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Titius-Bode law

(Titius-Bode rule, Bode's law)
(relationship between the distances between solar system planets)

The Titius-Bode law (or Titius-Bode rule or Bode's law) is an observed relationship between the semi-major axes of the solar system planets. It is now generally considered a coincidence. As a formula:

a = 2n × 3 + 4

The relationship was conceived in the 1700s when all the known planets, i.e., through Saturn, fit the pattern (within perhaps 5%) excepting one gap between Mars and Jupiter, and the subsequent discovery of Ceres (at the time considered a planet, currently considered the one asteroid that qualifies as a dwarf planet) filled the gap. Uranus also fit the pattern, and in fact, a planet with Uranus's orbit was predicted on the basis of the relation. But Neptune's orbit did not fit, being more like 20% away from the prescribed position.

The law is now considered a coincidence and curiosity, though it is occasionally contemplated when new planets or planet systems are uncovered. Perhaps the closest it comes to relevance is that stable orbits of significant bodies in a system must be spaced out to some degree.

Further reading: