Bode’s Law or more correctly Titius-Bode’s Law is named after two German astronomers, Johann Daniel Titius and
Johann Elert Bode, who 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 in small scale seems to obey the same laws on a much grander scale.”
Georgi Gladyshev, a Russian scientist, has proposed a 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 are there 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 Fibonnaci 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 involvesan interpretation of quantum mechanics, called pilot wave theory(l)!
(b) Bode’s Law (archive.org) *
(m) Atlantis, Volume 13, No.1 December 1959
Immanuel Velikovsky (1895-1979) was by profession a doctor of medicine, specialising in psychiatry. However, his fame is based on being arguably the most controversial catastrophist of the 20th century. He daringly proposed that the Earth had several close encounters with other planetary bodies that resulted in catastrophic consequences, including interference with the rotation of our planet. He speculated that Atlantis was probably destroyed during one of these cataclysmic events.
Some have seen the influence of Ignatius Donnelly’s Ragnarok, written seventy years earlier, in Velikovsky’s cosmic collision theories. Some commentators have noted how Velikovsky seemed reluctant to credit earlier writers, such as W. C. Beaumont and Johann Radlof (1775-1846)(b), with their contributions to the development of the theory of planetary catastrophism. Rens Van Der Sluijs has written an interesting two-part paper(d)(e) listing the catastrophists who preceded Velikovsky demonstrating a certain lack of originality on his part! Others take a more critical view of his ideas(g). In 1950, he responded to this criticism with a defensive piece(n), but I consider it inadequate as he continued to ignore the work of Radlof and Beaumont. Some years ago Ev Cochrane and Phil ‘Pib’ Burns also discussed Velikovsky’s reluctance to credit earlier writers for ideas used by him, compared with the recognition given by Clube & Napier to the work of Velikovsky(x).
Van Der Sluijs has written a two-part(k)(l) article on Velikovsky’s radical views regarding Venus as a comet-like body and how Aztec sources support some of his contentions.
Carl Sagan (1934-1996), was a well-known American astronomer, author and lecturer. He is considered a leading debunker of Velikovsky’s theories. He devoted much of his Broca’s Brain  to this end. Charles Ginenthal (1934-2017) produced an extensive rebuttal of Sagan’s criticisms in Carl Sagan & Immanuel Velikovsky . However, criticism of Velikovsky continues with varying degrees of ferocity, such as that of Leroy Ellenberger, a former supporter of Velikovsky, who contends that the data from the Greenland ice cores fail to support Velikovsky(s).
>Velikovsky and Einstein were acquaintances and as Nathaniel Lloyd wrote in his three-part blog on chronological revisionism(y) that when Velikovsky “asked Einstein to read his work and give an opinion. Einstein suggested that Velikovsky might have a hard time finding a publisher, specifically because “every sensible physicist” would realize that the catastrophes Velikovsky described would have completely destroyed the Earth’s crust. Nevertheless, Einstein was kind about his criticism, and Velikovsky was undeterred. But years later, in Einstein’s very last interview, his opinion was less delicate: ‘It really isn’t a bad book,’ he said, laughing. ‘The only trouble with it is, it is crazy’.”<
Velikovsky was initially inclined to link the disappearance of Atlantis with the eruption of Thera but later came to support a location between the Azores and the Mid-Atlantic Ridge(i). He was an early questioner of Plato’s figure of 9,000 years for the age of Atlantis, suggesting that it was exaggerated by a factor of ten[0037.152]. ”Whatever the source of the error, the most probable date of the sinking of Atlantis would be in the middle of the second millennium, 900 years before Solon when the earth twice suffered great catastrophes as a result of ‘the shifting of the heavenly bodies.’ These words of Plato received the least attention, though they deserved the greatest.”
Velikovsky offered intriguing evidence that on at least one occasion the early Egyptians experienced the sun rising in the west and set in the east(q)!
His other major contribution was in his questioning of the accepted Bronze Age chronologies of the eastern Mediterranean. Later writers, such as David Rohl and Peter James have built on his chronology work, while Gary Gilligan has added support for Velikovsky’s planetary theories as well. Others have accused Velikovsky of being over-dependent on his belief in the inerrancy of biblical chronology.
One website(a) provides us with a considerable amount of Velikovsky’s unpublished work, while another offers an encyclopedia of his work(c). A more general German site(f), in English, is also worth a visit.
The three of Velikovsky’s most popular books as well as some of his lesser-known papers are available as pdf files(j)(m).
Jan Sammer was an assistant to Velikovsky (1976-1978) and an archivist and editor for the Velikovsky Estate (1980-1983). He advises us that he was involved in the completion of Velikovsky’s unpublished book, In the Beginning, which can be read online(h). The book’s contents were originally intended to be part of Worlds in Collision. In it, you will find more details of Velikovsky’s claim that within the memory of man there was a time when we had no Moon, which he claims was subsequently ‘captured’ by the Earth.
According to Velikovsky, Venus was a relatively recent newcomer to our Solar System and the orbit of Mars had been disturbed, which would suggest that before the arrival of Venus, 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(t).
In 2012, Laird Scranton, published The Velikovsky Heresies, in which he reviews Velikovsky’s controversial theories in the light of scientific discoveries since his death. Not unexpectedly, Scranton does find evidence that supports some of Velikovsky’s contentions.
Ralph E. Juergens, an American engineer, supported Velikovsky with the idea that electromagnetic and electrostatic forces and not conventional celestial mechanics alone were responsible for the cosmic encounters witnessed and recorded by our ancestors(u).
In the late 1990s Sean Mewhinney (1944-2016), a Canadian researcher published a series of papers(w) that was highly critical of Velikovsky’s theories. Much of his criticism was focused on ice core data. Once again, Charles Ginenthal took up the challenge, responding with an extensive paper entitled Minds in Denial, later the title of an ebook  that include the original paper. Ginenthal also published a book on Electro-Gravitic Theory of Celestial Motion and Cosmology and its possible application to Velikovsky’s theories(v).
Some readers may wish to see a video by Wallace Thornhill, of Electric Universe fame, in which he discusses Velikovsky’s Astrophysics(o). There are several related papers and books, including some Velikovskian material, freely available online(p).