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Growth and Evolution
of Asteroids
Erik Asphaug
Department of Earth and Planetary Sciences, University of California Santa Cruz, Santa Cruz,
California 95064; email: [email protected]
Annu. Rev. Earth Planet. Sci. 2009. 37:413–48
Key Words
First published online as a Review in Advance on
January 22, 2009
planet formation, planetesimals, small bodies, accretion, NEOs
The Annual Review of Earth and Planetary Sciences is
online at earth.annualreviews.org
This article’s doi:
10.1146/annurev.earth.36.031207.124214
c 2009 by Annual Reviews.
Copyright !
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0084-6597/09/0530-0413$20.00
Abstract
Asteroids are what is left of the precursors to the terrestrial planets. They
are stunning in their diversity, ranging from charcoal-black worlds the size
of a hilltop, spinning like a carnival ride, to dog-bone-shaped metallic remnants of some cataclysmically disrupted planetary core, to worlds as stately
as Ceres and Vesta (and fragments thereof ), to garden-variety fractured and
blocky nuggets that dominate near-Earth space. Asteroid belts are common
around Sun-like stars. When properly seen as unaccreted residues, as scraps
on the floor of the planetary bakery, the diversity of asteroids can be fully
appreciated, for to paraphrase Tolstoy, accreted planets are all alike; every
unaccreted planet is unaccreted in its own way.
413
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1. ASTEROID BASICS
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Asteroids are small rocky planetary bodies. Like many definitions in planetary science, this one
has outliers and exceptions. It is also vague: small is not well defined, and rocky takes on a variety of geochemical and rheological meanings. But these concepts serve as an outline for the
study of asteroids, because understanding small is to characterize the transition from one realm
of geophysics to another—asteroids straddling the two—while describing rocky is to address
some of the fundamental aspects of meteoritics, itself a venerable discipline in search of geologic
context.
Sometimes asteroids are equated with planetesimals, which are the building blocks of terrestrial
planets. But this definition applies only insofar as asteroids are primordial. Nearly every asteroid
we see today, whether of primitive or evolved composition, is the product of a complex history
involving accretion followed by one or more episodes of catastrophic disruption. Energetic collisions among asteroids, in the aftermath of planet formation, have resulted in dynamical families of
smaller asteroids, most of them now mixed into the background population, but all with distinct
and indicative petrogenic relationships. Dozens, perhaps hundreds, of early asteroids grew large
enough to thermally differentiate, leaving scattered pieces of their metal-rich cores and, more
rarely, their mantles and crusts.
Asteroids represent stages on the rocky road to planet formation. Most of the matter that
survives from the original protoplanetary disk is bound into planets. But the unaccreted small
bodies of the terrestrial planet forming region—the asteroids—are fated to wander the solar
system at the whims of the larger dynamical bodies. They have stories to tell.
1.1. Primitive Bodies
The study of asteroids has emerged as one of the most active research areas in planetary science. One reason for this is the novel context of near-Earth space, where many asteroids reside,
transported from much larger populations elsewhere in the solar system. Another is the utility of
asteroids as tracers of the past history of planetary evolution: Having borne witness to the solar
system’s origin, they are like fossils to a paleontologist.
Every day, hundreds of tons of asteroidal fragments rain down on Earth, mostly in the form
of micrometeorites and sand- to pea-sized grains (shooting stars), few of which reach the ground.
Those that do mostly go undiscovered except when they land on rock-free deserts or ice sheets,
or are witnessed falling. Space missions are under way, and others planned, to bring back samples
from asteroids in order to make a rigorous connection between solar system origins, planetesimals,
planets, and the hundreds of tons of meteorites that are found on Earth.
The largest meteorites are too massive to transport. The 60-ton Hoba meteorite is a ∼1 × 3 ×
3 m tabloid of iron (a IVB nickel-rich ataxite) that sits where it landed 80,000 years ago in Namibia.
It is larger than the smallest asteroids observed in modern observational campaigns. This has
rendered the distinction between asteroids and meteoroids arbitrary; 50 m is often applied as the
cutoff.
By number, the population of asteroids is dominated at the smallest sizes, approximated by a
power law
Meteoroid: a
geologic mass in space
that is smaller than an
asteroid (D < 50 m)
414
n(D) = C D−α ,
(1)
where n(D) dD is the number of bodies in the size range D to D + dD, and C and α are positive
constants, with α typically around 3 (see below). This means that small asteroids are far more
numerous than large ones, whereas large asteroids possess most of the mass. A major struggle in
the science of asteroids is therefore to define what is typical: the innumerable rocks in space larger
Asphaug
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1 km
Itokawa
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Vesta
Eros
100 km
Mathilde
Figure 1
Typical asteroids? Itokawa, Eros, Mathilde, and Vesta span a factor of 1000 in size. The Vesta image is a
computer model based on HST data (B. Zellner, P. Thomas, and NASA/HST). Mathilde and Eros images
are from the NEAR mission (NASA/JPL/JHUAPL). Itokawa image is from the Hayabusa mission
(ISAS/JAXA). Ceres, Vesta, and a couple of other planetoids contain half the mass of asteroids, while small
bodies like Itokawa are the most typical and dominate near-Earth space.
than 50 m, or the handful of main-belt planets like Vesta and Ceres, which contain most of the
mass (see Figure 1).
Large asteroids are weighed from their perturbations on Mars and on each other (Williams
1984, Michalak 2000). Krasinsky et al. (2002) derived the total mass of the asteroid belt by analyzing
the motions of the major planets, processing high-precision ranging information relative to the
Viking and Pathfinder landers over a 21-year period. They modeled the 300 largest asteroids and
the major planets directly, and the residual gives the remaining mass of the belt. According to
their studies, the total main-belt mass is ∼1.8 × 10−9 M$ , where M$ is the mass of the sun; thus
∼3.6 × 1021 kg is the total mass of asteroids according to this study. That is four times the mass
of Ceres, ∼0.6% the mass of Mars, and ∼5% the mass of the Moon.
Asteroids are incredibly diverse. If gravity is the discriminant, then Itokawa is expected to be
as different from Eros, geologically, as Eros is from the Moon (see Table 1). Asteroid gravity
varies by more orders of magnitude than its variation among the terrestrial planets, including the
Moon. Composition also varies, from ice-rich to lunar-like to chondritic. Why do we lump Eros
and Itokawa into the same bin? Mathilde and Vesta? What do asteroids have in common? This is
a time to go exploring.
Each rendezvous with an asteroid has turned our geological understanding on its head, with
relevance close to home in areas of granular mechanics, landslides, earthquakes, faulting, and
impact cratering. Asteroids serve as important scale analogues, with the physics appearing familiar,
but with g varying from <10−5 g⊕ for the smallest asteroids to ∼1/30 g⊕ for Ceres and Vesta,
where g⊕ is the surface gravity of Earth.
One remarkable discovery of the past several years is that asteroids are commonly found in
double- and even triple-systems. This places them in the center of debates regarding the origin
www.annualreviews.org • Growth and Evolution of Asteroids
Chondritic: refers to
an asteroid or
meteorite composition
that is undifferentiated
from the condensible
solid component of the
original
protoplanetary nebula
(also known as solar
composition)
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Table 1
Gravity of some typical asteroids, compared with Vesta and the Moon
Asteroid or planetoid
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Itokawa
MBA: a main-belt
asteroid, from the
unaccreted planetary
debris disk between
Mars and Jupiter,
where most presentday asteroids are
found. The main belt
has a total mass
equivalent to ∼5% of
the mass of the Moon,
and half of this is
contained in the four
largest asteroids,
Ceres, Vesta, Pallas,
and Hygiea
NEA: a near-Earth
asteroid, which has
perihelion distance
q ≤ 1.3 AU and
aphelion distance Q ≥
0.983 AU. The NEA
population is
subdivided into
Apollos and Atens,
which are currently
Earth-crossing, and
Amors, which may
have been, or will be,
Earth-crossing on a
timescale shorter than
their collisional
lifetime
416
Diameter (km)
Gravity (cm/s2 )
0.33
∼0.01
Eros
20
Vesta
530
Moon
3474
∼0.4
∼22
162
of planets such as the Earth and Moon, or Pluto and Charon, although the processes of asteroid
binary formation are likely to be different. Because a binary asteroid is not quite accreted, studies
of binary and multiple-system mechanics are of great relevance to understanding the earliest stages
of planet formation. Observations of binary asteroids, and of fast-spinning single asteroids, have
taught us that many teeter at the brink of mechanical stability.
Taken in a broader context, asteroids are important players in the cosmic universe. There are
planets everywhere, and massive asteroid belts have been detected in the terrestrial planet-forming
regions around a significant fraction of young Sun-like stars. Meyer et al. (2008) use the Spitzer
Space Telescope to detect 24 µm mid-infrared emissions indicative of debris disks and identify
disks around 18% of stars ∼3 to 30 Ma in age, 12% of stars ∼30 to 300 Ma in age, and 2% of stars
∼0.3 to 3 Ga in age. At least approximately one-third and as many as two-thirds of Sun-like stars
in the survey exhibit this evidence for terrestrial planet formation.
The fact that disks become less common with stellar age, on a timescale of ∼100–300 Ma,
implies a timescale for disk clearing that is compatible with what is known from theoretical studies
of terrestrial accretion, presented in Section 3.2. As far as we understand that epoch in our own solar
system, what happened here appears to be happening there. If it were not for asteroids bumping
into one another, with accretion winning out over disruption, there would not be terrestrial planets,
nor perhaps life as we know it.
Nearly all of our original protoplanetary disk has cleared away; asteroids are residuals in pockets
of dynamical stability. Figure 2 plots all major and minor planet locations as they appeared at
the time of writing. The main-belt asteroids (MBAs) are the dominant population, forming a
broad torus where a planet might have formed had Jupiter not been where it was. A couple of
other important classes can be distinguished, including the near-Earth asteroids (NEAs) around
1–1.5 AU and the Trojan asteroids leading and trailing Jupiter that are categorized as asteroids
but may be cometary in composition.
Comets are not specifically a subject of this review (see Weissman et al. 2004, Luu & Jewitt
2002), although there are more similarities than differences (Figure 3). A dynamical distinction
between asteroids and comets is available in the context of the restricted 3-body problem, with
the Sun and Jupiter as the primary masses. For a small body (test particle) encountering a planet
in circular orbit about the Sun, the Tisserand parameter
!
TP = a P /a + 2 (1 − e 2 )a/a P cos i
(2)
is a dynamical quantity that is approximately conserved before and after the encounter, where aP
is the semimajor axis of the planet and (a, e, i) are the semimajor axis, eccentricity, and inclination
of the asteroid or comet. TP also gives the relative velocity between a small body and a planet
√
during close encounters, vrel = v P 3 − TP , where vP is the planet’s orbital velocity about the
Sun.
Objects with TP > 3 are not planet-crossing. Comets are therefore often defined dynamically as
having TJ < 3 (J = Jupiter), with Jupiter-family comets ( JFCs) having 2 < TJ < 3 and long-period
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Figure 2
Earth
Mercury
Mars
Venus
Trojans
(leading)
Trojans
(trailing)
Jupiter
Inner solar system
diagrams showing the
positions of all
numbered asteroids
and comets on
October 1, 2008. The
orbits and positions of
Mercury, Venus,
Earth, Mars, and
Jupiter are shown; the
Trojan, main-belt,
Hilde, and near-Earth
asteroid populations
are evident. Asteroids
are yellow dots and
comets are
sunward-pointing
wedges. The top
diagram is plotted
from above the ecliptic
plane (the plane
containing the Earth’s
orbit), whereas the
bottom diagram is
plotted from the edge
of the ecliptic plane. In
both diagrams, the
vernal equinox is to
the right, along the
horizontal axis. Figure
courtesy of Paul
Chodas (NASA/JPL).
