The Titus-Bode Rule of planetary distances is a curiosity in the annals of astronomical observation. First proposed by Johann Titius in 1766, it was later published by Johann Bode in 1772. In simple terms, the Titius-Bode rule predicts the distances of planets from the sun according to a simple equation:

a = (n+4)/10

where a is the semi-major axis of the orbit in A.U. (Astronomical Units) and

n = 0 , 3, 6, 12, 24, 48, …

The definition of 1 A.U. = distance from the earth to the Sun. The long axis of the ellipse is called the major axis, while the short axis is called the minor axis. Half of the major axis is termed a semimajor axis. The length of a semimajor axis is often termed the size of the ellipse. It can be shown that the average separation of a planet from the Sun as it goes around its elliptical orbit is equal to the length of the semimajor axis. Thus, by the “radius” of a planet’s orbit one usually means the length of the semimajor axis.

So, for the planets and dwarf planets in our solar system:

Table of Solar System bodies

The rule seems to break down for Neptune and especially for Pluto and Eris. Some have said this oddity is mere coincidence. If so, it’s quite a big one. It follows 7 planets quite well and almost 8. Pluto is not a planet now, and does not follow the trend, nor does Eris.

It is possible that this rule is a consequence of the gravitational makeup of the solar system. Perhaps other planetary systems have a Titius-Bode rule as well. It is interesting to ponder on and simple enough for anybody to play around with. Simple equations, known numbers to compare, and many an astronomer that think it is mere coincidence. Something fundamental is here perhaps, it just hasn’t been recognized yet. Explain discrepancies in Neptune, Pluto and Eris and something important will have been revealed.

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