
rm ?rubble pile? has been used to describe several dif-
tes among a spectrum of possible asteroidal structural
. Discussions of the possibility that asteroids may be
d of ?a loose agglomeration of material held together
onally? dates back at least as far as Mariner 9 studies
s and Deimos (cf. Veverka et al. 1974). This idea was
d upon in reports from 1977 to 1979 (Chapman 1978,
al. 1979, Hartmann 1979) and the first use of the term
ile? appeared in Davis et al. (1979, p. 533).
an (1978) suggested that the collision rates and ener-
e asteroid belt are sufficient to fragment most asteroids;
ignificant collisions on larger asteroids, the body may
ment (not disperse) and form a ?pile of boulders? with
al strength (Chapman 1978). Davis et al. (1979) reiter-
ea that larger asteroids are most likely internally frac-
t gravitationally bound ?rubble piles of megaregolith.?
o include some discussion of the type of target material
ersus weak) and the outcomes that could occur with
catastrophic and barely catastrophic impacts. Almost
des later, Davis et al. (1996) made a modification of
inal definition when discussing the asteroid Ida, sug-
hat the few large coherent pieces of a rubble pile could
iently in physical contact to transmit compressive shock
us allowing such features as antipodal grooves.
ann (1979) examined collisions between comparably
dies; the study quantified the relationship of the two
terms of the mass, density, and energy of impact. One
otential outcomes from such a collision (greater than
size) is complete disruption and subsequent reassem-
granular bodies that then lithify into breccias. This pro-
atastrophic dispersal (Hartmann 1979) is defined as the
n in which half the fragments are dispersed to infinity
emaining half fall together again to make a brecciated
her collisional outcomes described in this study ranged
objects rebounding from each other with little effect to
dispersal of both asteroids.
Shape of Rubble Piles
lla et al. (1982) suggested that asteroids with diame-
diamete
a size
geneou
though
1969, F
that rub
rium fig
shape f
an ellip
et al. 19
fragme
spheroi
rotation
ment si
sisting
have re
general
average
domly
offsets
are not
the foll
Strengt
Rece
asteroid
sile str
compar
which
(Love a
lisions,
target w
and gro
Asphau
33 km
asteroid
1997).
in the g
and Ah
or frag
get dam
1998).
(less th
asteroid
gravity
be rubb
be rotat
Harris
and siz
meterseen ?100 and 300 km could have been completely
ted by energetic collisions and then reaccumulated into
iles. More recent studies based on smoothed particle
namics suggest that asteroids a few hundred meters in
with neg
disruptio
cate tha
chains fr could also be rubble piles (Love and Ahrens 1996)?
uch smaller than previous studies proposed. Homo-
masses subjected to self-gravitational interactions are
to take ellipsoidal equilibrium shapes (Chandrasekhar
arinella et al. 1981). Farinella et al. (1982) suggested
ble piles sustain a shape that approximates the equilib-
ure of a fluid of similar density and spin rate. A stable
r a body in hydrostatic or gravitational equilibrium is
oid (Chandrasekhar 1969, Farinella et al. 1981, Catullo
84, Zappala et al. 1984). Gravitationally reaccumulated
ts could have shapes that are approximately Maclaurin
s (moderate rotation rate) or Jacobi ellipsoids (fast
) (Farinella et al. 1981) depending on the largest frag-
e and distribution of smaller pieces. A rubble pile con-
f a mixture of particles of very different sizes might
ions of substantially different porosities, although in
materials with poor particle size sorting have lower
porosities (Pettijohn 1957). Models of particles of ran-
elected size and density can produce a wide range of
f the center of mass from the center of figure, and thus
articularly diagnostic (results for Eros are discussed in
wing).
