Titius-Bode Law

The Titius-Bode Law states that the distances of the major satellites of the Sun follow a definite exponential pattern. It was, until the discovery of Neptune, held to be a valid predictor of the positions of the planets. Neptune is perhaps the only exception to this law among the eleven planetary and dwarf planetary bodies in the solar system, but that one exception has convinced mainstream astronomers to reject the law as invalid. But a small number of contrarian astronomers, including at least one creationist, now suggest that the law ought to stand after all.

The Formula
The classical formula for the Titius-Bode Law is:

$$D = \frac{A+4}{10}$$

where D is the semi-major axis measured in AU (that is, multiples of Earth's semi-major axis) and

$$A = 3\cdot2^{n-1}$$

where n = 1 for Venus, 2 for Earth, and so on. (In the special case of Mercury, A = 0.)

Predictive value
The semi-major axes of the first seven classical planets, and the dwarf planet Ceres, approximate the values that the Titius-Bode Law predicts very closely. Indeed the Titius-Bode Law aided directly in the discovery of Ceres. Furthermore, the discovery of Uranus was held to validate this law, because the formulation of this law, and its prediction of the semi-major axis of a planet beyond Saturn, anticipated the discovery of Uranus--the semi-major axis of which was very close to the value that the Titius-Bode Law predicted.

Beginning with Neptune, however, the semi-major axes fall well short of the Titius-Bode Law. Yet the table still shows an interesting pattern, in that the semi-major axes of Pluto and Eris are barely less than one-half the distances predicted by the Titius-Bode Law. Moreover the aphelion of Eris is almost double that for Pluto.

But a closer inspection of the distances for the last three planets reveals another interesting pattern: Pluto's orbit is very close to where Neptune's orbit ought to be--and Eris's orbit is less than 10 AU short of where Pluto's orbit ought to be.

Discussion
Technically, Neptune, Pluto, and Eris are in violation of the Titius-Bode Law. Remarkably, however, that law holds for all of the planets (plus the dwarf planet Ceres) inside of Neptune. And in the case of Pluto and Eris, those "violations," such as they are, are remarkably "regular." These are not the numbers of the random assortment of distances that one would expect from the nebula hypothesis of the formation of the sun and its satellites. Rather, these numbers suggest a catastrophic event in the distant past that altered the orbit of Neptune and either (a) also altered the orbits of Pluto and Eris, or else (b) injected those two dwarf planets into orbits that, while violative of the Titius-Bode Law, were nevertheless semi-regular. That the orbits of Pluto and Eris are the most steeply inclined of all the orbits of the satellites of the Sun (except for comets) is further suggestive evidence of catastrophe.

Conclusion
The Titius-Bode Law did not survive mainstream scrutiny, primarily because most astronomers regarded the more-inward position of Neptune as a fatal counterexample to it. But since that event, the scientific community has seen the discoveries, decades apart, of Pluto and Eris. These two dwarf world have vastly inclined and highly eccentric orbits that, nevertheless, have positions that would almost seem to conform to the Titius-Bode Law were Neptune not present. Findings like these cast doubt on the earlier decision to abandon this Law and suggest an alternative explanation: that God in fact set the planets in their orbits according to this Law, but a subsequent cataclysmic event or sequence significantly altered the elegant mathematical pattern of the outer reaches of the solar system.

Reference

 * Bishard, Clint. "Order in the Orbits: Our Mathematically Minded Creator." , January 13, 2007. Accessed January 24, 2008.

Lei de Titius-Bode