44 Encyclopedia of the Solar System
them. For conditions likely to exist in the solar nebula, the
net result was that each embryo lost angular momentum
and migrated inward towards the Sun. This is calledtype-I
migration.Migration rates are proportional to an embryo’s
massMand the local surface density of gasgas:
da
dt≈− 4(
M
Msun)(
gasa^2
Msun)(
vkep
cs) 2
vkep (12)wherecsis the sound speed in the gas andvkepis the orbital
velocity of a body moving on a circular, Keplerian orbit.
Type-I migration became important after embryos grew to
about 0.1 Earth masses. Migration rates can be uncomfort-
ably fast, with a 10-Earth mass body at 5 AU migrating into
the Sun in 10^5 years in a minimum-mass nebula. It is possi-
ble that many objects migrated all the way into the Sun and
were lost in this way, and the question of how other bodies
survived migration is one of the great unresolved questions
of planet formation at present.
Oligarchic growth in the inner solar system ended when
embryos had swept up roughly half of the solid material.
However, these embryos were still an order of magnitude
less massive than Earth. Further collisions were necessary
to form planets the size of Earth and Venus. With the re-
moval of most of the planetesimals, dynamical friction weak-
ened. As a result, interactions between embryos caused
their orbits to become more inclined and eccentric. The
embryos’ gravitational focusing factors became small, and
this greatly reduced the collision rate. As a result, the last
stage of planet formation was prolonged, and the Earth may
have taken 100 Ma to finish growing.
Embryos underwent numerous close encounters with
one another before colliding. Each encounter changed an
embryo’s orbit, with the result that embryos moved con-
siderable distances radially in the nebula. Numerical cal-
culations show that the orbital evolution must have been
highly chaotic (Fig. 18). As a result, it is impossible to pre-
dict the precise characteristics of a planetary system based
on observations of typical protoplanetary disks. Other stars
with nebulas similar to the Sun may have formed terres-
trial planets that are very different from those in the solar
system.
The radial motions of embryos partially erased any chem-
ical gradients that existed in the nebula during the early
stages of planet formation. Mixing cannot have been com-
plete however because Mars and Earth have distinct com-
positions. Mars is richer in the more volatile rock-forming
elements, and the two planets have distinct oxygen isotope
mixtures. Unfortunately, we have no confirmed samples of
Mercury and Venus, so we know little about their com-
position. Mercury is known to have an unexpectedly high
density, suggesting it has a large iron-rich core and a small
mantle. This probably does not reflect compositional differ-
ences in the solar nebula because there is no known reason
why iron-rich materials would preferentially form closer to
FIGURE 18 Four artificial planetary systems generated by
numerical simulations of planetary accretion. Each horizontal
row of symbols represents one planetary system, with symbol
radius proportional to planetary radius, with the largest objects
similar in size to the Earth. The shaded segments show the
composition of each planet in terms of material that originated in
four different portions of the nebula. Planets in these simulations
typically contain material from many regions of the nebula. The
row of gray symbols shows the terrestrial planets of the solar
system for comparison.the Sun than silicate materials. A more likely explanation
is that Mercury suffered a near-catastrophic impact after
it had differentiated, and this stripped away much of the
silicate mantle. Mercury’s location close to the Sun made it
especially vulnerable in this respect because orbital veloci-
ties and hence impact speeds are highest close to the Sun.
Earth and Venus are probably composites of ten or more
embryos so their chemical and isotopic compositions rep-
resent averages over a fairly large region of the inner solar
system. Mars and Mercury are sufficiently small that they
may be individual embryos that did not grow much beyond
the oligarchic growth stage. It is currently a mystery why
Earth and Venus continued to grow while Mars did not.
It may be that Mars formed in a low-density region of the
nebula or that all other embryos were removed from that
region without colliding with Mars.
As embryos grew larger, their temperatures increased
due to kinetic energy released during impacts and the de-
cay of radioactive isotopes in their interiors. Short-lived iso-
topes such as^26 Al and^60 Fe, with half-lives of 0.7× 106
and 1.5× 106 years, respectively (Table 1), were particu-
larly powerful heat sources early in the solar system. Bodies
more than a few kilometers in radius would have melted if
they had formed within the first 2 Ma when the short-lived
isotopes were still abundant. Embryos that melted also dif-
ferentiated, with iron and siderophile elements sinking to
the center to form a core, while lighter silicates formed a
mantle closer to the surface.