of Rubble Piles
t studies suggest that many smaller objects, including
s, may be held together by self-gravity, not by the ten-
ngth of the material. Such an asteroid would not be
ble to the strength-dominated laboratory targets from
any characteristics of asteroids have been estimated
d Ahrens 1996). According to models of asteroid col-
craters can form in the ?gravity scaling regime? on a
here gravity, not physical strength, controls crater size
th (Veverka et al. 1974, Greenberg et al. 1994, 1996,
et al. 1996, Love and Ahrens 1996). Several large (19?
n diameter) craters were observed on 243 Mathilde, an
that is itself only 53 km in diameter (Veverka et al.
tickney crater on Phobos is also thought to have formed
avity scaling regime (Asphaug and Melosh 1993, Love
ens 1996). A target in this gravity regime must be weak
ented (Richardson et al. 1998), because a weak tar-
pens the propagation of shock waves (Asphaug et al.
arris (1996) studied the rotation periods of 107 small
n 10-km) asteroids and observed that none of these
s rotate faster than the theoretical breakup limit for a
dominated object, suggesting that small asteroids could
e piles (lack tensile strength), since solid objects could
ng at nearly any speed (Bottke et al. 1998). Pravec and
2000) analyzed the distribution of asteroid spin rates
s, concluding that asteroids larger than a few hundred
re mostly loosely bound, gravity-dominated aggregates
ligible tensile strength. In addition, models of the tidal
n of gravitationally bound asteroids and comets indi-
t these objects may have created the abundant crater
ound on the Earth and the Moon (Bottke et al. 1997).
Meteori
Mete
materia
mon me
Rubin e
25% of
cias. A
differen
29% of
sent an
the LL
of differ
had a c
of paren
Evidenc
disparit
ing rate
the wid
various
1988).
Stoffl
fraction
fragmen
Howeve
and rea
shocked
the colli
that mo
(shock
concurs
and reas
shocked
Fragm
from dif
and 23%
breccias
have thu
of a pare
the rego
(locally
Thomas
the effic
into bre
and sol
asteroid
materia
significa
regolith
survive
In su
teroids c
terial; h
regolith
body.
h
v
i
r
e
o
a
e
i
e
g
t
e
n
v
y
e
a
e
p
b
o
u
)
s
c
r
y
o
o
y
s
twEROS?S POROSITY AND IMPLICATIONS FOR
tical Evidence of Rubble Piles
oritical evidence indicates that disaggregated asteroidal
l may not be rare as witnessed by the relatively com-
teoritic breccias. Early petrologic studies (Binns 1967,
t al. 1983) indicated that 62% of the LL chondrites,
the H chondrites, and 10% of the L chondrites are brec-
more recent study (Benoit et al. 2000) suggests slightly
t percentages of meteoritic breccias: 41% of the LL,
the L, and 22% of the H chondrites (percentages repre-
average of each of the groups, LL, L, and H). Most of
breccias are genomict breccias (composed of LL clasts
ent petrologic types), suggesting that the LL group has
omplex collisional history that may include episodes
t body disruption and reassembly (Rubin et al. 1983).
e supporting breakup and reassembly includes the
y between petrologic types and metallographic cool-
s in ordinary chondrites (e.g., Taylor et al. 1987) and
e range of cooling rates observed in components of
meteoritic breccias (e.g., the aubrites, Okada et al.
er (1982) suggested that some amount (perhaps a small
) of heavily shocked rock would be created during the
tation, disruption, and reassembly of the parent body.
r, Taylor et al. (1987) have suggested that the breakup
ssembly of an asteroid may not produce significantly
material at all, depending on the sizes and velocities of
ding bodies. Examination of meteoritic material reveals
st meteorites are unshocked or only weakly shocked
stage 3; Scott et al. 1989, Stoffler et al. 1991), which
with the Taylor et al. (1987) conclusion that breakup
sembly of a parent body may not produce much heavily
material.
