Why do planets form at specific distances from the sun according to Titius-Bode law?

Titius-Bode is interesting, because apparently there's no real theory behind it. It works in our solar system for all of the planets until Uranus, but Neptune, Pluto, and Kuiper Belt objects don't. "There is no solid theoretical explanation of the Titius–Bode law, but if there is one it is possibly a combination of orbital resonance and shortage of degrees of freedom: any stable planetary system has a high probability of satisfying a Titius–Bode-type relationship.

Astrophysicist Alan Boss states that it is just a coincidence, and the planetary science journal Icarus no longer accepts papers attempting to provide 'improved' versions of the law.

So I guess someone should just look up the law and paste it here.

Johann Daniel Titius (German) discovered a simple mathematical rule that closely fits the orbits of the planets in our solar system in 1776. It was published by the partially blind Johann Elert Bode in 1772. Hence the name of the law.

One of its fascinating conjectures is that it predicts a planet between Mars and Jupiter - where we have the asteroid belt. It was also formulated before the discovery of Uranus whose position it predicted. It also seems to work for moons around some planets like Saturn but fails for Jupiter's moons.

However it doesn't work too well for Neptune and Pluto. So perhaps the law is not so simple. The original law was: a = ( n + 4 ) / 10 where n = 0, 3, 6, 12, 24, 48 ... The modern version relates the mean distance of the planet from the Sun (in astronomical units) (1 AU = 147,597,000 km ) a = 0.4 + 0.3 k where k = 0, 1, 2, 4, 8, 16, 32, 64, 128 (sequence of powers of two and 0) The end results match quite well.

This simple arithmetic relationship does not explain why the planets are in these positions. The noted Journal Icarus now refuses to accept attempts to improve the arithmetical law which it holds matches by coincidence - implying the rule, if it exists, is based on more physical laws perhaps related to turbulence. Now that we are discovering extrasolar planets it may allow us to compare the planet distributions of other solar systems.

We have really only the one sample to formulate such an important rule.

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