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Titius-Bode Law or Rule is the observation that orbits of planets in the solar system follow a simple arithmetic rule quite closely.
It was discovered in 1766 by Daniel Titius and "published" in 1772 by Johann Elert Bode, thus the name.
It states that the mean distance a of the planet from the Sun is in astronomical units:
a=0.4 + 0.3*k
where k=0,1,2,4,8,16,32,64,128 (sequence of powers of two and 0)
Here are the distances of planets calculated from this rule and compared with real ones:
| Planet | n | T-B rule distance | Real distance |
|---|---|---|---|
| Mercury | 0 | 0.4 | 0.39 |
| Venus | 1 | 0.7 | 0.72 |
| Earth | 2 | 1.0 | 1.00 |
| Mars | 4 | 1.6 | 1.52 |
| - | 8 | 2.8 | - |
| Jupiter | 16 | 5.2 | 5.20 |
| Saturn | 32 | 10.0 | 9.54 |
| Uranus | 64 | 19.6 | 19.2 |
| Neptune | - | - | 30.1 |
| Pluto | 128 | 38.8 | 39.5 |
We can see that there are two exceptions:
- There is no planet between Mars and Jupiter. However there exists the Asteroid Belt between Mars and Jupiter. (The first Asteroid. Ceres being discovered by Piazzi in 1801 with a mean distance of 2.77 a.u.)
- There is no place for Neptune However we believe that something strange happened to the last three planets of the solar system, perhaps a passage of a large mass close to the system (see Nemesis). This is just a hypothesis.
Here is a plot of this law against real planet distances: http://rozeta.com.pl/~jochym/tblaw.png
There is no solid theoretical explanation of the Titius-Bode law, and we do not know if this is just a numerical coincidence or a more fundamental cosmological rule.
Currently the most likely explanation is that orbital resonance from major orbiting bodies create regions around the Sun that is free of long-term stable orbits. Results from simulation of planetary formation seem to support that laws like the Titus-Bode law indeed is a natural consequence of planetary formation, according to the current theories in this area.
Recent discoveries of extrasolar planetary systems also indicate that some form of this rule may be present universally, but the evidence is still too weak to draw any strong conclusions.