ental meteoritic breccias, thought to be debris derived
ferent lithologies, comprise 5% of the H, 22% of the L,
of the LL chondrites (Rubin et al. 1983). Fragmental
lack solar flare particle tracks and solar wind gases and
s been assumed to have not formed within the regolith
nt body (Rubin et al. 1983). However, we point out that
lith on Eros is typically one to tens of meters in thickness
it may exceed 100 meters) (Barnouin-Jha et al. 2000,
et al. 2001, Zuber et al. 2000) and we do not know
iency with which portions of the regolith are lithified
ccias (and are thus protected from solar flare particles
ar wind gases). Additionally, the rate of gardening on
al sized bodies is unknown and thus it is not clear if
l buried tens or hundreds of meters down experiences any
nt solar wind exposure during its residence time in the
. Clearly the upper loose portion of the regolith does not
a journey to the Earth?s surface in a recognizable form.
mmary, the meteoritical evidence clearly shows that as-
Eart
are hea
gree of
have su
on thei
propos
trum fr
creted
Coh
in coll
If som
the fra
or rota
increas
of seco
Hea
possibl
dergon
Chapm
ble pile
that th
the num
the dis
Rub
definiti
from th
ally bo
Hartma
(1999)
relative
reassem
ity, as w
of size
for mix
intersti
In ea
ing inc
porosit
microp
Flynn e
is the p
as the g
porosit
(such a
These
membeommonly produce heavily fragmented or brecciated ma-
owever, all this material could have been produced in a
and there is no evidence demanding a rubble pile parent
of the l
we use
Tenta
asteroidINTERNAL STRUCTURE 97
IMPLICATIONS OF COLLISIONAL
DISRUPTION/MODIFICATION
-based and spacecraft imaging confirm that asteroids
ily cratered and have thus experienced a significant de-
mpact-induced fracturing. Certainly individual asteroids
ffered differing amounts of internal fracturing depending
collisional histories. For the purpose of this study we
three states of structural modification along the spec-
m a completely coherent to a totally disrupted and reac-
steroid (Fig. 1).
rent but fractured. The target body is mildly fractured
sions but is still a coherent, strength-dominated body.
fractures have passed completely through the asteroid,
ments have not undergone any significant movement
ion relative to the original structure of the asteroid. This
in porosity (and decrease in bulk density) is an example
dary porosity as defined by Fraser (1935).
ily fractured. The asteroid has been heavily fractured,
through several large collisions, and fragments have un-
small displacement/rotation (consistent with the
n (1978) and Davis et al. (1979) definition of a rub-
). We infer that this structure would have more porosity
coherent but fractured model, owing to an increase in
ber of fractures and void space (macroporosity) between
laced/rotated fragments.
le pile. For the purposes of this paper we adopt the
n that a rubble pile is an asteroid that was reaccreted
e remnants of a disrupted parent body into a gravitation-
nd granular body (i.e., consistent with descriptions in
nn (1979), Asphaug et al. (1998), and Wilson et al.
. This definition implies little internal strength and a
ly high porosity as a result of the voids created by the
bly of the dispersed fragments. The amount of poros-
ith terrestrial rocks, would depend upon the distribution
and shapes of the particles and on the opportunities
ing the smaller size fractions among the larger particle
es (Pettijohn 1957).
ch of these three models the relative amount of fractur-
eases, resulting in higher porosity. Two general types of
are discussed when describing asteroids and meteorites:
rosity and macroporosity (Consolmagno and Britt 1998,
t al. 1999, Wilkison and Robinson 2000). Microporosity
rosity inherent in a meteorite sample, on the same scale
rain size, manifested as small cracks and voids. Macro-
is the void porosity between (large) coherent pieces
between the pieces of a rubble pile) within an asteroid.
o generalized classifications of porosity represent end-
rs; a continuum of porosity probably exists, but because
ack of asteroid ground truth and for ease of discussion,
these terms for clarity.