Trojans
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Periodic cometary nuclei
Wild 2 (D = 5 km)
Tempel 1 (D = 6 km)
Primitive asteroid
253 Mathilde (D = 53 km)
Figure 3
Two periodic cometary nuclei and the only primitive asteroid imaged to date. Figure of comet 81P/Wild 2 (left) from the Stardust
mission; figure of comet 9P/Tempel 1 (center) from the Deep Impact mission; figure of asteroid 253 Mathilde (right) from the NEAR
mission (NASA images). All are dark, low-density bodies. Mathilde is much larger than the comets (D = 53 km); no cometary nucleus
larger than ∼10 km and no primitive asteroid smaller than Mathilde has been clearly imaged; a mission to a ∼1–10 km primitive
asteroid is a scientific priority. The largest comets have appeared irregular (1P/Halley, 19P/Borrelly), whereas the smaller comets have
appeared relatively spheroidal—opposite to the trend observed so far for asteroids.
NEOs: near-Earth
objects, including
comets, asteroids, and
all other small objects
that have perihelion
q ≤ 1.3 AU and may
collide with Earth
418
and Halley-type comets having TJ < 2. The distinction is illustrative and useful, since it preserves
populations that get scattered by Jupiter.
Comets are also defined compositionally as being ice-rich as opposed to rocky and specifically,
as capable of developing a coma if it comes close to the Sun. But the dynamical and compositional
definitions do not always coincide. Recent observations have revealed water ice in the spectra
of a number of the asteroids of the outer main belt; Hsieh & Jewitt (2006) have adopted the
term main-belt comets (MBCs) for such objects, some which exhibit comae. Bottke et al. (2002b)
calculate on the basis of dynamical integrations that 6 ± 4% of NEOs (near-Earth objects) are
extinct Jupiter-family cometary nuclei.
How ice-rich must an asteroid be to be a comet? A geological distinction between comets
and asteroids might be available on the basis of the response to impact cratering, analogous to
glaciology, where a rock pile with an ice fraction of only a few percent can be called a glacier on
the basis of rheology. A characterization of large impact structures might thus distinguish comets
from asteroids when their spectra and potential for activity don’t give them away.
Comets are orders of magnitude more abundant in the solar system than asteroids. The total
mass of the main belt is only ∼5% the mass of the Moon, according to calculations of gravitational
influence by Krasinsky et al. (2002), or ∼4 times the mass of Ceres. The total mass of comets in
the Edgeworth-Kuiper belt (the cometary equivalent of the main belt, between 30 and 50 AU)
is hundreds of times greater, estimated at ∼5–20 lunar masses ( Jewitt et al. 1998), most of it in
a collection of Pluto-sized bodies. The “scattered disk” of comets contains an additional ∼4–40
lunar masses (Luu et al. 1997, Trujillo et al. 2000). To this we add the Oort cloud, which has been
estimated at ∼1 Earth mass (e.g., Stern & Weissman 2001) or even more.
Despite representing orders of magnitude more material, comets occupy a proportionately
larger volume of space. They are sparsely distributed and orbit the Sun much less frequently than
asteroids. The timescale of collisional evolution of asteroids is thus orders of magnitude faster.
While as many as ∼100 or more short-period JFCs like 3552 Don Quixote and 1997 SE5 have
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ended up in near-Earth space, they are anomalous; the NEO population is dominated by the rocky
objects that are more readily delivered from the main belt.
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1.2. Asteroid Populations
The largest repository of asteroids is the main belt between the orbits of Mars and Jupiter. MBAs
are bounded by two mean-motion resonances with Jupiter, the 5:1 at 1.78 AU and the 2:1 at
3.28 AU (see Figure 6). The NEAs leak inwards from the main belt on a timescale of tens of
millions of years (Morbidelli et al. 2002) and comprise an ongoing dynamical sampling of MBAs.
There is a systematic size bias between NEAs and MBAs. Smaller asteroids are more easily
dislodged from the main belt, owing to the strongly size-dependent, and surprisingly important,
Yarkovsky nongravitational force described below. This radiation force can cause a sub-kilometer
asteroid to migrate an astronomical unit or more, but it is generally negligible for asteroids larger
than ∼10 km. Yarkovsky migration causes the leakage of asteroids into nearby mean-motion
resonances and secular resonances, at which point their orbits are gravitationally destabilized by
the action of major planets (Vokrouhlický & Farinella 2000).
1.2.1. Size distribution. There are one or two million MBAs, and a thousand NEAs, larger than
1 km. Their size distribution n(D) is well approximated by a power law or segmented power law,
derived from the cumulative number N of asteroids larger than D. The derivative n = dd N
= C D−α ,
D
where α ≥ 0. This is equivalent to a power law mass distribution: m ∝ D3 and d m ∝ D2 d D, so
d N = Bm−(α+2)/3 d m. Because cumulative, differential, and mass and size distributions are all
sometimes reported, it is important to be familiar with their conversion.
For the main belt, a Subaru telescope survey by Yoshida & Nakamura (2007) obtains α *
2.3 for asteroids D < 1 km, transitioning to α * 2.7 for larger sizes. Sloan Digital Sky Survey
commissioning data indicate a slope α * 2.3 for 0.4 km < D < 5 km, transitioning to a steep
α ∼ 4 for D > 5 km (Ivezic et al. 2001). The break in slope at D ∼ 5 km can be regarded as a
broad “bump” as it shallows out again for D > 20 km. Differences between surveys may be due to
alternate approaches in mapping magnitudes to MBA diameters.
For small NEAs, the size distribution is steep. Brown et al. (2002) report α = 3.7 in the range
0.1 m < D < 200 m, based on satellite detection of large fireballs extrapolated to telescope results;
this is not far from the case α = 4 of equal mass in equal logarithmic bins described below. This
steep NEA size distribution is likely the result of the physics that delivers them to near-Earth
space—impacts that create numerous small asteroids at the expense of large ones and dislodge the
small ones the fastest, and the nongravitational Yarkovsky force that preferentially mobilizes small
members of the population.
Assuming that the 1908 Tunguska explosion was an event with energy ∼10 Mt, the mean
recurrence interval of such events on Earth is estimated by Brown et al. as ∼1000 years, although
the frequency of large fireballs is a topic of great controversy.
Mean-motion
resonance: when two
bodies orbiting a
massive central body
exert a periodic
gravitational influence
on one another due to
their mean motions
(orbital frequencies)
being the ratio of two
small integers
Secular resonance:
a periodic gravitational
influence that occurs
when the rates of
precession of the
orbits of two bodies
about a massive central
body are synchronous
1.2.2. Comminution and disruption. The power-law characteristics of rock comminution
(Gaudin 1939) is applicable to asteroids. One can write
log p = k log D + log A,
(3)
where p is the percentage of the total mass contained in asteroids with diameters between D1
and D2 , and k and A are constants (Hawkins 1960). D is the geometric mean diameter between
logarithmic size limits, and p is the mass found in incrementally finer sieves. The mass in an interval
dN is md N = Bm(1−α)/3 d m, and the mass between D1 and D2 is found by integrating; assuming
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a uniformly logarithmic interval Di+1 = β Di one obtains p = AD4−α , so k = 4−α. Thus, when
α = 4, there is equal mass in every logarithmic size interval; in the case of steady-state comminution
α < 4, there is more mass at larger size intervals.
Experiments reported by Gaudin (1939) of quartz rocks ground in a rock mill have α ≈ 3
early on and end with α = 3.5 after 10 h. In a landmark paper applying disruption physics
to asteroids, Dohnanyi (1969) examined collisional cascades in which the products of asteroid
disruption become impactors responsible for further asteroid disruption. Assuming that disruption
physics is invariant with size, any reasonable starting population was found to relax to α = 3.5.
But the comminution of asteroids involves more complicated physics than the grinding of rocks
in a mill. The exterior of an asteroid is pummeled while the interior is sheltered, for instance,
and the whole mass is cratered, comminuted, and vibrated episodically. Eventually an asteroid
suffers the fatal blow that sends its pieces asunder, forming asteroid families. The recipe is one
part geophysics, one part astrophysics.
The assumption of a self-similar collisional cascade is a poor (but useful) one because the
dominant physics changes at the size of typical asteroids. Asteroids D ! 1 km appear to be governed
by structural and mechanical forces, and larger asteroids by self-gravitation. These are the strength
and gravity regimes discussed further below, which have opposite trends in terms of effective impact
strength. Even within each regime it is not sure that self-similarity applies.
Mechanical strength varies considerably with size and strain rate. Static strength decreases with
size, because there are larger irregularities in a larger rock. Strain rate also decreases with the size
scale of a collision, further diminishing the dynamic strength (summarized in Asphaug et al. 2002).
But the largest asteroids have significant gravitational overburden, leading to increasing impact
strength. Because the trends are opposite, the impact strength (measured as Q ∗D , the impact kinetic
energy per unit mass required to disrupt a body; Davis et al. 1985) is a V-shape plotted versus size,
with minimum Q ∗D around D ≈ 100 m (Figure 4).
The largest asteroids are melted and stratified, further increasing their binding energy by
concentrating dense metals at the center. Differentiated asteroids are thus more difficult to disrupt,
by a factor of ∼3, than Figure 4 indicates, based on SPH collisional models described below.
Another distinction for large planetoids is that they gravitationally focus slow bodies onto collision
course, and are thus more heavily bombarded. This is expressed as a gravitationally enhanced cross
section that increases the geometric cross section π ( D2 )2 by a factor
"
#
v2
f g = 1 + es2 c .
(4)
v∞
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Gravitational focusing is significant where random velocities v∞ are smaller than the escape velocity
vesc . Although it enhanced the flux of low-velocity bombarding material for large planetoids early
on, focusing no longer plays a role in asteroid evolution.
Even in idealized self-similar collisional systems, there are boundary effects associated with the
cutoff at the large end (Ceres) and at the small end (dust swept away by the solar wind). Bumps
and wiggles in the asteroid size distribution have been attributed to the removal of dust, which
would otherwise collisionally disrupt the sand-sized particles. An excess of sand causes gravels to
disrupt, and so on. The result is a superposition of waves in an otherwise straight power law (Davis
et al. 2002). Similarly, the steep V-shape of Figure 4 may strip out the D = 100 m objects that
are the most easily disrupted; their efficient removal would enhance the representation of D ∼
3–4-km asteroids (their targets) relative to a straight power law, consistent with the observed size
distribution (see Figure 5).
The red curve in Figure 4 derives from simulations beginning with solid unfractured spheres
(Benz & Asphaug 1999), probably not a realistic starting condition. The other curves come from
420
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109
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Q*D (erg/g)
108
107
106
105
104
102
103
104
105
Target radius (cm)
106
107
Figure 4
The catastrophic disruption threshold of asteroids is characterized by Q ∗D , the impact kinetic energy per
gram of target required to leave behind no remnant (reaccreted or otherwise) larger than half the original
mass. Strength diminishes with size owing to size- and rate-dependent strength effects (Asphaug et al. 2002),
while beyond D ∼ 100 m self-gravitational binding catches up, making it increasingly difficult to disrupt
massive targets. Figure adapted from Benz & Asphaug (1999), whose numerical result is the dark red curve;
other curves (see references therein) are from a variety of published scaling theories and are indicative of the
uncertainty in catastrophic disruption theory.
similarly optimistic assumptions or extrapolations. In reality, asteroids are complex entities whose
impact strength properties may have little to do with the physical behavior of laboratory rocks
(the strength-scaling assumption) or fluidized spheres (the gravity-scaling assumption). There is
much work to be done on the experimental and modeling front (see most recently Leinhardt &
Stewart 2008) and in conducting geophysical investigations at asteroids.
