A previous posting introduced a concept that has echoed down the ages:
As Above, So Below.
The concept of As Above, So Below can be seen embedded in the cosmology of Johannes Kepler [Mysterium Cosmographicum – 1596] because he thought the five Platonic solids dictated the structure of the universe.
Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids, enclosed within a sphere that represented the orbit of Saturn.
Phi in the Sky – As Above So Below
Robert James Moon implicitly combined the concept of As Above, So Below with the cosmology of Kepler [in the 1980s] when he proposed that the protons in the naturally occurring elements are “determined by the vertices of two identical pairs of nested [platonic] solids” in much the same way “that Kepler determined the orbits of the planets”.
Moon developed a nested model, using the Platonic solids to define the atomic nucleus in much the same way that Kepler determined the orbits of the planets of the solar system.
In Moon’s “Keplerian atom,” the 92 protons of the naturally occurring elements are determined by the vertices of two identical pairs of nested solids.
The Geometric Basis for the Periodicity of the Elements – Laurence Hecht
Page 18 – May-June 1988 – 21st Century
Phi in the Sky – As Above So Below
Intriguingly, in the 1970s, Timo Niroma developed a cosmology based upon atomic weights whilst pondering the mechanics of the Titius-Bode Law.
In 1772, Johann Elert Bode, aged only twenty-five, completed the second edition of his astronomical compendium Anleitung zur Kenntniss des gestirnten Himmels, into which he added the following footnote, initially unsourced, but credited to Titius in later versions:
This latter point seems in particular to follow from the astonishing relation which the known six planets observe in their distances from the Sun. Let the distance from the Sun to Saturn be taken as 100, then Mercury is separated by 4 such parts from the Sun. Venus is 4+3=7. The Earth 4+6=10. Mars 4+12=16. Now comes a gap in this so orderly progression. After Mars there follows a space of 4+24=28 parts, in which no planet has yet been seen. Can one believe that the Founder of the universe had left this space empty? Certainly not. From here we come to the distance of Jupiter by 4+48=52 parts, and finally to that of Saturn by 4+96=100 parts.
The cosmology of Timo Niroma led him to restate the concept of As Above, So Below:
“What happens in small scale seems to obey the same laws on a much grander scale.”
I have wondered since the 1970’s, when I discovered the following law, which is inspired by the Titius-Bode law, works.
First I divided the planets into three groups so that each group consisted of three planets.
Then there were the leftovers, that remained as a loose group, the so called Kuiper belt.
The groups were:
1. The small planets that were born from the heavy debris that remained near the Sun:
Mercury, Venus and the double planet Earth/Moon.
2. Then the main ring consisting of dirty gas, meaning gas with still some heavy elements:
Mars, debris with too small amount of dust to coalesce and small sister of sun, Jupiter.
Solar wind seems to have swept the light elements to the end of this ring.
3. The ring of relatively light gas, from which were born
Saturn, Uranus and Neptune.
The three rings (plus possibly the Kuiper belt) adjusted to their places avoiding arithmetic resonance, but remaining in a geometric resonance to each other.
This also happened inside the rings, when gravity began to coalesce the material into three rings, which with one exception then coalesced into planets. The resonance placed the planets into the low and high end of the ring plus into the geometrical, not arithmetical center of it.
What is amazing, is that it seems that the same resonance law that placed the planets into their positions, reigns also in the nucleus of the atom, where the average amount of neutrons seems to make the atomic weight (the average of the reigning isotopes) behave in equal ways as the resonance of planets.
What happens in small scale seems to obey the same laws on a much grander scale.
Before I introduce my equation, I remark that actually it needs a factor, let’s call it k, with which the atomic weights should be multiplied.
But when we use kilometers as the distance measure of planets, it is so near to 1, that for clarity’s sake I have omitted it.
When using some non-SI measure stick, such as miles, you need it.
Then let’s begin with the first planets.
