#### Golden Mean

# Bode’s Law

**B****ode’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 with Venus and/or Mars during the 2nd millennium BC.

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)}.

^{(a) } https://arxiv.org/abs/1602.02877

^{(b)} https://www.chilton-computing.org.uk/acl/applications/statistics/p005.htm

^{(d) } https://www.sjsu.edu/faculty/watkins/bode2.htm

^{(f) } https://www.fq.math.ca/Scanned/22-1/lombardi.pdf

^{(g)} https://www.insilico.hu/liesegang/history/history.html

^{(h)} https://malagabay.wordpress.com/2014/05/05/as-above-so-below-georgi-gladyshev/

^{(i)} https://file.scirp.org/pdf/NS_2015051816303613.pdf

^{(j)} https://malagabay.wordpress.com/2014/05/03/as-above-so-below-timo-niroma/

^{(k)} https://www.researchgate.net/scientific-contributions/2021145656_Michael_W_Ovenden

^{(m)} *Atlantis, *Volume 13, No.1 December 1959

Also See: Saturn Theory & Doug Yurchey

# Saturn Theory

The Saturn Theory^{(b)} suggests a radical revision of our understanding of the recent history of our solar system. It involves the re-positioning of Saturn, Venus, Earth and Mars and that this complex celestial drama was recorded in the mythologies of the ancient world. There are a number of competing models the theory, one has Earth as a satellite of Saturn, while another has our planet at least closer to Saturn. The late Amy Acheson (1946-2005) suggested that a vindicated Saturn Theory will demonstrate that *“Atlantis was not an earthly location”* but was a celestial *“variation of the mythical home of the gods”* ^{(a)}.

Although I am a supporter of catastrophism I find it hard to accept any of the Saturn Theory’s variants. I am also a convinced euhemerist and believe that myths often contain cores of historical reality. Unfortunately myths can be notoriously ambiguous and consequently where they record remarkable sights in the sky what is interpreted as a close encounter by one person can with equal conviction be seen as an approaching comet by another.

For me the clincher is that the previous arrangement of the solar system, posited by the Saturn Theory, would conflict with the relative harmony of Bode’s Law, even if we do not understand its underlying principles. A 1974 paper^{(c)} by Oreste and Margaret Lombardi compared Bode’s Law with the Fibonnaci Sequence and the Golden Mean when applied to our solar system. The authors concluded *“that there is some underlying law involving gravitation and the golden mean that determines both aphelion and apogee distances.”* With respect to some underlying gravitational principle, R. Louise, the French astronomer, remarked^{(d)}: *“that satellite systems** mimic the planetary system suggests some possible unsuspected property of gravitation.” *

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! All this is a coincidence too far.

^{(a) }https://othergroup.net/thoth/thotiv04.txt

^{(b)} www.jordanmaxwell.com/images/documents/saturn-theory.pdf

^{(c)} www.fq.math.ca/Scanned/22-1/lombardi.pdf

^{(d) }https://articles.adsabs.harvard.edu/full/1982M%26P….26…93L