Johann Titius, a German astronomer, discovered a numerical relationship describing the relative distances of the then-known planets from the sun. Another German astronomer, Johann Bode, popularized the relationship and, as is often the way of science, became associated with it. It is often called Bode's law; occasionally, Titius-Bode law. The semimajor axes of the orbits of the planets follow the relationship:

a = 0.4 + 0.3 x 2ⁿ

where a is the semimajor axis is astronomical units (AU) and n takes values minus infinity, 1,2,3, etc.

This was strictly a numerological relationship and, to this day, has resisted compelling physical rationale. The value for n=3, 2.8 AU, corresponds to the location of the asteroid belt, and gives mild support for the hypothesis that the asteroids come from a failed or exploded planet.

The first test of the law occurred a few years later (1781) when William Herschel discovered Uranus --- at the distance predicted by the relationship. Neptune, the next planet to be discovered, is much closer to the Sun than predicted by the law. Pluto occupies the n=8 position instead. Another oddity is that the first term in the relationship is minus infinity rather than, say, zero. This suggests that the underlying physical law is somewhat different than the current form.

Recently, the first planets outside our Solar System have been discovered orbiting pulsars (the central stars of which are neutron stars). It appears that these planets also obey the Titius-Bode law. Some other solar systems don't seem to follow this "law", but only some of the planets in these systems have been discovered.

It is interesting that this simple relationship has been known for over 300 years but still defies physical proof (or disproof).