tive porosity ranges can be assigned to each of the three
structural models from terrestrial and lunar analogs
98
Sa
Breccia
Breccia
Breccia
Breccia
Welded m
Lunar reg
Coconino
Lappajarv
?Shocked
Unconsol
Nonindur
Gravel
Bunter sa
Welded tu
(Table I
sity ran
1999) (o
more de
do not e
fication
micropo
herent b
Micro
5 to 24
terrestri
and Gre
ratory a
the terre
macrop
ysis of
logs fou
are rem
that a co
to smal
slightly
fracture
that the
tative of
ered tha
sandsto
these m
craters (
lithified
pact sam
tured as
ranging
i
it
e
y
c
i
la
al
u
-
i
e
b
r
h,
im
i
n
ie
s
n
. W
an
f
a
t
l
at
o
i
ti
io
e
re
ac
h
et
s
m
r
s
scWILKISON ET AL.
TABLE I
Porosities of Rocks
mple Porosity (%) Reference
Lunar samples
17.4 Horai and Winkler (1976)
14.1 Horai and Winkler (1976)
24 Horai and Winkler (1980)
4.9 Fujii and Osako (1973)
icrobreccias 18.4?43.9 Chao et al. (1971)
olith 46 Carrier et al. (1991)
Terrestrial impact samples
sandstone 24 Ahrens and Gregson (1964)
i breccias up to 20 Kukkonen et al. (1992)
sandstone? up to 23 Short (1966)
Common rocks
idated sand 38.7?44.8 Schopper (1982)
ated sand 33.8?51.3 c.f. Davis (1969)
63.4 Cohen (1965)
ndstone 5.8?30.8 Schopper (1982)
ff 14.1 Keller (1960)
). OC meteorites generally fall within the bulk poro-
ge 0?15% (Consolmagno and Britt 1998, Flynn et al.
utliers from the 0?15% porosity range are discussed in
tail below). Ordinary chondrite (OC) meteorite samples
xhibit abundant fractures or other post-formation modi-
that would affect their bulk porosity (their porosity is all
rosity). Thus we propose a range of 0?15% for the co-
ut fractured asteroid model.
porosity values for lunar breccias generally range from
% measured from small samples, and porosities from
al impact sites range from 20 to 24% (Table I). Ahrens
gson (1964) shocked Coconino sandstone in the labo-
nd measured the porosity at 24%. A detailed study of
strial Lappajarvi breccias investigated both micro- and
orosity of impact rocks (Kukkonen et al. 1992). Anal-
materials from the Lappajarvi drill core and resistivity
nd that ?the apparent and rock sample porosity profiles
arkably similar in their overall shape, which indicates
nsiderable part of the effective porosity of rocks is due
l-scale pores and vesicles. The apparent porosities are
higher than the core sample porosities as a result of
s? (Kukkonen et al. 1992). This conclusion indicates
porosity of the drill core (up to 20%) itself is represen-
the whole rock unit (impact site). Short (1966) discov-
t shock-lithified sand formed coherent masses (?shocked
ne?) during cratering explosions at the Nevada Test Site;
asses resembled shocked sandstones found at meteorite
such as Wabar, Saudi Arabia). The porosity of the shock-
Find
is adm
can hav
particle
for ver
and me
terrestr
fall or
minim
change
notorio
of 100
terrestr
less, th
that ru
Anothe
regolit
An est
60 cm)
collisio
porosit
and rea
tling a
?30%
fined in
rough
data) o
are obt
Implica
We i
ferenti
morph
time (F
acteris
disrupt
fractur
of the
from e
tinguis
us to d
this illu
ity esti
the inte
Compo
Tele
sand masses ranges up to 23% (Short 1966). These im-
ples (lunar and terrestrial) suggest that the heavily frac-
teroid model proposed above could have total porosity
from 15 to 30%.
