A mathematical formula which generates, with a fair amount of
accuracy, the semimajor axes of the planets in order out from the
Sun. Write down the sequence
0, 3, 6, 12, 24, ...
and add 4 to each term:
4, 7, 10, 16, 28, ...
Then divide each term by 10. This leaves you
with the series
0.4, 0.7, 1.0, 1.6, 2.8, ...
which is intended to
give you the semimajor axes of the planets measured in
Bode's law had no theoretical justification when it was first
introduced; it did, however, agree with the soon-to-be-discovered
planet Uranus' orbit (19.2 au actual; 19.7 au predicted).
Similarly, it predicted a missing planet between Mars and Jupiter,
and shortly thereafter the asteroids were found in very similar
orbits (2.77 au actual for Ceres; 2.8 au predicted). The series,
however, seems to skip over Neptune's orbit. The form of Bode's
law (that is, a roughly geometric series) is not surprising,
considering our theories on the formation of solar systems, but
its particular formulation is thought of as coincidental.