Bode's Law

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Bode's Law notes that the distances of the planets from the Sun follow a simple mathematical pattern. The law holds true for Mercury, Venus, Earth, the asteroids, Jupiter, Saturn, and Uranus. Neptune and Pluto are perhaps the only exceptions to this law among the eleven planetary and dwarf planetary bodies in the solar system.

Contents

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 actual values of peri- and aphelion, semi-major axis, and the Titius-Bode predicted semi-major axis for the eleven known planets and dwarf planets are shown below:

Name Perihelion Aphelion Semi-major axis Titius-Bode prediction Inclination Sidereal year
Mercury 0.307 AU 0.468 AU 0.387 AU 0.4 AU 7.005° 88 da
Venus 0.718 AU 0.728 AU 0.723 AU 0.7 AU 3.395° 225 da
Earth 0.983 AU 1.017 AU 1.0 AU 1.0 AU 365.24 da
Mars 1.381 AU 1.666 AU 1.524 AU 1.6 AU 1.851° 1.881 a
Ceres 2.545 AU 2.987 AU 2.766 AU 2.8 AU 10.587° 4.599 a
Jupiter 4.952 AU 5.455 AU 5.203 AU 5.2 AU 1.305° 11.857 a
Saturn 9.02 AU 10.05 AU 9.537 AU 10 AU 2.484° 29.458 a
Uranus 18.286 AU 20.096 AU 19.191 AU 19.6 AU 0.744° 84.07 a
Neptune 29.81 AU 30.327 AU 30.069 AU 38.8 AU 1.769° 164.88 a
Pluto 29.658 AU 49.305 AU 39.482 AU 77.2 AU 17.142° 248.09 a
Eris 37.77 AU 97.56 AU 67.668 AU 154 AU 44.187° 577 a

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

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