46 Encyclopedia of the Solar System
wheretCHURis the time of separation from a CHondritic
Uniform Reservoir,λ=(ln 2/half-life) is the decay constant
for^182 Hf (0.078 per million years) and (^182 Hf/^180 Hf)BSSI
is the bulk solar system initial ratio of^182 Hf to^180 Hf.
Tungsten-182 excesses have been found in Earth, Mars,
and the HED meteorites, which are thought to come from
asteroid Vesta, indicating that all these bodies differenti-
ated while some^182 Hf was still present. Iron meteorites,
which come from the cores of differentiated planetesimals,
have low Hf/W ratios and are deficient in^182 W. This means
these planetesimals must have formed at a very early stage
before most of the^182 Hf had decayed. New, very precise
(^182) Hf– (^182) W chronometry has shown that some of these
objects formed within the first few hundred thousand years
of the solar system (Fig. 8).
New modeling of the latest^182 Hf–^182 W data for mar-
tian meteorites also provides evidence that Mars grew and
started differentiating within about 1 Ma of the start of the
solar system. This short timescale is consistent with runaway
growth described earlier. So far, isotopic data for other sil-
icate objects has not been so readily explicable in terms of
very rapid growth. However, asteroid Vesta certainly formed
within about 3 Ma of the start of the solar system (Fig. 8).
The existence of meteorites from differentiated aster-
oids suggests that core formation began early, and this is
confirmed by^182 Hf–^182 W chronometry. Therefore, most
planetary embryos would have been differentiated when
they collided with one another. Although Mars grew ex-
tremely rapidly, Earth does not appear to have reached
its current size until the giant impact that was associated
with the formation of the Moon (see Section 8).^182 Hf–^182 W
chronometry for lunar samples shows that this took place
35–50 Ma after the start of the solar system. Geochemical
evidence has been used to argue that the formation of the
Moon probably happened near the end of Earth’s accretion,
and this is consistent with the results of Moon-forming im-
pact simulations. This is also consistent with the W isotopic
composition of the silicate Earth itself (Fig. 20). This shows
that the Earth accreted at least half of its mass within the
first 3× 107 years of the solar system. However, the data
are fully consistent with the final stage of accretion being
around the time of the Moon-forming impact. Because the
Earth accreted over a protracted period rather than in a sin-
gle event, it is simplest to model the W isotope data in terms
of an exponentially decreasing rate of growth (Fig. 20).
F= 1 −e−(1/τ)×t (14)
whereFis the mass fraction of the Earth that has accu-
mulated,τ is the mean life for accretion in millions of
years (Fig. 20) andtis time in millions of years. This is
consistent with the kinds of curves produced by the late
George Wetherill who modeled the growth of the terres-
trial planets using Monte Carlo simulations. The W isotope
data are consistent with a mean life of between 10 and
FIGURE 20 The mean life of accretion of the Earth (τ)isthe
inverse of the time constant for exponentially decreasing
oligarchic growth from stochastic collisions between planetary
embryos and planets. The growth curves corresponding to
several such mean lives are shown including the one that most
closely matches the calculation made by the late George
Wetherill based on Monte Carlo simulations. The mean life
determined from tungsten isotopes (Fig. 8) is in excellent
agreement with Wetherill’s predictions.
15 Ma, depending on the exact parameters used. This is
fully consistent with the timescales proposed by Wether-
ill. From these protracted timescales, it is clear that Earth
took much longer to approach its current size than Mars or
Vesta, which probably formed from different mechanisms
(Fig. 8).
7. The Asteroid Belt
The Asteroid Belt currently contains only enough material
to make a planet 2000 times less massive than Earth, even
though the spatial extent of the belt is huge. It seems likely
that this region once contained much more mass than it
does today. A smooth interpolation of the amount of solid
material needed to form the inner planets and the gas gi-
ants would place about 2 Earth-masses in the Asteroid Belt.
Even if most of this mass was lost at an early stage, the
surface density of solid material must have been at least
100 times higher than it is today in order to grow bodies
the size of Ceres and Vesta (roughly 900 and 500 km in
diameter, respectively) in only a few million years.
Several regions of the Asteroid Belt contain clusters of
asteroids with similar orbits and similar spectral features,
suggesting they are made of the same material. These clus-
ters are fragments from the collisional breakup of larger
asteroids. There are relatively few of these asteroid fami-
lies, which implies that catastrophic collisions are quite rare.
This suggests the Asteroid Belt has contained relatively little