The Origin of the Solar System 41
Supernovas are sufficiently energetic that they could tear
apart a molecular cloud core rather than cause it to collapse.
Shocks waves with a velocity of at least 20–45 km s−^1 are
capable of triggering collapse, but if the velocity exceeds
∼100 km s–^1 , a molecular cloud core will be shredded in-
stead. If the supernova was sufficiently far away, the shock
wave would have slowed by the time it reached the molec-
ular cloud core. However, the supernova cannot have been
more than a few tens of parsecs away; otherwise,^41 Ca (with
a half life of only 0.104× 106 years) would have decayed
before it reached the solar nebula. The former presence
of^41 Ca in CAIs may provide the best constraint on the
time between nucleosynthesis of the short-lived isotopes
and their incorporation into the solar system. To do this, it
will be necessary to ascertain the particular stellar source(s)
that gave rise to these isotopes, so that the initial amount of
(^41) Ca can be calculated.
5. Early Stages of Planetary Growth
Dust grains are a relatively minor constituent of protoplan-
etary disks, but they represent the starting point for the for-
mation of rocky planets like Earth, and possibly also gas-rich
planets like Jupiter. These grains are small, typically 1μm
in diameter or less. In a microgravity environment, elec-
trostatic forces dominate interactions between such grains.
Charge transfer during grain collisions can lead to the for-
mation of grain dipoles that align with one another forming
aggregates up to several centimeters in size. Freshly de-
posited frost surfaces make grains stickier and increase the
ability of grain aggregates to hold together during subse-
quent collisions.
Laboratory experiments show that low-velocity collisions
between grains tend to result in sticking, while faster col-
lisions often cause grains to rebound. Irregularly shaped
micron-sized grains often stick to one another at collision
speeds of up to tens of meters per second. Fluffy aggre-
gates may stick more readily than compact solids as some of
the energy of impact goes into compaction. However, the
primary components of chondritic meteorites are compact
chondrules, so further compaction cannot have played a
big role in the formation of their parent bodies. In general,
sticking forces scale with the surface area of an object, while
collisional energy scales with mass and hence volume. As
a result, growth becomes more difficult, and breakup be-
comes more likely, as aggregates become larger. It is possi-
ble that early growth in the solar nebula took place mainly as
the result of large objects sweeping up smaller ones. This
idea is supported by recent experiments that found that
small dust aggregates tend to embed themselves in larger
ones if they collide at speeds above about 10 m/s.
Dust grains, grain aggregates, and chondrules would
have been closely coupled to the motion of gas in the so-
lar nebula. The smallest particles were mainly affected by
Brownian motion—collisions with individual gas molecules,
which caused the particles to move with respect to one an-
other, leading to collisions. Particles also settled slowly to-
ward the disk’s midplane due to the vertical component of
the Sun’s gravitational field. Settling was opposed by gas
drag so that each particle fell at its terminal velocity:vz=−(
ρ
ρgas)(
vkep
cs)(
rz
a^2)
vkep (5)whererandρare the radius and density of the particle,ρgas
is the gas density,ais the orbital distance from the Sun,z
is the height above the disk midplane, andcsis the sound
speed in the gas. Herevkepis the speed of a solid body
moving on a circular orbit, called theKeplerian velocity:vkep=√
GMsun
a(6)whereMsunis the mass of the Sun. Large particles fell faster
than small ones, sweeping up material as they went, in-
creasing their vertical speed further. Calculations show that
micron-sized particles would grow and reach the midplane
in about 10^3 –10^4 orbital periods if these were the only pro-
cesses operating.
If the gas was turbulent, particles would have become
coupled to turbulent eddies due to gas drag. Particles of
a given size were coupled most strongly to eddies whose
turnover (rotation) time was similar to the particle’s stop-
ping time, given byts=ρr
ρgascs(7)Meter-sized particles would have coupled to the largest
eddies, with turnover times comparable to the orbital pe-
riodP.In a strongly turbulent nebula, meter-sized particles
would have collided with one another and with smaller par-
ticles at high speeds, typically tens of meters per second.
Gas pressure in the nebula generally decreased with dis-
tance from the Sun. This means gas orbited the Sun more
slowly than solid bodies, which moved at the Keplerian ve-
locity. Large solid bodies thus experienced a headwind of
up to 100 m/s. The resulting gas drag removed angular mo-
mentum from solid bodies, causing them to undergo radial
drift toward the Sun. Small particles withtsPdrifted
slowly at terminal velocity. Very large objects withtsP
were only weakly affected by gas drag and also drifted slowly.
Drift rates were highest for meter-sized bodies withts ̃P
(see Fig. 16), and these drifted inward at rates of 1 AU ev-
ery few hundred years. Rapid inward drift meant that these
bodies collided with smaller particles at high speeds. Rapid
drift also meant that meter-sized objects had very short life-
times, and many were probably lost when they reached the
hot innermost regions of the nebula and vaporized.