sitionall
Pieters
Eros fro
and theng a terrestrial or lunar analog for a rubble pile asteroid
tedly problematic. Unconsolidated terrestrial sediments
porosities of 20?50% or even over 60% (Table I). The
size sorting is critical in determining the porosity, and
fine terrestrial sediments, particle shapes, compaction,
hanism of deposition affect porosity greatly. The best
al analogs for rubble pile structures may be fresh rock-
ndslide deposits and mine dumps, as they would have
effects of fluvial addition or removal of fines that can
porosity. Measurement of such porosities, however, is
sly difficult, and the analogy may not avoid the effects
1000-fold difference in compressive stresses between
al rubble pile deposits and small asteroids. Nonethe-
analogies and geometry of packing fragments suggest
ble piles could have porosities well in excess of 30%.
potential analog for a rubble pile asteroid is the lunar
which is composed of unconsolidated lithic fragments.
ate of lunar regolith porosity in situ (for the top 0?
s 46 ? 2% (Carrier et al. 1991). Finally, modeling of the
al breakup and gravitational assembly process predict
s of ?40% for asteroids that have undergone breakup
sembly (Wilson et al. 1999). However, subsequent set-
d relithification may lower this value to the range of
e adopt >30% as the porosity for a rubble pile (as de-
this manuscript). Clearly these porosity boundaries are
d will remain so until direct measures (such as seismic
a statistically significant population of asteroid interiors
ined.
ions for the Parent Body Models
lustrate the evolution of the parent body models (undif-
ed coherent, onion shell, heterogeneously heated, meta-
sed planetesimal, and differentiated coherent) through
g. 1, columns 2?4); each model and its resulting char-
cs are classified according to the three modification/
n models proposed (coherent but fractured, heavily
d, and rubble pile). As demonstrated by Fig. 1, many
sulting structural models are not easily distinguishable
h other. Even existing remote sensing data may not dis-
between the resulting structural models, let alone allow
ermine the unaltered parent body structure. We include
tration to emphasize the importance of using the poros-
ate, along with existing remote sensing data, to infer
nal structure of an asteroid.
DISCUSSION
ition
opic spectral data indicated that Eros might be compo-
y heterogeneous on a hemispheric level (Murchie and
1996). However, color and spectral measurements of
m the NEAR Shoemaker Multispectral Imager (MSI)
near-infrared spectrometer (NIS) did not confirm this
result (M
NEAR
data ind
Ca, and
dinary c
et al. 20
sults are
(Veverk
ditional
Eros to h
2000). F
figure ar
out larg
be expe
(Thoma
calculat
Porosity
Cons
of 15 ord
Another
from 0
well-do
porosity
FIG. 2
Both stud
porosities
(1999).
r
n
ro
r
r
.
s
f
r
s
e
s
o
r
t
t
a
e
o
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e
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,
9
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:
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c
eEROS?S POROSITY AND IMPLICATIONS FOR
urchie et al. 2000, Murchie et al. 2001, Bell et al. 2001).
Shoemaker X-ray/gamma-ray Spectrometer (XGRS)
icate that Eros has an elemental composition (Fe, Mg,
Al, ratioed to Si) consistent with undifferentiated or-
hondritic (H, L, or LL) meteoritic material (Trombka
00). NEAR Shoemaker NIS spectra and MSI color re-
also consistent with an ordinary chondrite composition
a et al. 2000, Murchie et al. 2001, Bell et al. 2001). Ad-
ly, NEAR Shoemaker magnetometer results also show
ave a composition consistent with LL OCs (Acuna et al.
inally, the fact that Eros?s center of mass and center of
e nearly coincident (as described in the next section) rule
e inhomogeneities in its internal density, which would
cted if Eros exhibited large internal compositional units
s et al. 2001). These results allow us to compare the
ed density for Eros to that of OC meteorites.
olmagno and Britt (1998) measured the microporosities
inary chondrites and found them to range from 0 to 15%.
