Interlude 6-1

INTERLUDE 6-1 The Titius—Bode "Law"

A close look at the list of semi-major axes of the known planets (see Table 6.1) reveals considerable regularity in their orbits. The spacing of the orbits increases more or less geometrically as we move out from the Sun: at any point in the list, the distance to the next planet out is about twice that to the next planet in.

Is there some underlying structure to the solar system? In 1766, in search of an answer to that question, the German astronomer Johann Titius came up with a simple formula that "predicted" quite well the orbits of the then-known planets, Mercury through Saturn. Johann Bode, a better-known astronomer of the day, later popularized this relationship among the planets' orbits, so that it now is usually known as the Titius—Bode law, or even just Bode's law. We must emphasize that it is not a law at all, in the scientific sense, but rather just a rule for determining the approximate orbital semi-major axes of the planets. Nevertheless, the "law" part of the name has stuck.

The rule for determining the planets' orbits is as follows. Start with 0.4, the distance (in A.U.) from the Sun to Mercury. Then add to it, successively, 0.3 (to arrive at Venus, with an orbital semi-major axis of 0.7 A.U.), 0.3 (to reach Earth, at 1.0 A.U.), 0.6 (Mars: 1.6 A.U.), 1.2 (—: 2.8 A.U.), 2.4 (Jupiter: 5.2 A.U.), and 4.8 (Saturn: 10.0 A.U.) to arrive at the (approximate) orbital distances of the known planets, plus one extra "planet" between Mars and Jupiter. The relation between

successive orbits is easily seen—after Venus, the added term (that is, the interplanetary spacing) simply doubles at each step. Even the fictitious extra "planet" is acceptable—it corresponds to the middle of the asteroid belt! Thus it was that this rule appeared to contain some deep insight into our planetary system.

The test of any theory is its predictive power. According to the Titius—Bode rule, the next three planets beyond Saturn should lie at 19.6, 38.8, and 77.2 A.U. When Uranus was discovered in 1781, it fell close to the prediction, at 19.2 A.U. Speculation was rife that the next planet would also lie where the "law" decreed it should. Sadly, the rule fails for Neptune, which lies only 30 A.U. from the Sun. However, if we ignore Neptune, Pluto is in just about the right place!

Few people today take the rule sufficiently seriously to bother to look for a scenario in which Neptune started out in the "right" orbit and somehow got moved farther in toward the Sun, perhaps leaving Pluto behind. Still, the regularity of the "law" was appealing to astronomers of the eighteenth and nineteenth centuries, as it suggested some fundamental harmony in the structure of the solar system, and, to some extent, that appeal remains today.

The Titius—Bode rule is not the result of any known planetary interaction, nor is it even very accurate. Yet many astronomers suspect that it may be telling us something about the formation of the solar system—they just don't know quite what.