Titius - Bode and numbers
KnowledgePosted by Hanne Tue, November 27, 2018 12:12:05The law of Titius-Bode, previously incorrectly called the law of Bode, is a formula from astronomy published by the German astronomer Bode (1747-1826) and discovered in 1766 by Titius (1729-1796), but later it turned out to be no natural law at all. She gives the distance from planets to the sun according to their rank number.
Based on this law, Titius too concluded that there was something missing between Mars and Jupiter.
In his 1766 translation of Bonnet's work, Johann Daniel Titius added some of his own paragraphs. There are two parts to Titius's intercalated text. The first part explains the succession of planetary distances from the Sun:
Take notice of the distances of the planets from one another, and recognize that almost all are separated from one another in a proportion which matches their bodily magnitudes. Divide the distance from the Sun to Saturn into 100 parts; then Mercury is separated by four such parts from the Sun, Venus by 4+3=7 such parts, the Earth by 4+6=10, Mars by 4+12=16. But notice that from Mars to Jupiter there comes a deviation from this so exact progression. From Mars there follows a space of 4+24=28 such parts, but so far no planet was sighted there. But should the Lord Architect have left that space empty? Not at all. Let us therefore assume that this space without doubt belongs to the still undiscovered satellites of Mars, let us also add that perhaps Jupiter still has around itself some smaller ones which have not been sighted yet by any telescope. Next to this for us still unexplored space there rises Jupiter's sphere of influence at 4+48=52 parts; and that of Saturn at 4+96=100 parts.
Also the following footnote was found in Johann Elert Bode’s second edition of his astronomical compendium Anleitung zur Kenntniss des gestirnten Himmels (1772), initially unsourced, but credited to Titius in later versions (in Bode's memoir can be found a reference to Titius with clear recognition of his priority):
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.
Take notice that, those are exactly the numbers of Kepler’s geometric row, as mentioned in my previous blogpost.
The Titius equation is:
a = 0,4 + 0,3 × 2^(n - 2)
With:
a distance of planet in astronomical units
n ranknummer of planet, measured from sun.
So:
n: |
Calculated distance from sun |
Real distance from sun |
n = 1 |
a = 0,4 + 0,15 = 0,55 |
(Mercury): 0,387 |
n = 2 |
a = 0,4 + 0,3 = 0,7 |
(Venus): 0,723 |
n = 3 |
a = 0,4 + 0,6 = 1,0 |
(Earth): 1,000 |
n = 4 |
a = 0,4 + 1,2 = 1,6 |
(Mars): 1,524 |
n = 5 |
a = 0,4 + 2,4 = 2,8 |
Almost correct for Ceres and the planetoïds: a ~ 2,8 |
n = 6 |
a = 0,4 + 4,8 = 5,2 |
(Jupiter): 5,203 |
n = 7 |
a = 0,4 + 9,6 = 10,0 |
(Saturn): 9,537 |
n = 8 |
a = 0,4 + 19,2 = 19,6 |
(Uranus): 19,191 |
n = 9 |
a = 0,4 + 38,4 = 38,8 |
(Neptune 30,069) |
n = 10 |
a = 0,4 + 76,8 = 77,2 |
Distance where scatterd disc objects of KuiperBelt are to be found, like dwarplanet Eris (67,8); they do have very excentric orbits |
When Uranus was discovered in 1781 and Ceres in 1801, these discoveries were considered a strong proof that the law was true and reliable. For the later discovered planet Neptune (1846) and dwarf planet Pluto (1930), the actual distance significantly decreased.
Some astronomers believe that the phenomenon of path resonance can explain the space between the planets to a certain extent. However, it is assumed today that it is a mathematical 'coincidence':
But is this merely a "coïncidence" or is there a real unified concept behind it?
One of Albert Einstein’s most famous statements is “God does not play dice with the universe”. His use of the word God is to be interpreted as the existence of natural laws of great mathematical beauty, whatever form they might take. He felt that natural laws could not be like the throw of dice, with inherent randomness or probability, which excludes coïncidence …
My personal intake, based on what I have discovered so far, is that there are no coïncidences at all. There is indeed a governing law. So will I be able to prove it ?
TBC