42 Encyclopedia of the Solar System
FIGURE 16 The lifetime of solid particles orbiting at 1 AU
from the Sun in the minimum-mass solar nebula when the
particles drift inward due to gas drag. Drift rates are fastest for
meter-sized particles, which are lost in a few hundred years
unless they rapidly grow larger.
The short drift lifetimes and high collision speeds expe-
rienced by meter-sized particles have led some researchers
to conclude that particle growth stalled at this size because
particles were destroyed as fast as they formed. This is often
referred to as the meter-sized barrier. This remains an open
question however, due to a shortage of experimental data
regarding the physics of collisions in a microgravity envi-
ronment and uncertainty about the level of turbulence in
the solar nebula.
The presence of nebular gas was not entirely detrimen-
tal to growth. Experiments have shown that gas drag can
reduce the effect of destructive impacts onto boulder-sized
bodies, as collision fragments become entrained in the gas
and blown back onto the surface of the larger body. Nu-
merical simulations also show that chondrule-sized particles
would be strongly concentrated in stagnant regions in a tur-
bulent nebula, a process calledturbulent concentration,
thus increasing the chance of further growth.
Bodies larger than 1 km generally took a long time
to drift inward due to gas drag. These objects were also
large enough to have appreciable gravitational fields, mak-
ing them better able to hold on to fragments generated in
collisions. For these reasons, growth became easier once
bodies became this large. Much effort has been devoted to
seeing whether kilometer-sized bodies could have formed
directly, avoiding the difficulties associated with the meter-
sized barrier.Gravitational instability(GI) offers a pos-
sible way to do this. If the level of turbulence in the nebula
was very low, solid particles would have settled close to the
nebula midplane, increasing their local concentration. Ra-
dial drift of particles may also have concentrated particles
at a particular location. If enough particles became concen-
trated in one place, their combined gravitational attraction
would render the configuration unstable, allowing the re-
gion to become gravitationally bound and collapse. If the
particles were then able to contract enough to form a single
solid body, the resulting object would be roughly 1–10 km
in radius. Such an object is called aplanetesimal.
Gravitational instability faces severe obstacles however.
As solid particles accumulated near the nebula midplane,
they would have begun to drag gas around the Sun at Ke-
plerian speeds, while gas above and below the midplane
continued to travel at sub-Keplerian speeds. The velocity
difference between the layers generated turbulence, puff-
ing up the particle layer until a balance between vertical
sedimentation and turbulence was reached. This balance
may have prevented particle concentrations from becom-
ing high enough for GI to occur. Calculations suggest that
the solid-to-gas ratio in a vertical column of nebula material
had to become roughly unity before GI would take place.
This means that the concentration of solid material had to
become enhanced by 1–2 orders of magnitude compared
to the nebula as a whole. If a region of the disk did start to
undergo GI, it would only contract to form a planetesimal if
the relative velocities of the particles in that region became
low enough. Turbulence and radial drift both lead to large
relative velocities between particles and may have rendered
GI ineffective.
The difficulties associated with both the meter-sized bar-
rier and gravitational instability mean that the question of
how planetesimals formed remains open for now. However,
the fact that roughly half of young stars have debris disks
of dust thought to come from asteroids and comets implies
that growth of large solid bodies occurs in many protoplan-
etary disks, even if the mechanism remains obscure.6. Formation of Terrestrial Planets
The growth of bodies beyond 1 km in size is reasonably
well understood. Gravitational interactions and collisions
between pairs of planetesimals dominate the evolution from
this point onward. A key factor in determining the rate of
growth isgravitational focusing. The probability that two
planetesimals will collide during a close approach depends
on their cross-sectional area multiplied by a gravitational
focusing factorFg:Fg= 1 +v^2 esc
vrel^2(8)wherevrelis the planetesimals’ relative velocity, andvescis
the escape velocity from a planetesimal, given byvesc=√
2GM
r(9)whereMandrare the planetesimal’s mass and radius, re-
spectively. When planetesimals pass each other slowly, there