1.3. Shaping the Main Belt
Jupiter’s dynamical forcing sculpts the asteroid population, as evident in Figure 2 and Figure 6.
The main belt is bounded by the 5:1 and 2:1 mean-motion resonances at 1.8 and 3.3 AU, respectively, where n:m is the ratio of mean motions, the number of times n that the asteroid orbits
the Sun for every m times Jupiter does. In between are several clearings and gaps that occur at
low-order resonances, most prominently the 3:1 at 2.5 AU (see also Figure 8).
These are the Kirkwood gaps that form when small asteroids migrate into the resonances,
which serve as dynamical sinks. Once a small asteroid becomes planet-crossing, its dynamical
lifetime is less than a few tens of Ma (Gladman et al. 1997) until it collides with a planet or the
Sun, or is ejected. This dynamical leakage is the main pathway from the main belt to near-Earth
space, and the force that nudges small asteroids into these resonances is sunlight.
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106
Incremental number
105
104
103
102
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101
100
1
10
100
1000
Diameter (km)
Figure 5
Estimated main-belt asteroid size distribution ( Jedicke et al. 2002; figure courtesy W. F. Bottke). The size
distributions of minor body populations are sometimes described as straight power laws with bumps and
wiggles, or as segmented power laws representing different physical regimes, e.g., different sources and
collisional physics.
1.3.1. Yark and YORP. The Yarkovsky effect is a cumulative dynamical force that results from
the anisotropic reradiation of thermal photons. On a rotating asteroid, the hotter afternoon
hemisphere emits photons with relatively high momentum, p = E/c, where E = hν is photon
energy and c is the speed of light. Photon emission thus produces a Sun-powered thrust that can
move small asteroids by several AU over their history, pushing them into gravitational resonances
350
Mean motion resonance:
(asteroid : Jupiter)
3:1
5:2
7:3
2:1
Asteroids (per 0.0005 AU bin)
300
250
200
150
100
50
0
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
Semi-major axis (AU)
Figure 6
The 156929 asteroids known as of 2007 plotted as a histogram of distance from the Sun. Figure courtesy
Alan Chamberlin and the Solar Systems Dynamics group at JPL (http://ssd.jpl.nasa.gov). The Kirkwood
gaps are found at the low-order mean motion resonances with Jupiter.
422
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or into collisions with planets. There is also a seasonal Yarkovsky effect, associated with the hotter
summer hemisphere.
The Yarkovsky force is computed from an asteroid’s length of day, albedo, thermal inertia,
distance from Sun, shape, and photometric phase function. Thermal inertia is usually the largest
uncertainty:
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%=
√
ρc κ,
(5)
where ρc is the volumetric heat capacity and κ is thermal conductivity. The greater the heat
capacity, or the greater the conductivity, the more thermal energy a parcel can soak up either
by absorbing it or conducting it away; therefore the maximum day/night temperature variation
on a planetary surface is greatest for materials with low thermal inertia. For lunar regolith in
vacuum % ∼ 50 J s−1/2 K−1 m−2 ; for bare rock % ∼ 2500 J s−1/2 K−1 m−2 . The day/night
temperature difference that drives the Yarkovsky effect is also related to asteroid size and rotation; very fast rotators and very small asteroids are almost isothermal. The average thermal
inertia measured for NEOs is % ∼ 300 J s−1/2 K−1 m−2 (Delbo’ et al. 2007), with a trend of
higher thermal inertia for smaller asteroids (e.g., 150 s−1/2 K−1 m−2 for Eros, 700 s−1/2 K−1
m−2 for Itokawa). Images of Itokawa appear rocky or gravelly, whereas Eros appears dusty, in
agreement with this trend. But no asteroid measured so far has rock-like thermal inertia (% >∼
1000s−1/2 K−1 m−2 ). In situ thermal investigations of small asteroids are required to resolve this
quandary.
Closely related to thermal inertia is surface roughness, which can be measured directly through
laser ranging from orbit, and can be obtained from Earth as the ratio of same-sense to oppositesense circularized polarization of reflected radar energy. Roughness at the radar wavelength (typically tens of cm) increases the same-sense circular polarization. This SC/OC ratio (Benner 2008)
together with thermal inertia provide fundamental information about the surface geology of asteroids, and can be of great aid in mission planning. Interestingly, Eros and Itokawa have about
the same decameter-scale radar roughness, although visibly, Itokawa is lacking in dust, and has a
roughness derived from laser ranging that is, on average, equivalent to the roughest parts of Eros
(Abe et al. 2006).
The Yarkovsky effect (Yark) has been directly measured on small asteroids using radar astrometry (Chesley et al. 2003). The force scales with surface area D2 so the acceleration scales with
D−1 , all else being equal. Since bodies with lower thermal inertia have higher diurnal temperature
variation, Yark may drop off somewhat more gradually with size, more like D−0.6 , if the trend
observed by Delbo’ et al. (2007) applies. Yark is thus only significant for asteroids smaller than
tens of km. Since this includes the vast majority of asteroids, it has led to significant evolution of
the architecture of the solar system and is responsible for the delivery of so many diverse asteroids
to near-Earth space and meteorites to Earth.
A companion effect is called YORP (Rubincam 2000), and it is a torque that spins asteroids into
fast rotation when the emission of thermal photons has chirality. Like the Yarkovsky effect, YORP
depends on the asteroid’s shape, albedo, rotation, heliocentric distance, and material thermal
parameters. Even an isothermal asteroid can experience this radiative torque. Change in spin by
YORP has been directly measured (Lowry et al. 2007, Taylor et al. 2007) and is spinning up some
small asteroids on ∼105 year timescales. According to Rubincam (2000), an asteroid as large as
10 km might double (or halve) its rotation rate every few hundred million years. Because YORP, like
Yark, scales with ∼1/D, the spin rate of a small asteroid like namesake 54509 YORP (D ∼ 100 m),
www.annualreviews.org • Growth and Evolution of Asteroids
Yarkovsky effect: a
thermal force in which
diurnal heating of a
rotating object in
space leads to emission
of higher momentum
photons on its hotter
(afternoon)
hemisphere, changing
the orbit of a
meteoroid or small
asteroid depending on
its shape, thermal
properties, and spin
Regolith: loose
granular material on
the surface of an airless
body, processed by
eons of impact
bombardment,
possibly extremely
porous under an
asteroid’s microgravity
conditions
YORP: the
Yarkovsky-O’KeefeRadzievskii-Paddack
effect in which
asymmetric thermal
radiation applies a
torque to a meteoroid
or asteroid, sometimes
over a timescale that is
short compared with
dynamical or
collisional evolution
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Patroclus and Menoetius
2001 SN263
Figure 7
Asteroid 617 Patroclus (left) is the first known binary Trojan asteroid; the image was captured in 2005 by
Franck Marchis using adaptive optics at the 10-m Keck telescope. Patroclus is D * 120 km, and its
companion Menoetius (father of Patroclus) is D * 110 km. Their mutual orbit has Porb = 4.3 days at a
separation of 640 km (F. Marchis/UC Berkeley). Asteroid 2001 SN263 (right) is the first known NEO
triple-system. It was imaged at the Arecibo radio observatory by Michael Nolan in Feb. 2008, as seen in this
delay-Doppler image. Initial data reduction reveals the primary asteroid to be ∼2 km in diameter, the larger
moon ∼1 km, and the smallest about 0.3 km (M.C. Nolan, Arecibo Observatory).
which is already spinning with a period of only 12 min, is expected to double in a few 100,000
years, perhaps flinging it apart.
The spin-up of asteroids can have dramatic consequences (Scheeres 2007) and is likely to be
a mechanism for global reshaping and resurfacing and satellite formation (Walsh et al. 2008) and
binary evolution (Ćuk 2007), as discussed further below. A detailed review of Yark and YORP is
found in Bottke et al. (2006b).
Family: asteroids
occupying a compact
region of dynamical
space, indicating a
common origin from
an impact disruption
event
1.3.2. Groups and gaps. Inner solar system resonances with Jupiter and Saturn create not only
gaps but also groups within sheltered regions of dynamical space, as seen in Figure 8. One group
is the Hilda asteroids, which librate at the 3:2 mean motion resonance near 4.0 AU, forming a
subtle triangular distribution in space (see Figure 2). Another group is found at the 1:1 resonance
at 5.2 AU—leading and trailing Jupiter by 60◦ at its orbital distance from the Sun. These are the
Trojan asteroids1 , which occupy halo orbits (in the Jupiter-fixed frame) about either of the two
stable minima (the leading L4 and trailing L5 Lagrangian points) of the Jacobi energy integral in
the reduced 3-body problem. Are Hildas and Trojans asteroids? The one Trojan asteroid whose
density has been measured, 617 Patroclus (Marchis et al. 2006; Figure 7) is cometary, with ρ ∼
0.8 g/cm3 . For comparison, the density determined for the 1–2-km diameter Jupiter family comet
Shoemaker-Levy 9 was about 0.6 g/cm3 (Asphaug & Benz 1994, 1996), and the Deep Impact
mission target 9P/Tempel 1 appears similar (Richardson et al. 2007).
1.3.3. Families. Asteroid families are clusters in dynamical space (Figure 8) that are indicative
of a common origin during impact disruption (Hirayama 1918). They are distinct from groups in
1
The leading ones at the L4 are sometimes called the Greeks, and are named after Greek heroes in the Trojan war, although
Achilles’s dear friend Patroclus somehow made it into the L5 Trojan camp.
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b
Proper i versus a
Proper i versus e
18
18
16
16
14
14
12
12
10
i
8
10
8
6
6
4
4
2
2
0
2.0
2.2
2.4
2.6
2.8
3.0
a (AU)
3.2
3.4
3.6
0
0
0.04
0.08
0.12
0.18
e
0.20
0.24
0.28
Figure 8
Asteroid proper elements are orbital elements in which solar precession and planetary perturbation effects have been removed; unlike
standard (osculating) orbital elements, which vary over thousands of years, proper elements remain approximately constant over
millions of years, bringing youthful asteroid dynamical clusters into high focus. (a) A slice through the semimajor axis; the Kirkwood
gaps (see also Figure 6) show up in the main belt at the primary mean motion resonances with Jupiter. (b) The clusters of asteroids that
show up most vividly in proper e − i space are the asteroid families that result from catastrophic collisions; the most dense clusters are
generally the youngest. Asteroids in a given asteroid family are, however, out of phase and well-mixed in Cartesian space. Image from
Petr Scheirich.
being related to a source (parent asteroid) rather than a sink (chaotic boundary domain) or trap
(stable domain). Some of the larger asteroid families, notably Koronis, are boxed in by resonances.
Using hierarchical clustering methods (Zappala et al. 1995) applied to proper elements, hundreds
of asteroid families have been discovered, and about one-third of all asteroids have been determined
to be members of a known dynamical family. Because the lifetimes of most families are considerably
younger than the age of the solar system, most asteroids have at one time been part of families
long since dispersed.