Their distance corresponds to atomic weight of the element number 2.5*n, where n is the number of planet from the sun.
When the atomic weight is multiplied by (k*) tens of millions of kilometers, we get the distance of the planet.
Mercury 58 mill.km / 2=helium, 3=litium –> (4+6.94)/2= 5.5 / 106%
Venus 108 mill.km / 5 = borium –> 10.8 / 100%
Earth 150 mill.km / 7=nitrogen, 8=oxygen –> (14+16)/2=15.0 / 100%
Now the gap between the two first rings means that we must add 3.5 elements (1 for the preceding group and 2.5 for the distance of the group) so that Mars does not correspond to element 10 but 11, and the next series goes 11*n, where Mars gets the number one, asteroids 2 and Jupiter 3.
Mars 228 mill. km / 11 = sodium –> 23.0 / 99%
asteroids 472 mill. km *) / 22 = titanium –> 47.9 / 99%
Jupiter 778 mili. km / 33 = arsenium –> 74.9 / 104%
*) Calculated from the densest group avg. (Binzel-Gehrels-Matthews, Arizona, 1989)
Now to the third group. Albeit the elements are ending just before Uranus, but let’s try.
Now we need to add for the gap 26.5 elements (2 for the groups, and 2.5 and 2*11 for the distances of the groups), so that Saturn equals element 59.5 instead of 44 (2+2.5+11).
The series goes then 59.5*n, where Saturn is 1, Uranus 2 and Neptune 3.
Saturn 1427 mil.km / 59=praseodyme, 60=neodyme –> (140.91+144.24)/2=142.6 / 100%
Uranus 2871 mil.km / 119 –> 295 *)
Neptune 4497 mil.km / 178.5 –> c. 460 **) /c. 98%
*) extrapolated from elements 116 and 118
**) estimate based on the known part of the element table
Questions arise, how and why.
The fit is however so good, that it somehow cries for an explanation. And without it, it would give some hints, how our solar system got started.
And also how the average number of neutrons in atoms get their number.
Timo Niroma: Titius-Bode of my own
Although the cosmology of Timo Niroma [as stated] includes elements of numerology [aka hocus-pocus of unknown origin in the formulas] it is also incorporates real world atomic weights coupled with real world SI units.
However, double checking Timo Niroma’s calculations highlights a couple of very curious coincidences that suggest the numerology is an artefact [used to emulate the Titius-Bode Law] that should simply be ignored.
The calculated mean orbital distance for Mercury results in an error of 5.52% and falls within the Aphelion-Perihelion range.
Coincidentally, the calculated value for Lithium is within 0.597% of Mercury’s Aphelion.
The calculated mean orbital distance for Venus results in an error of 0.10% and falls within the Aphelion-Perihelion range.
The calculated mean orbital distance for Earth results in an error of 0.29% and falls within the Aphelion-Perihelion range.
Coincidentally, the two elements used to calculate the Earth’s mean orbital distance are also the main components of Earth’s lower atmosphere: Nitrogen-78%, Oxygen-21%.
The calculated mean orbital distance for Mars results in an error of 0.86% and falls within the Aphelion-Perihelion range.
The calculated mean orbital distance for Jupiter results in an error of 3.77% and falls within the Aphelion-Perihelion range.
The calculated mean orbital distance for Saturn results in an error of 0.54% and falls within the Aphelion-Perihelion range.
This suspicion is greatly reinforced when Timo Niroma’s cosmology is used to interpret the curious banding in the Asteroid Belt.
The semi-major axis of an asteroid is used to describe the dimensions of its orbit around the Sun, and its value determines the minor planet’s orbital period.
In 1866, Daniel Kirkwood announced the discovery of gaps in the distances of these bodies’ orbits from the Sun. They were located at positions where their period of revolution about the Sun was an integer fraction of Jupiter’s orbital period.
Hopefully, somewhere along the line, further research may start to answer Timo Niroma’s big questions: how and why?