Bode’s Law or more correctly Titius-Bode’s Law is named after two German astronomers, Johann Daniel Titius and
Johann Elert Bode, proposed in the 18th century that there was a mathematical relationship between the then six known planets and their distance from the sun, with each one roughly twice the distance as the previous planet. Although the idea was conceived by Titius, it was Bode who gave it greater prominence, when he used it to predict the existence of Uranus and later Ceres in the Asteroid Belt. At that point, it was accepted as a ‘law’.
In the 19th century, Urbain LeVerrier and John Couch Adams working independently, used the Titius-Bode model combined with calculations based on Newton’s Law of Gravity to predict where the next planet, Neptune, should be found. Kamienski wrote a short paper comparing the formulae of LeVerrier & Adams with that of Titius-Bode(m).
The subject has been debated throughout the 20th century. I.J. Good, a British mathematician who worked with Alan Turing during the war at Bletchley Park, offered a paper in support of Titius-Bode in 1968(b). Bradley Efron, an American statistician, proposed an opposing view(c). Both papers are best suited to the mathematically advanced.
The late Timo Niroma has offered some interesting observations(j) on the mechanics behind Titius-Bode and developed a cosmology based upon atomic weights, noting that “What happens on a small scale seems to obey the same laws on a much grander scale.”
Georgi Gladyshev, a Russian scientist, has proposed an explanation for Titius-Bode based on the work of Raphael Liesegang(g) who proposed the concept of ‘periodic precipitation’. Gladyshev applied Liesegang’s theory to the early stages of the formation of our Solar System(h)(i). Hopefully, this may bring us closer to the physics behind the distribution of the planets!
It has also been proposed that a Titius-Bode-Type ‘rule’ seems to be applicable to planetary satellite systems(d) and there appears to be evidence(a) that Titius-Bode is also applicable to exoplanetary systems!
The Titius-Bode Law has also been linked with the Fibonacci Series(e) as well as the Golden Mean(f).
Velikovskian catastrophism proposes[0037.152] that Atlantis was destroyed as a result of the periodic close encounters of our planet and Moon with Venus and/or Mars during the 1st & 2nd millennia BC. According to Velikovsky, Venus was a relatively recent newcomer to the Solar System and the orbit of Mars had been disturbed, which would suggest that prior to the arrival of Venus and the displacement of Mars, Bode’s Law would have been invalidated! C.J. Ransom has tackled this head-on in The Age of Velikovsky [1880.90]. However, his defence of Bode and Velikovsky was rejected by Dr M. M. Nieto(n).
Louis Jacot (1906- ) was a Swiss economist and jurist who added the study of science and philosophy to his intellectual toolkit. He developed some novel cosmological theories, including enthusiastic support for Bode’s Law which he described as “the great key to the mysteries of the Universe.”  While this may be overstating his case, I cannot help feeling that Bode’s Law is an expression of cosmological principles operating in a manner not as yet identified! At its simplest, the question is, are we to believe that the spacing of the planets came about purely by chance or is there an unrecognised force or forces at play?
For my own part, I have always felt that Bode’s Law was a highly convincing concept, but unfortunately, I do not have the mathematical or astronomical ability required to objectively verify its reality, nor the proposed Fibonacci Sequence and the Golden Mean relationship with it. It would appear that acceptance of Bode would create difficulties not just for the Saturn Theory but also for Velikovsky’s idea that Venus was just a large piece of ejecta from Jupiter that had catastrophic close encounters with Earth and Mars, within human experience, just a few thousand years ago. Such an idea would mean that prior to the Saturnian rearrangement of the planets or the Velikovskian creation of Venus, the positional relationship of the planets probably did not conform to any known mathematical model but after this/these calamitous events everything ‘coincidentally’ settled into orbits that are now claimed to conform to Bode, Fibonacci and the Golden Mean! Can we believe that after careening around the solar system including a number of close encounters with Earth that all the planets adopted new orbits that conformed with Bode’s Law? Surely, this is a coincidence too far?
Although the ‘Law’ has been generally abandoned by mainstream scientists, there is still interest in some quarters. One of those was the British astronomer, the late Michael Ovenden (1926-1987) who produced a modified version of the original formula(k). Another version involves an interpretation of quantum mechanics, called pilot-wave theory(l)!
W.I. Newman, M.P. Haynes, and Y. Terzian “have considered the psychological tendency to find a pattern where none exists, and have also discussed how inappropriate inferences regarding astronomical phenomena have been drawn from statistical analyses.” (o)
(m) Atlantis, Volume 13, No.1 December 1959
(o) Redshift Data and Statistical Inference, Astrophys. J., 431, 147, 1994. *