1.3.4. Binaries. Almost 200 binary minor planets have been discovered, primarily through
lightcurve analysis, and almost one-sixth of NEAs are binary systems (see Figure 7). Binaries
may form by tidal passage near a planet, akin to what happened to comet Shoemaker-Levy 9
(Asphaug & Benz 1996, Bottke & Melosh 1996), or they may form by a catastrophic disruption
event (Durda et al. 2004). Capture by dynamical friction and 3-body encounters (Goldreich et al.
2002) is possible in the early outer solar system but unlikely for asteroids. A promising scenario
for binary formation among NEAs is fission in the aftermath of YORP-induced rotation (Walsh
et al. 2008), based on the fact (Pravec & Harris 2007) that most known binaries would be close to
the spin barrier discussed above if combined into a single body. Once a binary is formed, YORP
continues to torque both members of the system, and rotational-orbital coupling may drive the
binary to greater semimajor axis (e.g., Ćuk 2007).
Understanding binary formation and evolution is undoubtedly an important component to
understanding planetesimal accretion, family origins, and asteroid shape, surface, and structural
evolution. A dedicated mission to a binary minor planet would have very high scientific merit.
www.annualreviews.org • Growth and Evolution of Asteroids
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25 km
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Eros (NASA)
0.25 km
Itokawa (JAXA)
Figure 9
Asteroids Eros (NASA) and Itokawa (ISAS/JAXA). Itokawa (longest dimension 540 m) is about 70 times
smaller than Eros (longest dimension 34 km) but appears every bit as geologically complex; for relative scale
see Figure 1.
2. STRANGE NEW WORLDS
Eros is the largest of the Amor dynamical group of NEAs and is the first small body ever orbited
by a spacecraft (Veverka et al. 2000). 25143 Itokawa was visited by the Hayabusa mission in
late 2005 (Fujiwara et al. 2006), the second asteroid rendezvous (Figure 9). Orbiting was only
undertaken at Itokawa in discrete arcs, where one applies tiny thrusts to hold a desired position
or trajectory—in this case trailing a bit behind the terminator, where asteroid gravity balances the
solar wind that blows the spacecraft downstream. Navigating the smallest asteroids is a lot like
sailing.
2.1. Eros
Rubble pile: a
geologic mass whose
chief binding force is
gravitation, but whose
central pressure is far
lower than the
strength of rock.
Dynamically, an
asteroid or comet that
cannot hold onto its
own pieces if it is spun
up by gentle stresses
such as tides or YORP
426
The first look at Eros revealed an oddly shaped rock of monolithic structure (Veverka et al. 2000)
rotating every 5.26 h, cracked and faulted by impacts (Prockter et al. 2002), a “shatter pile.”
However, others looking at the same data (Asphaug et al. 2002) saw a modestly cohesive rubble
pile of talus and dirt, heaped by impacts into an odd shape, the faults being fissures in low-gravity
dirt—a true rubble pile.
The data for Eros consist of high-resolution images, compositional characterization (Trombka
et al. 2000), a shape model (Thomas et al. 2000, Zuber et al. 2000), a bulk density (2.7 g/cm2 ;
Yeomans et al. 2000), and a well-characterized dynamical state (Miller et al. 2002). A reasonable
compositional match is found in ordinary chondrites, common meteorites that have similar spectral
and albedo characteristics, but a higher bulk density ∼3.4–3.7 g/cm3 . If made of this material, Eros
has a porosity of ∼25%, the same as for talus piles and sand beds on Earth, but also consistent
with a highly faulted structure. Arguing for structure on the basis of density or composition is, for
Eros, inconclusive.
A shattered monolith structure for Eros is argued on the basis of irregular shape—only a body
with structural integrity can support a ridged topography—and the existence of faults that seem to
require bedrock geology. As to the first argument—which has been applied to comet Halley and
other irregular bodies—gravity is also irregular, owing to the peanut-like shape and fast rotation.
Eros is actually rather flat: local slopes at 100 m baseline (Zuber et al. 2000) are generally shallower
than ∼20◦ , relative to the local geopotential, except for inside crater rims that are at the angle of
repose (Figure 10). Eros has the shape one expects for a rubble pile.
Asphaug
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50
45
40
35
30
Slope
25 (degrees)
20
15
10
5
0
Figure 10
Slopes of asteroid 433 Eros taken at 100 m baseline, from the NEAR laser altimeter experiment (Zuber et al.
2000; figure reproduced from Asphaug et al. 2002). The shape model for Eros is shaded in degrees of slope
between the surface normal and the vector of gravitational acceleration in the rotating frame of reference.
The crater rims and a few other areas have local slopes of 30◦ –40◦ , whereas noncratered areas are relatively
“flat,” like a landscape in lunar regolith.
As to the argument that faults require bedrock, consider the physics of the ∼10 to 100-m-wide
scarps on Eros. They are supported in the walls of long, linear fractures, some extending for
kilometers, mostly running in parallel (Prockter et al. 2002). Similar structures are found on other
asteroids, including Ida, Gaspra, and Phobos. One idea (e.g., Fujiwara & Asada 1983, Asphaug
et al. 1996) is that these fractures are the result of impact stresses focusing in the finite body of
the asteroid and interacting with the free surface. Other ideas include thermal stresses (Dombard
& Freed 2002) and body stresses induced by changes in spin.
Faulting can occur in a granular matrix. Any visitor to a beach knows that sand can fracture
when it is cohesive relative to the applied stress, and therefore micro-cohesions support scarps in
microgravity. Cohesion measured for lunar regolith (∼104 −105 dyn cm−2 ; Mitchell et al. 1972)
exceeds the gravitational overburden in the upper ∼10–100 m on Eros, so that its regolith may
support a fractured exterior, even though the same material brought back to Earth would behave
as an incohesive pile. This hypothesis, that Eros is a fractured rubble pile, makes sense in light
of the thousands of fractures mapped on Eros (Buczkowski et al. 2008), whose formation in a
solid bedrock seems impossible to achieve without jumbling the structure of the asteroid, unless
the fracture stress is minuscule. If so, then impacts or other stresses create the fault patterns by
opening up cracks in the upper tens of meters of dirt, not in solid rock. Continuous deformation
throughout the interior (bending or torsion) would be expressed as continuous global-scale fault
structures, whereas impact reverberation might create en echelon fissures.
www.annualreviews.org • Growth and Evolution of Asteroids
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1m
2m
Eros
Itokawa
Figure 11
(left) Close-up image of asteroid 25143 Itokawa, as imaged by the Hayabusa spacecraft prior to its sample collection attempt in
November 2005. Hayabusa is now en route to Earth, perhaps ferrying a few grains of asteroid material following two touch-and-go
sampling attempts; arrival at Earth is expected in June 2010. The scale is given at lower right (Univ. Tokyo /JAXA). (right) The final
image of asteroid 433 Eros taken from a range of 120 meters (cropped) (NASA/JPL).
2.2. Itokawa
S-type: the most
common type of
asteroid in near-Earth
space; the parent
bodies of the stony
ordinary chondrite
meteorites; moderate
albedo with silicate
spectral absorptions
C-type: the most
common type of
asteroid in the main
belt, likely the parent
bodies of the primitive
carbonaceous
chondrite meteorites;
very low albedo and
reddish spectral slope
428
We speculate about the internal structure of Eros even after a one-year rendezvous. Smaller
asteroids appear even stranger by degrees. When the Japanese Hayabusa spacecraft (Fujiwara
et al. 2006) arrived at 25143 Itokawa in late 2005, the images it acquired (Figures 1 and 11) defied
all expectations.
Only 1/200,000 the mass of Eros, Itokawa was expected to be a monolith, or perhaps a couple
of massifs resting together with a sprinkling of coarse regolith. Surface gravity is smaller than even
the imperceptible jostling experienced by spacecraft in low-Earth orbit; any loose regolith was
expected to have floated free, ejected by impacts and other processes. Instead, what was discovered
was a coarse pile of rocks on a landscape almost devoid of recognizable craters, with global-scale
flat gravel expanses (“seas”). It appears to be a rubble pile (Fujiwara et al. 2006), but what is inside
remains conjecture.
2.3. Classes of Asteroids
Asteroids are divided into taxonomic groups and types on the basis of their spectroscopic and
photometric properties. (New classes and sub-classes of asteroids have been developed on the
basis of combined visible and infrared observations; see Bus and Binzel 2002. This review sticks to
the traditional Tholen taxonomy; see Burbine et al. 2002.) Near-Earth space and the inner main
belt are dominated by S-types like Eros and Itokawa.
But only ∼15–20% of all known asteroids are S-types. More common throughout the main
belt (approximately 75% of known asteroids) are the C-type asteroids that dominate the middle
and outer main belt. The only C-type asteroid imaged by spacecraft is Mathilde (Figure 3 and
Figure 12), observed during the 1997 NEAR flyby; the Martian satellites Phobos and Deimos are
also loosely in this group.
Asphaug
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253 Mathilde
216 Kleopatra
Figure 12
Two radically distinct major asteroids illustrate the diversity of the main belt: one a primitive and extremely
porous rocky body, and the other a spinning equilibrium figure of iron. (left) 453 Mathilde (D = 53 km) was
the first flyby target of the NEAR mission; it has a half-dozen gargantuan craters and a density of ∼1.3 g
cm−3 (see text). It is also one the most slowly rotating bodies in the solar system, Prot = 17.4 days
(NASA/APL). (right) 216 Kleopatra, shown in a shape model reconstructed from ground-based radar
observations at Arecibo (Ostro et al. 2000), is a metallic M-class object 220 km long, with a bulk density of
about 6 g/cm3 if one fits an equilibrium shape to its rapid 5.4 h rotation. The radar-determined surface
porosity is about 50%, comparable to the porosity of the upper meters of the lunar regolith (Ostro/JPL).
Generally speaking, as one goes from the inner solar system to the outer solar system, one goes
from S-type to C-type domains, possibly on account of the more rapid timescale of planetesimal
accumulation closer to the Sun (see Section 3).
The complete taxonomy of asteroids includes numerous sub-groupings. C-, P- and D-type
asteroids are as dark as charcoal (visual albedo p v ∼ 0.05) and reddish; they are presumably made
of the same materials as the most primitive meteorites, the carbonaceous chondrites, which include
complex organic molecules in addition to silicate minerals and reduced iron and other metals.
D-types are particularly red at long infrared wavelengths and may be rich in organic compounds.
S-type asteroids are several times brighter than C-type asteroids (visual albedo pv ∼ 0.15) and
have distinct silicate absorption bands; they are probably made of similar materials as those of the
most common meteorites, the ordinary chondrites, which are moderately evolved but unmelted
chondritic rocks.
The M taxonomic class was originally conceived as consisting of metallic fragments of differentiated planetary cores, either blasted apart in some cataclysmic event or otherwise missing
their mantle rock (see below). Metallic asteroids are expected to have rock-like rheology at cold
temperatures, but there is no past or planned spacecraft visit to a metallic M type (e.g., Kleopatra
in Figure 12), and we might not find out for decades.
One advancement based on mid-infrared spectroscopy (Rivkin et al. 2000) is that the M-type
asteroids larger than ∼65 km are likely to be of hydrated silicate mineralogy, not metallic. Thus
the largest metallic M-types, for instance 216 Kleopatra (∼220 × 90 km; Figure 12) and 16 Psyche
(D * 250 km), are anomalous and uncommon (though perhaps representing the bulk of the mass
of the M types). Asteroid 21 Lutetia, the large (D * 100 km) M-class flyby target of the Rosetta
mission to comet 67P/Cheryumov-Gerisamenko is probably of non-metallic composition.