study (Flynn et al. 1999) reports OC microporosities
to 23% (n = 27). Unfortunately, the total number of
cumented OC microporosities is 42 (Fig. 2). The median
value of ordinary chondrities in each study was 6%, the
Bulk den
Micropo
Grain de
Total po
Micropo
Macropo
Notes
resent as
mation o
Micropo
median i
on the pr
with Ero
porosity
of Eros (
Note tha
in this es
rigorous
densities
averag
deviati
Flynn
Bjurbo
extrem
(Flynn
the ori
not rep
more s
We
0?15%
Britt 1
illustra
microp
Using
density
the bul
Yeoma
be 21?
macrop
total po
21% to
porosit
density
?26%
leave a
Mod
bly pro
dergon. Histograms of ordinary chondrite porosities from two datasets.
ies overlap in the 0?15% range of porosity; both studies have median
of 6%. (A) From Consolmagno and Britt (1998). (B) From Flynn et al.
in poro
in the o
neous o
ment sizINTERNAL STRUCTURE 99
TABLE II
Estimations of Eros?s Porosity
sity (OC) (g/cm3) 3.40 3.40 3.40 3.40 3.40
osity (OC) 0% 0% 15% 15% 6%
sity (OC) (g/cm3) 3.40 3.40 4.00 4.00 3.62
sity (Eros) 21% 21% 33% 33% 26%
osity (Eros) 0% 15% 0% 15% 6%
osity (Eros) 21% 6% 33% 18% 20%
Numbers in italics represent calculations; numbers not italicized rep-
umptions. Read down each column. Each column illustrates an esti-
Eros?s porosity starting with the average bulk density of OCs (row 1).
osities of the meteorite are assumed to be in the range 0?15% and the
6% porosity (row 2). Row 3 shows the calculated grain densities based
vious assumptions (rows 1 and 2). The grain density is then compared
?s bulk density of 2.67 g/cm3, resulting in the estimate of the total
f Eros (row 4). More assumptions are made about the microporosity
ow 5), which leads to the calculation of Eros?s macroporosity (row 6).
we have chosen to use the average bulk density (3.40 g/cm3) of OCs
imation. If there were more porosity and density data available, a more
pproach would be to estimate the porosity of Eros using varying bulk
and microporosities of OCs and varying microporosities of Eros.
s were 6.5% and 6.4%, (respectively), and the standard
ns were 4.1% and 6.8% (respectively). We note that
t al. (1999) measured the porosities of two pieces of
e to be 20% and 23% porosity. The Bjurbole samples are
ly friable to the point that they crumble with handling
t al. 1999). Clearly this texture is rare among OCs, and
in of this texture is not understood. Perhaps Bjurbole is
esentative of the original asteroid?s porosity but may be
milar to a regolith porosity.
hoose a more conservative measure of OC porosity,
a range at which both studies (Consolmagno and
98, Flynn et al. 1999) overlap (see Fig. 2). Table II
es our estimates of the porosity of Eros using varying
rosities of OCs and varying microporosities of Eros.
he range of porosity (0?15%) for OCs, the average bulk
of OCs, 3.40 g/cm3 (Wilkison and Robinson 2000), and
density of Eros, 2.67 ? 0.03 g/cm3 (Veverka et al. 2000,
s et al. 2000), we estimate the total porosity of Eros to
3% (Wilkison and Robinson 2000). We infer that Eros?s
orosity may be as high as 33% (0% microporosity, 33%
rosity) but must be greater than 6% (15% microporosity,
tal porosity) (Table II). Using the median value of 6%
of OCs, the average bulk density of OCs, and the bulk
of Eros, we estimate the total porosity of Eros to be
removing 6% microporosity from the asteroid would
macro- (or structural) porosity of ?20% (Table II).
ling of the collisional breakup and gravitational assem-
ess predict porosities of?40% for asteroids that have un-
breakup and reassembly (Wilson et al. 1999). Variationssity within an object might be detected by a difference
bject?s gravity field from that of a completely homoge-
bject. Assemblage of a rubble pile having a range of frag-
es should exhibit variations in porosity, and hence local
100
density
data in
et al. 2
The
accurat
has allo
center
figure f
radius
layer at
underd
combin
a mode
radius i
is cons
FIG. 3 ha
over 300 m l.
indicating ria
Prominen
(Lower le
western en
to indicate
Phobos (M. Four examples of morphologic features found on Eros that suggest the asteroid
(Cheng et al. 2001) of relief and it stretches for ?15 km in length (Veverka et a
that is formed in competent material (well above the angle of repose of loose mateWILKISON ET AL.
