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<   No. 530   2004-07-09   >

1 Iki Piki: {looking out the bridge windows to a giant ringed planet} Okay, starting our survey of this new planetary system.
2 Serron: It looks like the orbits are spaced according to some sort of geometric progression...
3 GM: {inexplicably and unreasonably excited} I used Titius' Law to generate the orbital parameters of the planets.
4 Spanners: Hmm. That doesn't Bode well.

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Johann Daniel Titius was a German astronomer who in 1766 first formulated a "law" that seemed to govern the relationship between the orbital distances of all the planets then known. Johann Elert Bode published this "law" in 1772, without attributing it to Titius. It later became known as Bode's Law, but is now commonly referred to as the Titius-Bode Law, reinstating credit for Titius.

The "law" itself says that the orbital distances of the planets follow a pattern given by the formula

d = 0.4 + 0.3×k
where k takes the values 0, 1, 2, 4, 8, 16, 32, 64, 128, ... (0, followed by 1, then each subsequent number being double the previous number).

This sort of works for Mercury, Venus, Earth, and Mars. The asteroid belt orbits roughly at the next expected distance, and beyond that the sequence seems to fit reasonably well for Jupiter, Saturn, and Uranus. Neptune does not fit at all, and Pluto's mean orbital distance is roughly where Neptune's "should" be according to the sequence.

In other words, and contrary to what some people have been led to believe, the Titius-Bode Law doesn't work and is not an established law of nature. There may well be some sort of mathematical relationship between the orbits of planets that form in a system, but if so it's more complicated than Titius-Bode and remains to be discovered.

Image of Saturn is Courtesy of NASA/JPL-Caltech.

2013-07-09 Rerun commentary: Orbital resonances and gravitational effects sort of do imply that the spacing of planets should increase as you go further out from the star, so some sort of simple geometrical sequence like Titius-Bode should give a roughly approximate sort of fit to the orbits. The details are a little more complicated and there is some leeway in the exact positions, so no regular formula is ever going to be perfect. So we end up with what we have, a rough fit with some big outliers.

Despite this, it's not a terrible model for certain things like fictional solar systems in science fiction game settings. In fact GURPS Space, the book I am holding in this comic, specifically uses such a system to design solar systems for use in games.

I've written more about the Titius-Bode law much more recently.

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