Space weathering of asteroid surfaces (see Sasaki et al. 2001 and references therein) can cause
all asteroids to redden and darken, or otherwise change their spectroscopic characteristics. What is
www.annualreviews.org • Growth and Evolution of Asteroids
M-type: a class of
asteroid with moderate
albedo and a flat,
featureless spectrum at
visible wavelengths;
some of these are
metallic parents of the
iron meteorites; many
are now known to be
hydrated silicates of a
very different origin
Space weathering:
the process of surface
reddening and
darkening that occurs
as minerals and
metallic inclusions are
exposed to the high
energy bombardment
of space
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Absolute magnitude:
H is what an asteroid’s
apparent magnitude
would be at zero phase
angle at 1 AU from the
Sun and 1 AU from
Earth, extrapolated
from observations. A
proxy for diameter
Equilibrium figure:
the shape of a rotating
planetary body whose
pressure gradients
balance the
gravitational and
centrifugal forces (e.g.,
a liquid)
430
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learned from studying the upper few microns of surface layering needs to be taken alongside what
has been learned from spacecraft observation, from meteorites, and from future in situ asteroid
studies.
2.4. Photometric Characterization
By measuring an asteroid’s absolute magnitude H (its visual magnitude at 1 AU from the Sun and
1 AU from Earth, at zero phase), one can estimate asteroid diameter D according to
D * 1329 km × 10−H/5 p v−1/2 ,
(6)
where pv is the visual albedo. For the average NEA albedo p v * 0.14, asteroid diameters D * 6,
2, 1, and 1/3 km correspond to H * 14, 16, 18, and 20. But pv varies by a factor of ∼3 between
S- and C-types, making C-types ∼50% larger than S-types of the same magnitude.
Asteroid rotation rates and shapes are derived from brightness variations. Sometimes these light
curves are simply periodic, with each half-rotation going from bright (face-on) to dim (end-on).
Simple models of rotating ellipsoids can be fit to many asteroid light curves by specifying the spin
pole, the principal axes’ dimensions, the albedo, and the phase function. Nonellipsoidal asteroids
that are rapid rotators are sometimes fit by some other equilibrium figure, such as a Roche binary
(see, for example, Figure 12b).
Many asteroid light curves cannot be explained by a single rigid body, leading to the understanding (Weidenschilling et al. 1989) that asteroids have satellites. From the detailed study
of light curves, Pravec et al. (2006) estimated that ∼15% of near-Earth asteroids with D >
0.3 km are binary systems with the diameter ratio of the pair >0.18. The percentage of binaries is particularly high among NEAs smaller than 2 km and decreases at large sizes. This observation confirmed the earlier study by Margot et al. (2002) of NEA binaries based upon radar
observations.
The orbital period P is related to the combined mass M of a binary asteroid system by P 2 =
2 3
4π a /GM, where G is the gravitational constant. If the system is resolved so that the semimajor
axis a is known, then M is deduced from P (the light curve period). The individual masses of
the components, and then their densities, are further derived by estimates of relative brightness
(relating to relative size).
A fundamental asteroid data set is the rotation period Prot versus D, derived from light curves
and plotted in Figure 13 (Pravec et al. 2002). For asteroids D ! 200 m, rotation rate attains a
maximum, a “spin barrier” of Pro t * 2.2 h, which is—probably not coincidentally—the fastest
rotation period a sphere of density ∼2 g/cm3 can rotate without throwing material off its equator.
The spin barrier is further shown by Pravec et al. (2007) to move to longer periods for asteroids
with greater light curve amplitude (oblateness), as would be expected of a sphere spinning itself
out into an ellipsoid.
Before we conclude that asteroids D " 200 m are rubble piles, and those smaller are monolithic,
we must note that internal friction (Holsapple 2007) could hold fast-rotating asteroids together
even in the absence of cohesion. As for larger asteroids that cluster near the spin barrier, the
mechanism by which they would lose mass during spin-up is not clear (see Walsh et al. 2008). It is
evident from the study of binary rotation rates (Pravec & Harris 2007) that the combined angular
momentum of most asteroid pairs lies at or near the spin barrier. A genetic mechanism for binary
formation may be that they spin up (by YORP) beyond this threshold and suffer a global landslide
that sheds a moon.
Asphaug
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1000
NEAs
MBAs + MCAs
0.1
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1
Spin barrier
10
10
P (h)
Spin rate (d–1)
100
1
100
0.1
0.01
0.1
1
10
100
1000
1000
Diameter (km)
Figure 13
Asteroid rotation rate ωrot (rotations per day, left axis) and rotation period Prot (h per rotation, right axis)
plotted versus asteroid diameter D (km), obtained by brightness (absolute magnitude) and brightness
variation (periodicity) studies of hundreds of asteroids. The “spin barrier” at Pro t * 2.2 h appears to be an
abrupt threshold transgressed by only one known asteroid larger than ∼300 m diameter. Near-Earth
asteroids (NEAs) are shown as circles; main-belt asteroids (MBAs) and Mars-crossing asteroids (MCAs) are
shown as small crosses. Figure courtesy of Petr Pravec.
2.5. Spectroscopy and Thermal Observations
Spectroscopy from Earth is usually disk integrated, taking in a hemisphere at once. It can be
rotationally resolved—recorded as the asteroid spins, documenting global-scale heterogeneity.
From visible and near-infrared spectroscopy one derives the taxonomic class and a wealth of
compositional information. From mid- to thermal-infrared studies, one obtains vital information
regarding thermal properties, important to understanding Yarkovsky and YORP evolution.
Combined thermal and visible observations solve independently for albedo, giving a constraint
on size and (via the light curve) shape. Spacecraft missions provide essential benchmarks in this
regard. Itokawa is a small S-type asteroid with absolute magnitude H ∼ 19. Müller et al. (2007)
reported pre-encounter ground-based thermal observations at 10 µm, leading to a shape model
of 520 × 270 × 230 m ( ± 10%); this was in excellent agreement with the shape measured by
Hayabusa of 535 × 294 × 209 m (Fujiwara et al. 2006).
2.6. Radar
The 305-m diameter Arecibo dish—larger than some of the asteroids it images—is the world’s
most powerful radio transmitter, capable of sending ∼0.5 MW pulses. It is also the world’s most
sensitive radio receiver, acquiring reflected energy <10−27 watt at high signal-to-noise. Arecibo
Observatory, together with the 70 m steerable dish at Goldstone Observatory, has been utilized
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with great success by the late asteroid radar pioneer Steve Ostro and his colleagues to provide
the most detailed images and dynamical information known about NEOs as well as important
characterization of main-belt asteroids and Earth-approaching comets. The topic is reviewed by
Ostro et al. (2002).
Asteroid radar operates by sending out a narrow beam of microwave energy toward a target
(3.5 cm at Goldstone, 13 cm at Arecibo), and by examining the echo in comparison to the transmitted signal. A circularly polarized signal enables studies of surface roughness and albedo, which
in turn lead to an understanding of the porosity and composition of the upper centimeters.
Radar is subject to two-way 1/r4 signal attenuation, and thus high-resolution images generally
require closest approaches !0.01 AU, although shape models and spin poles can be obtained at
lower signal-to-noise ratio (SNR). For the main belt, radar-derived shape models rival adaptiveoptics imaging, but the most significant main-belt radar data set is the detection of their surface
physical characteristics. Magri et al. (2007) report that M asteroids come in both metal-rich and
metal-poor varieties, as indicated above, and that C- and S-class MBAs have indistinguishable
radar albedo distributions. Benner (2008) correlates radar roughness with composition, opening
up new avenues in science and showing how radar detection is a valuable precursor to landed
missions and sample returns.
In addition to producing stunning images and other physical characterizations, radar provides
extraordinarily precise astrometry, allowing for highly refined dynamics, both orbital (about the
sun) and rotational (the asteroid system itself ). Chesley et al. (2003) describe its utility in asteroid
dynamical studies (in this case the first direct determination of the Yarkovsky effect), and Giorgini
et al. (2008) show how radar astrometry is an essential tool in retiring the risk of menacing
objects like Apophis. Scheeres et al. (1996) were the first to use radar-derived shape models and
spin states as initial conditions for studying particle dynamics about an asteroid, and Scheeres
et al. (2006) obtain a detailed understanding of the dynamical state of the 1999 KW4 system
(Figure 14b).
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2.7. Dynamical Constraints
Large asteroids have had their masses directly measured from their perturbations upon Mars and
on each other (Williams 1984, Michalak 2000). Krasinsky et al. (2002) derived the total mass of
the asteroid belt by analyzing the motions of the major planets, processing high-precision ranging
information relative to the Viking-1, Viking-2, and Pathfinder landers over a 21-year period.
They modeled the 300 largest asteroids and the major planets directly, and the residual gives the
“hidden mass” of the belt. According to their studies, the total main-belt mass is ∼1.8 × 10−9 M$ ,
where M$ is the mass of the sun, thus ∼3.6 × 1021 kg is the total mass of asteroids according to
this study. That is 400% the mass of Ceres, ∼0.6% the mass of Mars, and ∼5% the mass of the
Moon.
Asteroid masses are also determined through the study of multiple systems, via Kepler’s laws,
and through studies of rotational equlibrium. The primary density of 1999 KW4 (Figure 14b)
is ∼2 g cm−3 ; the satellite density is probably somewhat greater (Ostro et al. 2006). With Prot =
2.76 h, the primary is rotating close to the speed limit where debris goes into orbit (see Scheeres
et al. 2006). Slope maps of the primary including rotation show it to be near the angle of repose
at mid-latitudes; it may be a celestial debris flow with material migrating to the equator. Fine
particles that are shed from the equator may be swept out by the solar wind; larger rocks might
accumulate back onto the asteroid or onto the satellite, their fate depending on whether they
escape rock-by-rock or as a landslide.
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August 4, 1999
August 8, 1999
August 5, 1999
August 9, 1999
1999 JM8 (Arecibo and Goldstone)
b
1998 KW4 (Arecibo)
Figure 14
Two of the many asteroids imaged by the radar telescopes at Arecibo and Goldstone; for a complete list see
http://echo.jpl.nasa.gov. (a) 1999 JM8 is a D * 2.5-km S-type, the largest potentially hazardous asteroid
(PHA) to be studied in this level of detail (Benner et al. 2002). These are Doppler-delay images acquired in
1999, shortly after the object’s discovery, on the dates labeled (Benner/JPL). (b) 1999 KW4 is a binary system
(Ostro et al. 2006) that will come to within 13.5 lunar distances of Earth on May 25, 2019. This is another
potentially hazardous S-type whose high inclination (∼40◦ ) and large eccentricity (∼0.7) indicate that it has
undergone a near-Earth scattering encounter—possibly the event that created the binary by tidal disruption.
It will come within 6 lunar distances of Earth in 2036, close enough to transform its dynamical
configuration. This is a shape model fitted to the radar observations, with primary diameter Dα ≈ 1.5 km,
secondary diameter Dβ * 0.5 km, and separation a * 2.5 km (Ostro/JPL).
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3. ORIGINS
There all the barrel-hoops are knit,
There all the serpent-tails are bit,
There all the gyres converge in one,
There all the planets drop in the Sun.
William Butler Yeats, “Supernatural Songs”
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Asteroid origin is ceaseless, as most asteroids are born in the process of catastrophic disruption.
Any main-belt asteroid smaller than a few tens of km is unlikely to have survived intact throughout
solar system history. Asteroid evolution is also ongoing: Most small asteroids have been drastically
transformed in shape and structure over a few tens of millions of years by subcatastrophic collisions
and cratering. Small asteroids are also prone to dynamical perturbations of various kinds, so their
present orbits may be quite different from where they originated. Their surface textures and colors
are also readily modified on short timescales.
