Fractal Planets, Real

We may owe our lives to fractals

Experience with growth models suggested to physicists David Peak and Burt Donn that Diffusion Limited Aggregation (DLA) could mediate the growth at some early (and small) stage of development.

Instead of forming hard grains of sand, the dust motes diffuse through the cloud and form wispy, filamentary fractal dust balls.

Physical measurements of DLA clusters in 3-dimensional space suggest the dust balls should have mass dimension about 2.5, so

mass = radius^2.5

Yet the dust ball sweeps out a space with volume = radius³

So density = mass/volume = radius^2.5/radius³ = 1/radius^0.5

That is, the larger the dust ball, the more tenuous it is. This has two consequences, helpful for the formation of planets.

* The paths of these large dust balls are slowed by friction against the gas cloud, guaranteeing the relative speed of interaction is much smaller than the Keplerian orbital speed.

Consequently, these fractal wisps can collide and stick together, forming larger wisps.

* When large enough wisps collide, there can be some restructuring, melting at the collision sites.

Larger and larger cosmic dust balls colliding will experience more restructuring, more melting and compacting. Eventually these will form solid objects, planetisimals. If the transition from fractal to rock occurs when the resulting rock is large enough to grow by gravitationally accreting other stuff from the gas and dust cloud, then the rest of the standard model can be applied. That is, fractals may provide the transition between dust motes and planetisimals.

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