Information about Titius Bode Law

The Titius-Bode law (sometimes termed just Bode's law) is a hypothesis that the semi-major axes of planets in the solar system follow a simple rule. It was discredited with the discovery of Neptune in 1846.

History

It was proposed in 1766 by Johann Daniel Titius and "published" without attribution in 1772 by the director of the Berlin Observatory, Johann Elert Bode, thus the name. However, some sources say it was first proposed by Christian Wolff in 1724.

As originally stated by Titius, the "law" relates the semi-major axis, a, of each planet outward from the sun in units such that the Earth's semi-major axis = 10, with

where n = 0, 3, 6, 12, 24, 48 ..., with each value of twice the previous value; the resulting values can be divided by 10 to convert them into astronomical units (AU). For the outer planets, each planet is 'predicted' to be roughly twice as far away from the Sun as the next inner object.

When originally published, the law was approximately satisfied by all the known planets — Mercury through Saturn — with a gap between the fourth and fifth planets. It was regarded as interesting, but of no great importance until the discovery of Uranus in 1781 which happens to fit neatly into the series. Based on this discovery, Bode urged a search for a fifth planet. Ceres, the largest object in the asteroid belt, was found at Bode's predicted position in 1801. Bode's law was then widely accepted until Neptune was discovered in 1846 and found not to satisfy it. Simultaneously, the large number of known asteroids in the belt resulted in Ceres no longer being considered a planet. It is now understood that no planet could have formed in the belt, due to the gravitational influence of Jupiter.

The discovery of Pluto in 1930 confounded the issue still further. While nowhere near its position as predicted by Bode's law, it was roughly at the position the law had predicted for Neptune. However, the subsequent discovery of the Kuiper belt, and in particular of the object Eris, which is larger than Pluto yet does not fit Bode's law, have further discredited the formula and made it moot in the eyes of astronomers.

Data

Here are the distances of planets calculated from the rule and compared with the real ones:

Planet	k	T-B rule distance	Real distance
Mercury	0	0.4	0.39
Venus	1	0.7	0.72
Earth	2	1.0	1.00
Mars	4	1.6	1.52
(Ceres)1	8	2.8	2.77
Jupiter	16	5.2	5.20
Saturn	32	10.0	9.54
Uranus	64	19.6	19.2
Neptune	128	38.8	30.06
(Pluto)1	256	77.2	39.44

¹ Ceres was considered a planet from 1801 until the 1860s. Pluto was considered a planet from 1930 to 2006. A 2006 IAU proposal to define the term "planet" would have reclassified Ceres as a planet, but this resolution was modified before its ratification in late August 2006. The modification instead placed Ceres, Pluto, and Eris in the newly created category of "dwarf planet".

Theoretical explanations

There is no solid theoretical explanation of the Titius-Bode law, but it is likely a combination of orbital resonance and shortage of degrees of freedom: any stable planetary system has a high probability of satisfying a Titius-Bode-type relationship. Because of this, it has been called a "rule" rather than a "law". Astrophysicist Alan Boss states that it is just a coincidence. The planetary science journal Icarus no longer accepts papers attempting to provide 'improved' versions of the law. (Boss 2006:70|).

Orbital resonance from major orbiting bodies creates regions around the Sun that are free of long-term stable orbits. Results from simulations of planetary formation support the idea that a randomly chosen stable planetary system will likely statisfy a Titius-Bode law.

Dubrulle and Graner^[1][2] have shown that power-law distance rules can be a consequence of collapsing-cloud models of planetary systems possessing two symmetries: rotational invariance (the cloud and its contents are axially symmetric) and scale invariance (the cloud and its contents look the same on all length scales), the latter being a feature of many phenomena considered to play a role in planetary formation, such as turbulence.

There are a decidedly limited number of systems on which Bode's law can be tested. Two of the solar planets have a number of large moons that appear possibly to have been created by a process similar to that which created the planets themselves. The four large satellites of Jupiter plus the largest inner satellite — Amalthea — adhere to a regular, but non-Bode, spacing with the four innermost locked into orbital periods that are each twice that of the next inner satellite. The large moons of Uranus have a regular, but non-Bode, spacing. [1]

Recent discoveries of extrasolar planetary systems do not yet provide enough data to test whether similar rules apply to other solar systems.

See also

• Dermott's Law

Notes

References

• The ghostly hand that spaced the planets New Scientist 9 April 1994, p13
• ^{^} Alan Boss (October 2006). "Ask Astro". Astronomy 30 (10): 70.