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)!
(m) Atlantis, Volume 13, No.1 December 1959
Gerry Forster (1930-2004) was a British anomalist who devoted much of his time to researching the origins of humanity and the planet that we live on. According to any criteria, I would classify him as a prominent member of the ‘lunatic fringe’. He was an advocate for the Hollow Earth theory and proposed that mankind had originated on a planet, Astrida, in what is now the Asteroid Belt. Less controversially, he also wrote a 50-page paper on Atlantis entitled The Lost Continent Rediscovered(a) in which he closely follows the views of Ignatius Donnelly
The Exploded Planet Hypothesis (EPH) has its origins in the 18th century when the regular spacing of the orbits of the then known six planets, with the glaring exception of the apparently empty theoretical position between Mars and Jupiter, led to the formulation of the Titius-Bode Law. The discovery of Neptune in 1846 in a position that did not conform to the rule of Titius-Bode, led to its gradual abandonment. However, the discovery of Pluto in the 1930’s brought the ‘Law’ back into consideration as Pluto was in the position that should have been occupied by Neptune. The exceptions to the Titius-Bode law are the lack of a planet where the Asteroid Belt is and the position of Neptune. In 2003, a further planet, Sedna, was discovered at a distance of 8 billion miles from the sun, as predicted by Doug Yurchey on the Internet in 2002. Since then, further bodies have been discovered in the outer region of our solar system, one of which was larger than Pluto.
As you will see below, a credible explanation for the Asteroid Belt is on offer and if correct, it means that now ten of the eleven planetary orbits in our Solar System correspond with the prediction of Titius-Bode. Statistically, this must have some significance. Therefore, in order to reinstate the Titius-Bode ‘law’ back on the statute book it is important to find an acceptable explanation for Neptune’s orbit.
Particular planets with satellite systems also confirm Titius-Bode, such as the principal satellites of Jupiter, Saturn and Uranus. Furthermore, even at this early stage in our investigation of extrasolar planetary systems, one, 55 Cancri, has at least four planets whose orbits appear to follow a similar pattern(c).
The 19th century saw the discovery of more asteroids in the orbit where a planet would have been expected. As early as 1802 the suggestion that an exploded planet had originally occupied this position was considered. As more asteroids were discovered the idea gained support. However, there remained one major problem with the theory, namely, that the total mass of the known asteroids would not constitute one thousandth of our earth. So where did all the matter go?
Donald W. Patten (1929-2014) has made a study of Martian craters and discovered a number of anomalies. One such detail is that 93% of all craters 20 miles or greater in diameter are in one hemisphere, which led Patten to conclude that “Mars received about 86% of its craters in one catastrophic day”(e)(f) and that the other 14% are spread equally on both hemispheres and over all other time. The suggestion being that these craters were possibly caused by the disintegration of large asteroid or small planet!
Tom Van Flandern (1940-2009), the leading exponent of the EPH, explained; ‘Consider what would happen if the Earth exploded today. Surface and crustal rock would shatter and fragment, but remain rocks. However, rocks from depths greater than 40 km are under so much pressure at high temperature that if suddenly released into a vacuum, such rocks would vaporise. As a consequence, over 99% of the Earth’s total mass would vaporise in an explosion, with only its low-pressure crustal and upper mantle layers surviving’. This explanation would clearly account for the low total mass of the objects in the Asteroid Belt. Van Flandern has expanded on his theory in what many consider a landmark book, Dark Matter, Missing Planets and New Comets.
Van Flandern ascribes a date for this planetary explosion that is well before man existed on Earth. However, many of our ancient myths have been interpreted as describing celestial events in the vicinity of Earth that had a direct physical effect on our planet. Immanuel Velikovsky wrote extensively on these ancient tales and concluded that they referred to close encounters between Earth and Mars and separately with Venus.
The date of the Asteroid Belt collision or explosion was estimated in 2015 to be 470 million years ago after the identification of twin impact craters in Sweden(d).
If Titius-Bode is valid and Velikovsky’s planetary encounters real, we need to explain how they left their orbits in the first place and then must explain how they returned to their original positions. Ralph E. Juergens, an American engineer, supports 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(b). My personal hunch is that Van Flandern is correct about the explosion of a planet but wrong about the date of the occurrence.
The EPH may have a bearing on the demise of Atlantis in the shape of an asteroidal collision with Earth that in turn precipitated the ending of the last Ice Age and the consequential flooding of large areas of exposed land.
Alan Alford has a different view in The Atlantis Secret  in which he attempts to prove that Atlantis originated in an ancient myth concerning an exploding planet. However, this would require an event that occurred within the experience of speaking man for it to have been passed on in the form of myth.
(c) BBC Focus magazine (No. 169, October 2006 p.58-63)