A possible explanation for the Titus-Bode “law”.

[Igor Suman]

In Chladni figures on a circular plate, material accumulates at the nodes which can take the form of concentric circles.

 

Couldn’t a similar process have occurred in the proto-planetary disc of gas & dust ?. Vibrations from a slowly rotating, ( & precessing ?), sun sending out waves into the proto-planetary disc. This would create nodes where material would accumulate as in Chladni figures. These concentric nodes would seed planet formation and become the orbits of the planets. This could explain the geometric pattern of orbits in the Titus-Bode "law".

 

According to Wikipedia:-

"There is no solid theoretical explanation of the Titius-Bode law, and it is not known whether this is just a numerical coincidence or a more fundamental cosmological rule."

http://en.wikipedia.org/wiki/Bodes_law

 

Should I expect a telephone call from Stockholm ?

[swansont]

What waves would do this? Chladni plates are physically vibrating, creating a standing wave. IIRC the waves are integral distances, not the geometric progression of Bode's law.

[Igor Suman]

The concentric nodes in a disc of uniform thickness are equally spaced:-

 

 

The protoplanetary disc was not of uniform thickness: it would be thinner towards the edge,

producing nodes which were increasingly far apart.

[swansont]

The concentric nodes in a disc of uniform thickness are equally spaced:-

...

 

The protoplanetary disc was not of uniform thickness: it would be thinner towards the edge' date='

producing nodes which were increasingly far apart.[/quote']

 

 

So you need to model this and the effect it has, and come up with a reason you'd have a standing wave of some sort.

[Igor Suman]

Required conditions for standing waves:-

1. Medium to conduct waves.

2. A source of SHM.

3. Reflection of waves.

 

1. MEDIUM:-

The gas of the protoplanetary disc would have been tenuous, a fraction of the density of Earth’s atmosphere, but nevertheless capable of conducting pressure waves.

 

2. SHM:-

An oblate precessing sun would send out SHM waves into the protoplanetary disc.

Imagine a spinning top in the center of a child’s paddling pool with a few centimetres of water in it: the precessing top would send out SHM waves into the water.

 

3. REFLECTION:-

The edge of the protoplanetary disc would reflect any waves which reached it back to the center of the disc. This may seem anti-intuitive but it is true.

Try holding a 150cm length of rope by one end and waggling it back and forth to create waves, standing waves (nodes) will appear in the rope. The free (dangling) end of the rope must have reflected the waves for nodes to form.

The edge of the protoplanetary disc is analogous to the free end of the rope and would reflect any waves which reached it.

 

 

So the three conditions for standing waves (nodes) to exist in the protoplanetary disc are satisfied.

 

 

Should I hire "tails" from Moss Bros ?

[Igor Suman]

Here is a mechanism by which the early sun could transfer momentum to the material in the protoplanetary disc:-

http://www.spitzer.caltech.edu/Media/releases/ssc2006-15/release.shtml