, within the object. However, NEAR Shoemaker gravity
dicate that Eros has a nearly uniform density (Yeomans
000, Zuber et al. 2000).
tracking of the NEAR Shoemaker spacecraft has been
e to well under 100 m (Yeomans et al. 2000), and this
wed accurate comparisons of the center of mass with the
of figure. The center of mass offset from the center of
or Eros is ?52 m, or about 0.6% of the object?s mean
(Thomas et al. 2001). This offset can be simulated by a
high latitudes of approximately 250 m of material 30%
ense relative to the rest of the asteroid, or by many other
ations of thickness and relative density. This example of
stly different density layer only a few percent of the mean
llustrates the generally homogeneous nature of Eros and
istent with a layer of regolith on the surface.
Morphology
Structural continuity of an asteroid is suggested by the pres-
ence of grooves and ridges (Veverka et al. 1974, Thomas et al.
1979, 1992, 1994). Grooves are considered to be expressions of
structural features?especially when such features are in pre-
ferred directions and orientations (Veverka et al. 1994). Based
on observations of Phobos, two theories have been proposed as
explanations for pitted grooves: either they indicate the collapse
of loose material into fractures or they indicate the expulsion
of material from fractures (Thomas et al. 1979, Horstmann and
Melosh 1989). Gaspra has grooves that fall into two groups of
orientations; the pattern of grooves and ridges observed indicates
a global fabric that implies that Gaspra is a single, coherent ob-
ject (Thomas et al. 1994). Sullivan et al. (1996) suggest that thet set of ridges ?twist? (Veverka et al. 2000) consistent with an extensional stress en
ft) Square craters are known to form as a result of impact into a solid rock with a pree
d (?320? W) of Eros (MET 132151511, 132151569). (Lower right) Much of Eros
a competent lithology beneath the regolith (Veverka et al. 2000). In this mosaic tw
ET 135343994?135345734).s a global internal strength. (Upper left) Rahe Dorsum is a ridge with
2000). The steepest face of the ridge has a slope of greater than 60?,
l, Cheng et al. 2001) (MET 131968549?131969115B). (Upper right)
vironment in a competent material (MET 129525607?129525697).
xisting fracture pattern (Shoemaker 1963) such as those found on the
is patterned in a complex series of grooves and ?fabric? interpreted
o longitudinal grooves exhibit aligned pits similar to those found on
Igrooves
of less
Struc
Eros (V
clude s
alignm
2000).
exhibit
lineame
2001).
A pr
norther
through
This rid
it was c
2000).
(Cheng
of an E
sistent
or cohe
side of
ond set
fabric i
twist. T
15-km
nar feat
feature
to impa
they m
suggest
the sho
differen
younge
2000).
continu
Obse
gions o
ges, an
mechan
object (
indicate
cant int
All a
that it i
tal poro
Eros?s
for the
20%. T
Earth a
of impa
tured m
n
e
h
n
e
s
a
t
0
la
a
in
d
.
,
.
.
c
, E
d
, E
M
8
,
ti
0
-
m
in
8
I
p
d
o
E
b
.,
v
A
s.
d
.
o
u
,
.
ut
eEROS?S POROSITY AND IMPLICATIONS FOR
of Ida are internal fractures expressed in a surface layer
coherent materials.
tural features such as lineations have been observed on
everka et al. 2000, Prockter et al. 2000, 2001 and in-
inuous and linear depressions, topographic ridges, and
ent of sections of the terminator (Fig. 3) (Veverka et al.
