Why-Phi? – some Uranus-Neptune long-term resonances

Posted: May 8, 2019 by oldbrew in Fibonacci, Lucas, Maths, Phi, solar system dynamics
Tags: , ,


Continuing our recent series of posts, with Uranus-Neptune conjunction data an obvious starting point for the table is where the difference between the number of Neptune orbits and U-N synods is 1.

647 U-N takes a long time (~110,900 years) but the accuracy of the whole number matches is very high.

Lucas no. (7 here) is fixed, and Fibonacci nos. follow the correct sequence (given their start no.).
Full Fib. series starts: 0,1,1,2,3,5,8,13,21…etc.
Multiplier: 0,1,1,2,3
Addition: 1,1,2,3,5

The Neptune orbits are multiples of 26 with the same Fibonacci adjustment:
Add 0,1,1,2,3 to the Neptune column numbers to get an exact multiple of 26 (which will be the pattern number in the last column).

Three Neptune orbits are ‘dropped’ in the period, since 26 * 26 = 676, but there are only 673 N orbits.

The corresponding number for Uranus is 6 dropped orbits (51*26, -1320), reflecting the fact that it completes nearly 2 orbits of the Sun per Neptune orbit.

To check the results, multiply the synods number by 374.4507 (degrees) then divide by the Neptune orbits. The result will always be very close to 360 degrees.

Another U-N Phi/Fibonacci connection can be found straight from their orbit ratio:
164.79132 (N) / 84.016846 (U) = 1.961408
1.961408 * 4 = 7.845632 = 2.6152106 = 34/13 (>99.993% match)

That’s very close to saying that the U:N ratio = 1: 3/4 of Phi².
The two orbit periods are very close to 84(U) and 165(N) years.
84 = 21*4 and 165 = 55*3.
Since 21 and 55 are Fibonacci numbers the ratio is confirmed.

Comments
  1. tallbloke says:

    This is amazing. You’ve been right through the pairs from Earth Mars and found a similar expression for all of them which exhibits fibonacci series and Lucas numbers.

    Fancy trying an exoplanetary system next? 🙂

  2. oldbrew says:

    Maybe 🤔

    Just noticed that the 2nd and 5th (last) rows of the table sum to double the 4th row, e.g. 8+26 = 17*2. And the 1st and 4th rows sum to double the 3rd row, e.g. 26+440 = 233*2.

    This corresponds to Fibonacci numbers where F1+F4 = F3*2 e.g.:
    If F1 to F4 are 8,13,21,34 then 8+34 = 21*2.
    – – –
    Update – here’s the Neptune orbit pattern (rows 1,3, and 4) converted to Fib. nos.:
    26 = 13 * 2
    233 = 21 * 3 plus 34 * 5
    440 = 55 * 8

    Of course 233 is already a Fib. no.
    Listing the other Fib. nos. used: 2,3,5,8,13,21,34,55.

    https://en.wikipedia.org/wiki/Fibonacci_number

  3. oldbrew says:

    Another version of this table will appear tomorrow.

  4. tallbloke says:

    Wow. The music of the spheres indeed.

  5. oldbrew says:

    Version 2. This one’s more accurate, with bigger numbers. The start line is 4 times more than in Version 1 (i.e. the one in this blog post). The last line has almost 100% matches. Row 2 is the same as row 3 in the other table, except the pattern.

    Adding to the earlier comment – for every set of four consecutive numbers (N1-N4) in any column:
    N4 – N1 = 2 * N2
    N4 + N1 = 2 * N3

    That’s just the nature of this type of accumulator table.

    Adding the ‘+F’ number to the Neptune number always gives a multiple of 13.
    Adding the ‘+F’ number to the U-N synods number always gives a multiple of 5.
    The last column obviously has multiples of 4 less the ‘+F’ number.

  6. tallbloke says:

    The 4 and the seven you used in the first version are both Lucas numbers. Is it the case that Lucas numbers are the only numbers which give a solution which generates Fibonacci series in the final column? Would it get even more accurate if you went to a higher Lucas number?

  7. oldbrew says:

    Q1 – don’t know.
    Q2 – if the Lucas no. is higher than the relevant number in row 2 the formula goes negative.

  8. dai davies says:

    sqrt(7.845632) = 2.6152106

    Hoping to be able to make time to get into phi more now I’ve quit climate research.

    Particles -> molecules -> brain resonances -> our sense of beauty -> solar system formation [-> possibly soccer-ball cosmology (saw something on that but haven’t looked into it)]

  9. oldbrew says:

    dai – re ‘sqrt(7.845632) = 2.6152106’ – no it isn’t.

    But 7.845632 / 3 = 2.6152106

  10. dai davies says:

    OK, but algebra is still wrong. My bad guess. Still fascinating. Looking forward to digging deeper.

  11. oldbrew says:

    Something very similar here:
    https://tallbloke.wordpress.com/2017/01/08/why-phi-a-lunar-ratios-model/

    FMC:LAC = 1 : 7.8475526
    QBO:LNC = 1 : 7.8503233

    ‘the two ratios are very close to 1 : 3 x Phi²’

    Also: no. of Jupiter orbits in 5 lunar nodal cycles = 7.845157
    (34/13) * 3 = 7.8461538

  12. dai davies says:

    Do you know where the 3 comes from?
    As another reckless guess I’ll go for the fact we have a spatial 3D universe. 🙂

  13. oldbrew says:

    Nothing definite, but Jupiter-Saturn conjunctions go in groups of 3 (Kepler’s trigon).

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