But meteorites, which sample the asteroids, are largely primordial. It is therefore difficult to
say just what is meant by “asteroid origin,” since they are petrologically the most ancient, and
dynamically the newest, of planetary bodies. Because the dynamical and collisional lifetimes of
small asteroids are much shorter than the age of the solar system, we can distinguish dynamical
origins from petrological origins, and begin with the former.
3.1. Ages of Families
Most MBAs smaller than a few tens of km are catastrophic disruption remnants (Farinella et al.
1982). The ejection of sizable fragments upon impact, followed by the long-term dynamical forcing
by planetary encounters, resonances, and the Yarkovsky effect, causes families of asteroids to form
and disperse. The snapshot of the present epoch seen in Figure 8 will look similar in ∼10 Ma,
except that most of the smaller families will be gone, replaced by new ones.
Researchers date the time of formation of asteroid families by modeling their dynamics backwards until family members converge. A couple of smoking guns have proven quite young, and
their debris have been associated with the lunar and terrestrial impact record. The Karin family
(proper a = 2.87 AU, e = 0.044, i = 2.1; itself a subcluster of the Koronis family) and the
Veritas family (proper a = 3.17 AU, e = 0.065, i = 9.3) formed only ∼5.8 Ma and ∼8 Ma ago,
respectively (Nesvorný et al. 2002). The Datura family (Nesvorný et al. 2006) is dated to only
450,000 years ago.
Some of these very young families include binary asteroids, suggesting that binaries can be
formed during catastrophic collisions (Durda et al. 2004), either through ejection of bound pairs
or ejection of material into orbit about the target. But not necessarily; the creation of new satellites
around ∼1-km asteroids may take as little as ∼1 Ma if YORP spins them up as rapidly as postulated.
The Karin family members do not align perfectly at ∼5.8 Ma before present, when projected
back in dynamical time. Allowing for Yarkovsky drift, Nesvorný & Bottke (2004) obtain an excellent
convergence, but only if the fragment asteroids are of low thermal inertia—that is, regolith-covered
shortly after the catastrophic breakup event. If true, this would give insight into the process of
disruption.
The Baptistina family of asteroids has been shown through dynamical integrations (Bottke et al.
2007) to have formed during a collision ∼160 Ma involving parent asteroids modeled as 60-km
and 170-km diameter. One large fragment from this breakup is thought to have struck the Moon,
forming the rayed crater Tycho 108 Ma ago. A more infamous outcome of these simulations is that
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a ∼10-km fragment is likely to have struck the Earth 65 Mya, ending the Mesozoic era and leading
to the rise of mammalian life. But Baptistina is an S-type (Reddy et al. 2008), inconsistent with the
CM2 carbonaceous chondrite composition of the K/T impactor (Kyte 1998), so the jury is still out.
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3.2. Planetesimals to Planets
Asteroids represent the halfway point between the solar system’s turbulent beginnings and the
quiescent 4 Ga that have supported life on Earth.
The first stage of planetary accretion is among the most complex studies in astrophysics. As
they accumulate, planetesimals are entrained within a disk that undergoes violent shocks and
propagates gravitational waves and eddies. Magneto-rotational instabilities might lead to high
turbulent viscosities, which lead to radial transport and vertical mixing and viscous spreading.
Solid particles settle to the mid-plane, increasing the density so that planetesimals might eventually
coagulate. Electric discharge and impact heating take place sporadically. Outside this mid-plane
the young sun blasts the gas and sweeps away small material. Drag against the gas disk forces
meter-sized boulders to spiral in from the planet-forming region.
The chemical environment, too, is grossly out of equilibrium. The disk experiences a wide
range of temperatures and pressures and oxidation states, with sharp gradients in time and space.
Where the disk is optically thick, it can remain hot for thousands of years; where it is thin, it
can cool in days or even minutes. Thermodynamic energy is available from solar heating, shock
heating (by impacting globules striking the disk, by disk planetesimals colliding with one another,
and by shocks in the gas), compression heating (adiabatic work), and radionuclide decay. This
energy is transported radiatively and convectively.
One of the most baffling results from any recent space mission is NASA’s Stardust sample
return from periodic comet 81P/Wild 2 (Brownlee et al. 2006; see Figure 3), which includes an
abundance of refractory silicates, metal sulfides, and refractory oxides. These small grains, captured
in aerogel during a flyby through the coma, can have formed only in the terrestrial (inner) part
of the disk; how did they make it to the ice-rich region where comets form? It is a revolutionary
mission result, telling us that the solar system was exchanging matter across tens of AU during
the early stages of primary accretion.
Primary accretion:
the formation of the
first macroscopic
condensates in the
nebula, from
centimeter-scale lumps
in the disk to
kilometer-scale
planetesimals
3.2.1. A standard model. As terrestrial planet formation progresses the pace of events drops off,
so there appear to be stages that are logarithmic in time. Primary accretion, described further
below, begins with the Sun’s formation within a possibly dense cluster of young stars; it ends with
the condensation of dust- to boulder-sized solids in a hot, turbulent, violently irradiated disk.
Primary accretion is surprisingly rapid: solids collapse down onto the mid-plane of the nebula and
coalesce into dense swarms of meter- to kilometer-sized planetesimals in as little as a few tens of
thousands of years.
Over the next ∼1 Ma, these small solids grow into planetesimals resembling the most primitive
asteroids. This is also the timescale of the decay of 26 Al → 26 Mg, a radionuclide predating accretion
with half-life τ1/2 = 7.2×105 yr. Global melting ensues if planetesimals grow large enough and fast
enough, so there should be a wide diversity of metamorphic and igneous grades among meteorites,
in agreement with observation. After this epoch the internal heat sources shut down, asteroids
being too small to retain the heat produced by longer-lived radionuclides.
Over the next ∼10 Ma, the disk is quiescent and composed primarily of accreted solids. Gravitational instabilities early on cause large planetesimals to grow much more rapidly than small ones
(Greenberg et al. 1978, Wetherill & Stewart 1989); competition for matter thereafter slows down
the growth of larger bodies in comparison to small ones (Kokubo & Ida 1998).
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Figure 15
Artist’s conception of accreting planets clearing a gap out of nebular gas and dust, based on astronomical
interpretations of Spitzer Space Telescope observations of a ∼1 Ma old star system UX Tau A
(NASA/JPL-Caltech/T. Pyle/SSC).
Thus, runaway growth levels off into oligarchic growth, resulting in planetary embryos that
are comparably sized and uniformly spaced and follow approximately circular orbits (e, i ≈ 0).
They are perhaps Vesta to Moon- or Mars-sized, depending on the mass density of the disk.
Accretion is a lossy process, and the original disk mass is greater than the final terrestrial
planetary mass by a factor of perhaps ∼2 ± 1 that is removed by dynamical and gas drag and
scattering (Figure 15). This winnowing is most pronounced among the small bodies that are
most easily perturbed.
An epoch of large-scale impacts dominates the next 100 Ma, beginning at low velocity among
these like-sized bodies and evolving toward higher-velocity collisions among different-sized bodies. Low velocity refers to v∞ compared with the two-body escape velocity
!
(7)
ves c = 2G(Mi + Mt )/(Ri + Rt ).
Here, Mi , Mt and Ri , Rt are the masses and radii of the impactor and target, and G is the gravitational
!
2 + v2
constant. The impact speed at the moment of contact is the root square sum vimp = v∞
es c
and is at minimum the escape velocity. Because the population gets dynamically stirred up by the
largest body, v∞ is comparable to the escape velocity.
Low-velocity impacts transition to high-velocity impacts as close encounters gravitationally
excite the population. Planet-sized bodies go astray, as is believed to have happened when a
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Mars-sized body struck the Earth to form the Moon. In a series of papers that developed the
modern theory, Wetherill (1990) showed that Mars-sized protoplanets would have roamed the
main belt for the first 10–100 Ma. Mercury could have originated from beyond Mars (Wetherill
1994). Asteroids, then, are what’s left after roaming planets did their work (Chambers & Wetherill
2001).
To continue logarithmically, the next 1 Ga was an epoch where largely finished planets suffered
the remainder of the planetesimal bombardment, with occasional impact storms triggered by
the playing out of the final dynamical instabilities, as indicated by the late lunar cataclysm—the
pronounced spike in the cratering record ∼3.9 Ga before present, around the time life originated
on Earth. A final logarithmic step includes the placid times we enjoy today and the winding-down
of the thermodynamical inventories of the solar system, followed by the death of the Sun ∼10 Ga
after it all began.
3.2.2. Primary accretion. Direct knowledge of the earliest stage now exists from astronomical
observations (e.g., Meyer et al. 2008). As the hot orbiting mixture of dust and gas cools, larger
particles condense, leading to lowered opacity and further cooling and coagulation. The review
by Podosek & Cassen (1994) remains highly relevant. Particles orbiting with any inclination or
eccentricity must plow through the disk; the resultant damping settles them to the midplane on
a timescale of ∼100 years at 1 AU (Cuzzi & Weidenschilling 2006). What happens next in this
central sheet is a great unknown, and depends on the effect of turbulence.
Dust grains coagulate via Brownian motion and chemical or electrical sticking mechanisms
(Dominik et al. 2007). This can lead to sand- to boulder-sized agglomerates. Brownian motion
is an expression of modest turbulence, possibly set up by magneto-rotational instabilities in the
plasma and the dusty gas. However, too great a turbulence disrupts agglomerates faster than they
form. Benz (2000) and Leinhardt et al. (2000) studied collisions involving meter- to kilometer-scale
aggregates at ∼1–10 m/s random velocities, and determined their disruption to be a bottleneck to
further growth. A possible solution is that compactible aggregates damp the energy of collisions
and resist subsequent disruption.
Not only must turbulence be low, but the gas must go away before the growing planetesimals
spiral in. Once boulder-sized, they decouple and drag against the pressure-supported gas disk that
orbits the Sun at a sub-Keplerian velocity
#
"
−d P/dr
vg = 1 −
vk ,
(8)
2ρg *2k r
√
where vk = GM$ /r is the Keplerian velocity of the boulders, ddrP < 0 is the drop of pressure P
vk
with increasing heliocentric radius r, ρ g is the gas density, and *k = 2πr
is the Kepler frequency.
Decoupled solids spiral towards the Sun at an estimated 1 AU per ∼10–1000 years, so there is not
much time!
Multistage processes have been proposed to make primary accretion more efficient. The model
by Cuzzi et al. (2001) capitalizes upon large-scale turbulence by having small particles coalesce in
the disk eddies, analogous to how flotsam accumulates in a river. Thus the turbulence that would
bash planetesimals apart collects them together. The clustering of solids into localized regions,
either through random effects or through accumulation along stable zones, might lead to dense
swarms that can then undergo gravitational coagulation.
The problem of accreting meter-scale planetesimals is far from solved. But we know it occurred
rapidly because of the widespread melting of planetesimals caused by the decay of 26 Al. Heat can
only dissipate in a solid body by conduction or by volatile convection through pores and by
radiation from the surface. A 10-km chondritic body easily melts if it accretes much faster than
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Achondritic: refers to
an asteroid or
meteorite of evolved
or melted silicate
composition
12:33
τ 1/2 = 0.72 Ma, (as reviewed in Ghosh et al. 2006) or can undergo vigorous hydrothermal
convection (e.g., Travis and Schubert 2005).