Evidence of preexisting fabric in smaller craters, which
elongation in the direction of intersecting or adjacent
nts, has also been observed (Prockter et al. 2000,
ominent ridge system (Fig. 3; Rahe Dorsum) spans the
n hemisphere and geometrically defines a planar slice
the asteroid (Veverka et al. 2000, Prockter et al. 2001).
ge crosscuts structures such as Himeros, indicating that
reated after Eros retained its current shape (Veverka et al.
Rahe Dorsum has slopes well above the angle of repose
et al. 2001) and is continuous across more than a third
ros circumference, and it exhibits a morphology con-
with a compressive fault plane through a consolidated
rent material. A set of parallel ridges on the opposite
Eros, informally called the ?twist,? constitutes a sec-
of prominent ridges. A global extent of the asteroid?s
s suggested by the alignment of Rahe Dorsum and the
hese two features lie in one plane (within 400 m over a
length), and Rahe Dorsum by itself defines the same pla-
ure. Because of their different morphology, these surface
s probably represent different responses of a global fabric
ct erosion (the twist?) or stresses (Rahe Dorsum?), and
ay have formed at different times. Veverka et al. (2000)
ed that the large variation in directions and patterns of
rter lineations indicate that they were formed in many
t events. Grooves crosscut the oldest craters on Eros, but
r craters crosscut some of the grooves (Veverka et al.
These features all indicate that Eros possesses structural
ity and internal strength.
rvations of morphological features on Eros such as re-
f high slopes, continuous grooves, steep continuous rid-
d fault planes suggest that the asteroid possesses global
ical strength and is not strictly a gravitationally bound
Thomas et al. 2001, Zuber et al. 2000). These structures
that Eros, unlike rubble pile models, possesses signifi-
ernal strength.
CONCLUSIONS
vailable bulk compositional estimates for Eros suggest
s an OC type body, thus allowing us to estimate its to-
sity (21?33%) from measures of meteoritic material and
bulk density. Using the median value of microporosity
meteorites, we estimate that Eros has a macroporosity of
The rem
Eros is
estimat
lower t
collisio
porositi
and rea
such as
ments h
apparen
et al. 2
an imp
structur
gree of
fracture
Acuna, M
B. Toth
results
Ahrens, T
quartz,
Asphaug
ical mo
Asphaug
1996.
120, 15
Asphaug
Disrup
437?44
Barnouin
G. Neu
acteriz
(Fall),
Bell, J. F.
J. Jose
McFad
Robins
of 433
angle o
Benoit, P
non-tri
Binns, R.
teorite
Bottke, W
asteroi
Bottke, W
sized b
Carrier, W
lunar s
French
Catullo, V
distrib
Chandrashis value is consistent with impact breccias found on the
nd Moon, indicating that Eros has suffered a high degree
ct-induced fracturing (eliminating the coherent yet frac-
odel). Is Eros a heavily fractured or rubble pile asteroid?
New Ha
Chao, E. C
unshock
Lunar SNTERNAL STRUCTURE 101
aining circumstantial evidence leads us to believe that
ot a rubble pile (as defined here). First, the range of
s for Eros?s macroporosity, while not conclusive, are
an rubble pile models would suggest. Modeling of the
al breakup and gravitational assembly process predicts
s of ?40% for asteroids that have undergone breakup
sembly (Wilson et al. 1999), and rubble pile analogs
the lunar regolith and unconsolidated terrestrial sedi-
ve porosities greater than 40% (Table I). Second, the
homogeneity in mass distribution within Eros (Thomas
01, Yeomans et al. 2000, Zuber et al. 2000) suggests
usible continuity of density for a rubble pile. Finally,
l features on its surface show that it has a significant de-
ternal strength. Thus we conclude that Eros is a heavily
asteroid.
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