16
2 Aggregation
mechanisms to be far more complicated (see, e.g., Thommes, 2008). There is certainly a clear difference between the formation of gas giants, Jupiter and Saturn, on
the one hand, and stony terrestrial planets, on the other. The former condense from
gas clouds, mostly hydrogen and helium, in the outer reaches of the protoplanetary
disk in a manner similar to star formation, but they are too small on the stellar scale,
and fail to ignite nuclear reactions. The material building up inner terrestrial planets is of another sort, comprising dust and small particles, rich in heavier elements.
The difficulties in understanding the development of planetary systems are exacerbated by lack of evidence: there is only a single example open for study (and only
by observation rather than experiment). It is likely that the majority of stars have
planets, some of them, mostly gas giants, already detected, but there is little hope of
obtaining elucidating information from faraway stars, unless we may consult alien
astrophysicists, if such are ever found.
Gravitation has little effect on dust and small particles but they are apt to collide in a turbulent mass of debris rotating with different speeds. Some of them stick
together and are further compacted. Gravity becomes an important factor for planetesimals grown to about a kilometer in size, which will start aggressively accreting
smaller chunks. The situation becomes violent when collisions involve larger protoplanets – these are even called “oligarchs”, a reference to post-communist nouveaux
riches competing with similar abandon. Just such a collision between Earth and a
Mars-size planet caused our Moon to be born. Then, in a hundred or so million
years everything quietened down in our neighborhood, or almost so. Two asteroid belts remain, one placed between the regions of the gaseous and stony planets,
where planetesimals failed to aggregate, being perturbed by Jupiter, and another at
the outskirts of the Solar System.
Is it just a chance arrangement that we observe in the only planetary system we
know in detail? Probably so. The space within a few billion kilometers around the
Sun, and very likely of other stars, is full of bits and pieces of all kinds and sizes
(Fig. 2.3, right), occasionally bumping into mature planets, sometimes with dire
consequences, like the meteorite that wiped out the dinosaurs and another that may
wipe us out, unless we are vigilant enough to detect and deflect it. In the long run, as
mathematicians have proved, the entire planetary system is unstable, being driven
to chaos by small perturbations due to gravitational interactions between rotating
bodies, large and small. Thankfully, this “Arnold diffusion” acts on a time scale far
exceeding the lifespan of the Sun, but in binary stellar systems, instabilities develop
much faster, so it is unlikely that life could evolve there.
While we can only observe the motion of planets, asteroids, and comets and
speculate on their past and future, the aggregation of small particles can be studied
in the laboratory. It is best done in quiet conditions, in a suspension of colloidalsize particles sticking to each other as the suspension coagulates (Fig. 2.4, left).
When coagulation is fast, the structure is ramified, with branches protruding into
the surrounding fluid. There is a good reason for this, which is also important on a
molecular scale when crystals grow (Sect. 3.6): a branch protrudes in the direction
of supply of diffusing particles. With time, the structure becomes more compact, as
coagulated particles attract each other, and if aggregation is slow, a branched struc-
2 Aggregation
mechanisms to be far more complicated (see, e.g., Thommes, 2008). There is certainly a clear difference between the formation of gas giants, Jupiter and Saturn, on
the one hand, and stony terrestrial planets, on the other. The former condense from
gas clouds, mostly hydrogen and helium, in the outer reaches of the protoplanetary
disk in a manner similar to star formation, but they are too small on the stellar scale,
and fail to ignite nuclear reactions. The material building up inner terrestrial planets is of another sort, comprising dust and small particles, rich in heavier elements.
The difficulties in understanding the development of planetary systems are exacerbated by lack of evidence: there is only a single example open for study (and only
by observation rather than experiment). It is likely that the majority of stars have
planets, some of them, mostly gas giants, already detected, but there is little hope of
obtaining elucidating information from faraway stars, unless we may consult alien
astrophysicists, if such are ever found.
Gravitation has little effect on dust and small particles but they are apt to collide in a turbulent mass of debris rotating with different speeds. Some of them stick
together and are further compacted. Gravity becomes an important factor for planetesimals grown to about a kilometer in size, which will start aggressively accreting
smaller chunks. The situation becomes violent when collisions involve larger protoplanets – these are even called “oligarchs”, a reference to post-communist nouveaux
riches competing with similar abandon. Just such a collision between Earth and a
Mars-size planet caused our Moon to be born. Then, in a hundred or so million
years everything quietened down in our neighborhood, or almost so. Two asteroid belts remain, one placed between the regions of the gaseous and stony planets,
where planetesimals failed to aggregate, being perturbed by Jupiter, and another at
the outskirts of the Solar System.
Is it just a chance arrangement that we observe in the only planetary system we
know in detail? Probably so. The space within a few billion kilometers around the
Sun, and very likely of other stars, is full of bits and pieces of all kinds and sizes
(Fig. 2.3, right), occasionally bumping into mature planets, sometimes with dire
consequences, like the meteorite that wiped out the dinosaurs and another that may
wipe us out, unless we are vigilant enough to detect and deflect it. In the long run, as
mathematicians have proved, the entire planetary system is unstable, being driven
to chaos by small perturbations due to gravitational interactions between rotating
bodies, large and small. Thankfully, this “Arnold diffusion” acts on a time scale far
exceeding the lifespan of the Sun, but in binary stellar systems, instabilities develop
much faster, so it is unlikely that life could evolve there.
While we can only observe the motion of planets, asteroids, and comets and
speculate on their past and future, the aggregation of small particles can be studied
in the laboratory. It is best done in quiet conditions, in a suspension of colloidalsize particles sticking to each other as the suspension coagulates (Fig. 2.4, left).
When coagulation is fast, the structure is ramified, with branches protruding into
the surrounding fluid. There is a good reason for this, which is also important on a
molecular scale when crystals grow (Sect. 3.6): a branch protrudes in the direction
of supply of diffusing particles. With time, the structure becomes more compact, as
coagulated particles attract each other, and if aggregation is slow, a branched struc-