Timing is everything. So is location. Planetesimals forming closer to the Sun acquire a greater
fraction of Al-bearing silicates than those forming where ices dominate and form more rapidly,
and they are thus much more prone to melting. Large comets may also have melted interiors,
despite the lower silicate abundance, owing to their low heat capacity, low thermal conductivity,
and low melting temperature, provided they can win the race against τ 1/2 (as reviewed by Prialnik
et al. 2008).
Melting during planetesimal accretion was widespread; there appear to be ∼50 or more differentiated early planets whose cores are represented by meteorites, distinguished on the basis of bulk
composition (Fe and N) plus trace metals. Each iron meteorite reservoir bears a unique chemical
fingerprint; there are 14 classified groups plus hundreds of unclassified iron meteorites that belong to dozens of distinct parent bodies (Wood 1964). The possibility of multiple core-pockets
of iron on a single parent body appears unlikely given the runaway nature of core formation, but
it cannot be ruled out. Achondritic basalts, although not as abundant as irons, are just as diverse
and directly indicate multiple diverse parent bodies, presumably among the same ones sampled
by iron meteorites.
Why so few mantle and crustal rocks, and so many irons, among the meteorites? Burbine et al.
(1996) reviewed the problem and proposed that mantle material in the main belt undergoes rapid
breakdown in size whenever excavated from an asteroid, whereas the stronger iron relics survive.
But unless chondritic rock is much stronger than mantle rock, the same argument should get rid
of the chondrites as well, unless they were initially much more abundant. Or, chondrites could
fragment with a steeper size distribution than basalts, leading to dominance at the small sizes
pertaining to meteorites.
3.2.3. Chronology of differentiation and chondrule formation. Early solar system chronology
is established through the study of short-lived radioisotopic nuclides and their decay products;
these include Al-Mg (τ 1/2 = 0.72 Ma), Fe-Ni (τ 1/2 = 1.49 Ma), Mn-Cr (τ 1/2 = 3.7 Ma), Pb-Ag
(τ 1/2 = 6.5 Ma), Hf-W (τ 1/2 = 9 Ma), and Sm-Nd (τ 1/2 = 103 Ma). The reference point for
chronology is the solidification of the refractory Ca-Al inclusions (CAIs) that formed earlier (t0 ∼
4.567.3 Ga) than any other known solid (Amelin et al. 2002) and are commonly found in primitive
meteorites.
According to the thermal arguments, any silicate planetesimal larger than approximately 10–
50 km would have melted and differentiated had it accreted earlier than a few million years after CAI
formation. The preponderance of primitive rock in the meteorite collection might mean that accretion had not finished by this time, for otherwise all we would have are mafic and basaltic silicates
and irons and core-mantle mixtures such as pallasites. This reasoning, and the very precise dating of
chondrules, has pushed the chronology of so-called primitive bodies away from the starting point.
The evolved bodies accreted first: Iron meteorites and the most ancient achondrites predate the origin of chondrules by a few million years (Kleine et al. 2005). Primitive meteorites like Allende and
Orgueil do not represent the oldest bodies, but are latecomers that formed after the 26 Al was spent.
Distinct chronologies for accretion point to distinct locations within the disk. Accretion is
fastest inside of 1 AU and much slower further out, in proportion to the faster dynamical timescales
and greater density of material. Bottke et al. (2006a) calculate how rapidly forming inner solar
system asteroids are scattered by terrestrial planet formation to mix with the native chondrites of
the main belt. Had they formed early on and closer in, they would have melted, accounting for
the exotic diversity of main-belt asteroids and the presence of irons and basalts where accretion
timescales are much longer than a few million years. The scattering of molten planetesimals is
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applicable to the hypothesis of Asphaug et al. (2006) that gravitational and mechanical shears during
impacts resulted in pressure unloading of melts and partial melts, leading to exotic petrogenesis,
which is preserved in the unaccreted remnants of the solar system.
The origin of chondrules adds another layer to the mystery, in that these are melt droplets of
some kind, quite possibly themselves antecedent to global melting of planetesimals. Chondrules
are melted silicate spherules a few mm in size that are abundant in chondritic meteorites (reviewed
by Scott 2007). Over half the bulk mass of chondritic meteorites consists of chondrules, so they
represent a widespread epoch in planet formation that has been attributed to processes as diverse
as lightning, impacts, nebular shocks, compaction heating, and volcanic eruptions. Chondrules
cooled through their solidus at rates ranging from ∼10 to ∼1000 K/h—much slower than radiative
cooling of a mm-sized droplet, which is tens of seconds. Chondrule cooling appears to require a
hot background that disappears over a timescale of hours.
High-precision (∼0.1 Ma) timing of chondrule formation indicates that their formation ages
postdate the formation of the earliest basalts and iron cores by ∼2–3 Ma (Connelly et al. 2008).
The data are consistent with episodes of chondrule formation spanning a few Ma (e.g., Kleine
et al. 2005), contemporary with the transition from primary to secondary accretion, when sizable
planetesimals were first forming. Although impact origin of chondrules is not currently in favor,
we have a lot to learn, and large, late collisions deserve a closer look.
3.3. Large Collisions
In almost all simulations of late-stage planet formation, giant impacts are treated as “sticky ping
pong balls” undergoing perfectly inelastic collisions when they hit, forming a larger equal-mass
sphere that conserves linear momentum. This was proven untenable by Agnor et al. (1999), who
tracked angular momentum during such a calculation and showed that perfectly inelastic collisions
lead to planets with impossibly fast rotation.
Under perfect accretion, the acquisition of angular momentum is a 3D random walk that departs
from the origin; many of the planets studied by Agnor et al. (1999) thus end up with Pro t ≈ 1 − 2 h.
Some of the modeled planets experience rotational kinetic energy 15 MR2 ω2 exceeding the binding
energy of a self-gravitating sphere 3/5GM2 /R; equating these gives a fastest possible rotation of
√
Pmin = π/Gρ, or 1.2 h for a planet of density 3 g cm−3 . But rapid rotators deform into spheroids
and become unstable at rotation periods closer to ∼2 h.
Unrealistically fast rotations obtained in the simulations are the result of perfect sticking for
impacts faster than vesc , or at grazing incidence. The efficiency of giant impact accretion was
explored by Agnor & Asphaug (2004a), who used smooth particle hydrodynamics (SPH) to model
a wide array of giant impacts, at varying relative velocity, and with varying impactor-to-target mass
ratio (see Figure 16). These simulations used the same method that had been applied to giant
impact scenarios for the Moon’s formation (Canup & Asphaug 2001), beginning with differentiated
planets of Earth-like bulk composition (70 wt% rock, 30 wt% iron).
For velocities typical of this epoch of planet formation, approximately one-third to one-half of
giant impacts are hit-and-run collisions, with the impactor rebounding and contributing little mass
to the target (or in most cases, removing some of it). This is easily understood geometrically: the
most common impact angle is 45◦ , and, for similar-sized bodies, this is an angle at which most of
the colliding masses do not intersect but miss one another. Planets thus grow selectively, accreting
most of their matter by low-velocity or head-on collisions and not during high-velocity or grazing
events, as can be seen in Figure 17, which plots accretion efficiency. Hit-and-run outcomes cluster
along the line of 0 accretion efficiency and are the most common group of outcomes.Thus, the
fate of the unaccreted impactor is of considerable importance to asteroid and meteorite origins
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a
b
c
d
e
f
Rock
Iron
Figure 16
Hit-and-run impacts are common when planetary bodies of similar size collide at accretionary velocities
(Agnor & Asphaug 2004a). Typical collisions are shown here involving differentiated planetary embryos with
rock mantles (blue) and iron cores (red ) in a 70–30 wt% ratio. Target mass M is the mass of Mars; impactor
mass is (top) m = M/2 and (bottom) m = M/10. Impact velocities are typical of the late stage, with vimp =
1.5 vesc (top) and vimp = 2 vesc (bottom). Impact angle is 30◦ from head-on in both cases. These are SPH
simulations using the Tillotson equation of state. Collisions are shown before, during, and 3 h after the
impact, in side view; particles are overplotted. Mantle is lost (iron fraction-enriched) from impactor and
target in hit-and-run collisions. In ( f ) a chain of iron-enriched bodies derives from the impactor, a possible
explanation for iron meteorites with vastly different cooling rates coming from common parent reservoirs.
The impactor in (c) has lost over half its mantle and invokes a possible scenario for the origin of Mercury.
Figure from Asphaug et al. (2006).
(Asphaug et al. 2006). The impactor often sails on, severely transformed by the mechanical shears,
gravitational torques, and tides (Figure 16). In some cases it is shredded into a chain of bodies, with
those toward the center of the chain being iron-rich, and the others iron-poor. The prevalence
of hit-and-run collisions makes it a late-stage pathway for the origin of exotic igneous asteroids,
for volatile flux and iron-silicate intermingling, and for the bulk removal of planetary mantles and
the stripping of iron cores.
Every terrestrial planet is the aftermath of giant collisions, and given the above, one might expect significant compositional diversity among terrestrial planets of the sort that one sees between
the Earth and Moon. Venus and Earth are compositionally similar, whereas Mercury appears to
have less than half the mantle rock of similar-sized Mars, and Vesta and Ceres (Figure 18) vary
by almost a factor of 2 in density. There is clearly a trend toward greater diversity as one looks to
the smaller terrestrial planets, something that can be understood by the fact that large planets are
great homogenizers and were never ripped asunder the way that small planets were.
Collisional accretion is biased to favor the accumulation of iron cores at the expense of mantle
rock, because impacts expend most of their energy in the mantles and crusts of colliding planets
440
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Mass Impact
ratio angle
1
1:10
1:10
1:10
1:10
1:2
1:2
1:2
1:2
1:1
1:1
1:1
1:1
0.8
Accretion efficiency
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0.6
0.4
0°
30°
45°
60°
0°
30°
45°
60°
0°
30°
45°
60°
0.2
0
–0.2
–0.4
0
0.5
1
1.5
2
2.5
Velocity at infinity / two-body escape velocity
Figure 17
Accretion efficiency. Agnor & Asphaug (2004a) simulated giant impacts between differentiated terrestrial
planets (see Figure 15). This plot includes calculations presented
by Agnor & Asphaug (2004b). The velocity
$
2 + v 2 . According to dynamical integrations
at infinity v∞ is the random velocity; the impact velocity is v∞
es c
√
of late-stage accretion (Agnor et al. 1999), most giant impacts have Safronov number θ < 1 (v∞ > 2ves c ), in
which case the accumulation of mass is inefficient. Impact angles are 0◦ (dark blue), 30◦ (light blue), 45◦ (red ),
and 60◦ (orange). Target to impactor mass ratio is 1:1 (circles), 2:1 (squares), and 10:1 (triangles). Accretion
efficiency ξ is the mass of the largest postimpact body (M1 ) minus the mass of the largest preimpact body
−Mt
(Mt ), compared to the total mass accretable (Mi ). In the case of perfect accretion ξ = M1M
= 1; this occurs
i
for random velocities close to zero. The Moon-forming scenario favored by Canup & Asphaug (2001)
involves low velocity v∞ /vesc ! 0.1 and plots close to the red triangle in the upper left. In the limit of no
collision, or a perfectly elastic collision, or an impactor adding as much mass as it removes, M1 = Mt and
t
ξ ≈ 0. Erosion (ξ < 0; M1 < Mt ) plots below the line; catastrophic disruption (where M1 = Mi +M
) requires
2
events far to the right of this plot. The clustering of model outcomes at ξ ≈ 0 represents the preponderance
of hit-and-run collisions where the impactor bounces off largely intact (Asphaug et al. 2006).
and because exterior layers are of lower binding energy than cores. Thus, the most energetic
collisions can remove much of a planet’s mantle, either by a direct hit (Benz et al. 1988) or by
hit-and-run akin to Figure 16a–c. Removing a mantle by a direct hit requires very high collisional
velocity, far to the right of what is plotted in Figure 17, and far outside the mid-range of what is
expected (Agnor et al. 1999), whereas hit-and-run applies when v∞ is in the mid-range.
