Titius-Bode law, any analytical or numerical derivation?

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They say this is just by chance. But maybe some bright spark has come up with a mathematical derivation for it?

Alternatively, what about simulating the cloud of the early solar system on a computer. Would the Titius-Bode pattern of the planet distances arise?

Here's the law:

http://en.wikipedia.org/wiki/Titius-Bode_law
 

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They say this is just by chance. But maybe some bright spark has come up with a mathematical derivation for it?

Alternatively, what about simulating the cloud of the early solar system on a computer. Would the Titius-Bode pattern of the planet distances arise?

Here's the law:

http://en.wikipedia.org/wiki/Titius-Bode_law
The law relates the semi-major axis, a, of each planet outward from the sun in units such that...For the outer planets, each planet is 'predicted' to be roughly twice as far away from the Sun as the next inner object.

The four large satellites of Jupiter plus the largest inner satellite — Amalthea — adhere to a regular, but non-Bode, spacing with the four innermost locked into orbital periods that are each twice that of the next inner satellite.



this means that every third moon is twice as far away.
 
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Its among the more interesting things to say, read in history since there is a mystic code revealed behind the planetary distances.

Two or three last planets like Pluto don't match the pattern - fortunately now they're not considered planets.

Most likely its not a "law" but more like regularity that emerged from some other law - gravitational waves or waves of density of matter when system was formed.

More interesting reading:
- tidal waves
- gravitational resonance
- proof that Saturn's rings can not be solid
 
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gravitational waves or waves of density of matter when system was formed.
Gravitational waves? What are these? You mean the waves of density? How can there be waves of density in space?
 
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Gravitational waves

Gravitational waves? What are these? You mean the waves of density? How can there be waves of density in space?
he means like the spiral arms of a galaxy.
 
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Gravitational waves? What are these? You mean the waves of density? How can there be waves of density in space?
Now that you specified that expression and repeated it in public, I must add that "gravitational waves" don't entirely exist... they're still theoretical. Anyway that would be too weak in our solar system. The expression reminds me of something that can have a resonance and wave patterns - but I imagined that.

Waves of density are sound waves for example. Planets appear to be in order of larger and larger masses that differentiated from one cloud. Explosion is a wave no? Am I making impact?
 
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Am I making impact?
Not really, but thanks for the comments, they seem to come from an inventive mind and I appreciate that.
 
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Titus-Bode type of laws have been discussed in two papers by Graner & Dubrulle in Astronomy and Astrophysics, available to anyone on ADS. At ADS you can find many papers actually on the Titius-Bode law (note the "i" in Titius!) and here is the list.
 
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Thanks. I noticed this:

"The question of whether the observed patterns have some physical basis or are due to chance may be addressed using a Monte Carlo approach."

Monte Carlo sounds like repeating many times the simulation of the formation of the planets. I wonder if that's what is done here:

http://esoads.eso.org/abs/2003MNRAS.341.1174L
 
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Thanks. I noticed this:

"The question of whether the observed patterns have some physical basis or are due to chance may be addressed using a Monte Carlo approach."

Monte Carlo sounds like repeating many times the simulation of the formation of the planets. I wonder if that's what is done here:

http://esoads.eso.org/abs/2003MNRAS.341.1174L
Guess you will have to read the paper and find out. (full scanned article (GIF))
 
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Actually, the paper by Lynch is very interesting, because it shows that you cannot e.g. just use "a Monte Carlo procedure" to test whether a distribution is chance or not. Even if they do not show whether TB is real or not, it does make a good wake up call for researchers to think about what exactly they want to test. A continuation of this paper is done by Neslušan, which you can find here.

Also, after Graner & Dubrulle it should not come as a big surprise that Li et al. find something in their calculations that resembles a kind of Titius-Bode law.
 
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Kepler and Newton are like a story of how things become cosmology by observation, research and thought. Today the natural laws are less of an experience but then, Newton's las became a universal law, shown to rule far out into space in same way.
Today Kepler's laws are even wrong and he became known for a famous wrong question: why are there 6 planets? All of you believe it is just a coincidence. Kepler's solution was geometrical assembly of platonic solids - I don't know how many of those exist but now there's a 3D printer that can capture interest for experiments. Throwing rocket into orbit would be an experiment that makes sense however.
 
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Isn't it obvious looking at the saturn's rings that there are geometric progressions in thickness and distance of the rings - as well as some little degree of spiralness?
 

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