The overall trend in a collisional accretionary environment is the loss of atmosphere, ocean,
crust, and mantle, the preferential accretion of dense materials into growing planets, the sheddingoff of mantles, and the occasional disruption of single planets into multiples. This leads to a primary
physical and chemical bias, a dichotomy among the accreted and the unaccreted. If finished planets
are the loaves of bread, asteroids are the scraps on the floor of the bakery.
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Figure 18
Ceres and Vesta, the two largest asteroids, to scale, as imaged by Hubble Space Telescope (NASA). These are
among the highest-resolution images that exist for either until the Dawn mission arrives at Vesta in 2011 and
at Ceres in 2015 (Russell et al. 2004). (Left) Ceres, D * 900 km, imaged in 2004 (HST ACS/HRC). (Right)
Vesta, D * 530 km, imaged in 2007 (HST WFPC2). The figure of Ceres is consistent with a differentiated
spheroid of rock and ice in rotational equilibrium (Thomas et al. 2005). Vesta is missing much of its southern
hemisphere, the possible source of the V-class asteroids (Binzel & Xu 1993, Asphaug 1997).
3.4. Asteroids and Planets
Differentiation: the
process by which a
planet forms a core
and mantle through
the segregation of
dense iron from
silicate minerals
442
Planets still roam the main belt; the largest of these is Ceres (D ≈ 900 km; see Figure 18). Travis
& Schubert (2005) have shown that chondritic bodies of 100 km diameter undergo vigorous
hydrothermal convection for millions of years if they accrete early. Ceres’ evolution thus depends
on its composition and the timing of its accretion (McCord & Sotin 2005). Its global figure
(Thomas et al. 2005) is indicative of gravitational relaxation and differentiation. With a derived
bulk density of ∼2–2.5 g/cm3 (Michalak 2000), Ceres is speculated to be at least ∼1/3 water by
mass, and thus perhaps even a trans-Neptunian escapee. Ceres shows spectroscopic evidence for
a complex geologic history forming carbonates and clays (Rivkin et al. 2006).
The view that Ceres is a planet is likely to prevail once NASA’s Dawn mission arrives in 2015
(Russell et al. 2004) to begin its imaging, spectrometry, and gravity science campaigns. As for
Vesta—“the smallest terrestrial planet” (Keil 2002)—our perspective will also change when Dawn
arrives in 2011. Figure 1 shows the overwhelmingly large mass of Vesta compared to gardenvariety asteroids. Yet Vesta it is more intimately linked to asteroids than is Ceres, having its own
clearly recognizable taxonomic and dynamical family (see Burbine et al. 2002). Why Ceres has no
asteroid family, whereas Vesta does, is a mystery for another day.
Vesta has undergone global-scale volcanism as known from its basaltic spectral signature
(V-type) and its clear link to the HED (howardite, eucrite, and diogenite) basaltic achondrite
meteorites. It is the principal member of a family of several hundred small asteroids (Binzel & Xu
1993) that may have formed during the disruptive event that defines Vesta’s southern hemisphere
(Asphaug 1997).
Vesta is also the only known differentiated rocky asteroid to have survived the evolution of the
main belt more or less intact. The next largest basaltic asteroid is 1459 Magnya (D * 17 km).
Although fragments this large could have been ejected from Vesta’s mega-crater (Asphaug 1997),
Magnya appears to be dynamically and spectroscopically distinct, perhaps an isolated relic of
another disrupted planet.
Asphaug
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In the main belt, hit-and-run collisions would have disrupted Vesta-sized bodies during the
∼30 Ma period when Moon- to Mars-sized planets were found there (Chambers & Wetherill
2001). As long as these targets were around to be impacted by differentiated planetary embryos,
the shredded remains of these impactors would be expected, their bits and pieces surviving as exotic
asteroids and puzzling meteorites. In this manner, the puzzle of Vesta’s surviving crust can perhaps
be explained, in that it is not required to have dodged the fusillade of mega-impacts that would have
accompanied the catastrophic disruption of dozens of less fortunate iron meteorite parent bodies,
and would have mixed Vesta’s crust back into its mantle. Perhaps there was no such fusillade:
instead of dodging bullets, Vesta avoided colliding into larger bodies until they left the main belt.
3.5. Delivery to Near-Earth Space
Where an asteroid resides today is not usually where it was born. The same holds true for major
planets, but asteroids are particularly prone to this gravitational dance. While the major planets
are now dynamically stable on billion-year timescales, small asteroids keep migrating.
The Yarkovsky effect nudges small asteroids and meteoroids into resonances (Gladman et al.
1997, Farinella et al. 1998, Vokrouhlický & Farinella 2000) so that NEOs and meteorites provide
a relatively complete representation of the geologic, physical, and chemical record of solar system
history (Burbine et al. 2002). The physics of impacts introduces a systematic bias in that hard,
rocky asteroids eject faster fragments, which can make it to Earth on shorter timescales (before
they are disrupted). The stochastic nature of family-forming collisional events might introduce an
even more fundamental bias. The prevalence of young dynamical families confirms that today’s
NEOs are, by and large, discrete samplings of catastrophic disruption events in the main belt
that happened thousands to millions of years ago. With the discovery of extensive fossil beds
of meteorites (Schmitz et al. 2003) it is incontrovertible that the meteoroid flux is punctuated
by recent disruptions. The sampling of meteorites on Earth, and of small asteroids near Earth,
reflects that bias.
4. CONCLUSIONS
Looking from Earth we can see a few thousand discrete stars by naked eye on a dark clear night.
A backyard telescope reveals millions. Planets have been found around many of these stars, and
through observations of planetary transits we may soon acquire direct detections of Earth-like
worlds. Whether Earths are common depends in no small part upon the behavior of accreting
planetesimals. Nearly all of the original mass of our main belt was swept up in the chaos of planet
formation, so we may be fortunate not to have lost everything from our habitable zone.
As a spacefaring species, we can still review our history of asteroid missions in a single paragraph.
It began when Mariner and Viking encountered Phobos and Deimos, captured asteroids or native
moonlets later observed by other Mars missions. Galileo en route to Jupiter acquired the first
detailed images of main-belt asteroids, 951 Gaspra and 243 Ida, the latter accompanied by the
first confirmed small-body satellite, Dactyl. There have been subsequent asteroid flybys. The first
asteroid rendezvous was NEAR, which flew by 243 Mathilde (the largest asteroid and only C-type
yet visited) and went on to spend a year at 433 Eros. The second asteroid rendezvous was Hayabusa
at Itokawa in late 2005, from whose surface a small sample may be on its way to Earth. Dawn is
on its way, arriving at Vesta in 2011 and Ceres in 2015.
Our understanding of asteroids is biased toward those objects that we have studied in detail: the
near-Earth S-types Itokawa and Eros. Chondritic and primitive asteroids are more representative,
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and of these we have had a flyby look at one. As for the upcoming Rosetta flyby of Lutetia, and
Dawn’s discoveries at Vesta, we will be, as ever, surprised by their novelty and reminded that the
study of asteroids is just beginning.
DISCLOSURE STATEMENT
The author is not aware of any affiliations, memberships, funding, or financial holdings that might
be perceived as affecting the objectivity of this review.
ACKNOWLEDGMENTS
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This review is dedicated to Steve Ostro (1943–2008), champion of asteroid radar astronomy.
Writing and research were sponsored by NASA’s Planetary Geology and Geophysics Program
and by the University of California, Santa Cruz. I am grateful to my colleagues for generously
sharing their ideas and artwork, and I regret the errors and omissions that are inevitible in a long
review. I thank Katherine Armstrong for assistance in manuscript preparation.
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Contents
Volume 37, 2009
Where Are You From? Why Are You Here? An African Perspective
on Global Warming
S. George Philander ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 1
Stagnant Slab: A Review
Yoshio Fukao, Masayuki Obayashi, Tomoeki Nakakuki,
and the Deep Slab Project Group ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !19
Radiocarbon and Soil Carbon Dynamics
Susan Trumbore ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !47
Evolution of the Genus Homo
Ian Tattersall and Jeffrey H. Schwartz ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !67
Feedbacks, Timescales, and Seeing Red
Gerard Roe ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !93
Atmospheric Lifetime of Fossil Fuel Carbon Dioxide
David Archer, Michael Eby, Victor Brovkin, Andy Ridgwell, Long Cao,
Uwe Mikolajewicz, Ken Caldeira, Katsumi Matsumoto, Guy Munhoven,
Alvaro Montenegro, and Kathy Tokos ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 117
Evolution of Life Cycles in Early Amphibians
Rainer R. Schoch ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 135
The Fin to Limb Transition: New Data, Interpretations, and
Hypotheses from Paleontology and Developmental Biology
Jennifer A. Clack ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 163
Mammalian Response to Cenozoic Climatic Change
Jessica L. Blois and Elizabeth A. Hadly ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 181
Forensic Seismology and the Comprehensive Nuclear-Test-Ban Treaty
David Bowers and Neil D. Selby ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 209
How the Continents Deform: The Evidence from Tectonic Geodesy
Wayne Thatcher ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 237
The Tropics in Paleoclimate
John C.H. Chiang ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 263
vii
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Rivers, Lakes, Dunes, and Rain: Crustal Processes in Titan’s
Methane Cycle
Jonathan I. Lunine and Ralph D. Lorenz ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 299
Planetary Migration: What Does it Mean for Planet Formation?
John E. Chambers ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 321
The Tectonic Framework of the Sumatran Subduction Zone
Robert McCaffrey ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 345
Annu. Rev. Earth Planet. Sci. 2009.37:413-448. Downloaded from arjournals.annualreviews.org
by Annu Rev on 05/18/09. For personal use only.
Microbial Transformations of Minerals and Metals: Recent Advances
in Geomicrobiology Derived from Synchrotron-Based X-Ray
Spectroscopy and X-Ray Microscopy
Alexis Templeton and Emily Knowles ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 367
The Channeled Scabland: A Retrospective
Victor R. Baker ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 393
Growth and Evolution of Asteroids
Erik Asphaug ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 413
Thermodynamics and Mass Transport in Multicomponent, Multiphase
H2 O Systems of Planetary Interest
Xinli Lu and Susan W. Kieffer ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 449
The Hadean Crust: Evidence from >4 Ga Zircons
T. Mark Harrison ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 479
Tracking Euxinia in the Ancient Ocean: A Multiproxy Perspective
and Proterozoic Case Study
Timothy W. Lyons, Ariel D. Anbar, Silke Severmann, Clint Scott,
and Benjamin C. Gill ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 507
The Polar Deposits of Mars
Shane Byrne ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 535
Shearing Melt Out of the Earth: An Experimentalist’s Perspective on
the Influence of Deformation on Melt Extraction
David L. Kohlstedt and Benjamin K. Holtzman ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 561
Indexes
Cumulative Index of Contributing Authors, Volumes 27–37 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 595
Cumulative Index of Chapter Titles, Volumes 27–37 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 599
Errata
An online log of corrections to Annual Review of Earth and Planetary Sciences articles
may be found at http://earth.annualreviews.org
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Contents