Why Phi: giant planets update

Posted: October 26, 2014 by oldbrew in Maths, solar system dynamics

Solar system planets [image credit: BBC]

Solar system planets by size
[image credit: BBC]

The Why Phi series started with a discussion around ‘Relations between the Fibonacci Series and Solar System Orbits’ (link below)

Now NASA has updated its planetary data as of 20th October 2014. With the revised numbers (see below for source) we have to re-calculate the orbital relationships of the giant planets.

Amending the original numbers we find:
89 Jupiter-Saturn conjunctions = almost 1768 years
In Fibonacci numbers: 1768 = 34 x 13 x 2²

And there’s more…

Number of Uranus-Neptune conjunctions in the time of 89 J-S: 10.31461
Convert 10.31461 to a whole number: 10.31461 x 89 = 918.00029

So 89² J-S = 918 U-N = 34 x 27 U-N
In Fibonacci numbers: 89² J-S = 34 x 3³ U-N
The total period is about a year less than 89 x 1768y.

This fits very well with the original concept described here:

https://tallbloke.wordpress.com/2013/02/20/a-remarkable-discovery-all-solar-system-periods-fit-the-fibonacci-series-and-the-golden-ratio-why-phi/

NOTES

Revised data from NASA: http://solarsystem.nasa.gov/planets/profile.cfm?Object=SolarSys

Click on a planet then on ‘read more about’ (below ’10 Need-to-Know Things…’)

Alternative (more readable) sources with the same orbit numbers all on one page:
http://solarsystem.nasa.gov/planets/charchart.cfm
http://ssd.jpl.nasa.gov/?planet_phys_par
http://en.wikipedia.org/wiki/List_of_gravitationally_rounded_objects_of_the_Solar_System

Comments
  1. Alan Poirier says:

    There are some who believe God is a mathematician. I think it’s clear he’s a musician.
    https://orderinchoas.wordpress.com/2013/05/18/music-the-fibonacci-sequence-and-phi/

  2. oldbrew says:

    ‘Resonance is the tendency of a system to oscillate with larger amplitude at some frequencies than at others.’

    That’s probably a clue. Example – the Kirkwood gaps:

    http://en.wikipedia.org/wiki/Kirkwood_gap

  3. tallbloke says:

    Nice work OB. Great that progress is still being made while I’m embroiled in politics. This latest development certainly seems to confirm the original thesis.

  4. oldbrew says:

    Thanks TB. There’s a bit of a new angle on Neptune and Pluto too.

    The 3:2 resonance of Neptune and Pluto has long been known.
    http://upload.wikimedia.org/wikipedia/commons/c/c0/TheTransneptunians_73AU.svg

    We can add to that, based on NASA’s updated data:

    170(34 x 5) Neptune-Pluto = 507(13² x 3) Neptune = 337(13² x 2, -1) Pluto
    (bracketed numbers are all Fibonacci: 1,2,3,5,13 and 34)

    507:338 would be 3:2 exactly.

  5. Paul Vaughan says:

    The source is Seidelmann (1992):
    http://ssd.jpl.nasa.gov/?planet_phys_par

  6. oldbrew says:

    Maybe somebody at NASA has been reading Paul’s recent comments😉

  7. michael hart says:

    OB, When you say it fits well with the original concept, do you mean it fits better, or worse? Or still within the envelope of uncertainty?

  8. oldbrew says:

    MH: It fits better for the synodic match between J-S and U-N.

    But the ‘commensurability’ (as Hans Jelbring called it in his PRP paper) of Jupiter and Saturn at 89 J-S conjunctions is watered down slightly. I think he was using the ‘old’ data.

  9. Konrad says:

    Are these orbital patterns that develop after planets form, or due to rules governing matter during planet formation?

  10. oldbrew says:

    Konrad: that’s in the realms of theory but this is from a new paper.

    ‘Outward migration of Jupiter and Saturn in 3:2 or 2:1 resonance in radiative disks’

    http://arxiv.org/abs/1410.0543

    ‘Embedded in the gaseous protoplanetary disk, Jupiter and Saturn naturally become trapped in 3:2 resonance and migrate outward. This serves as the basis of the Grand Tack model.’

    So that has now evolved to a near 5:2 resonance.

  11. Does this change much if you actually use Phi (power or reciprocal series) which is the asymptote of Fibonacci Series. n Fib starts with that 0,1,1,2,3,5,8,13,21,34, then starts converging to.
    fib(n-1)/Fib(n) + Fib(n)/Fib(n) = Fib(n)/Fib(n-1) = Fib(n+1). True for all n, including 0, and all negative n this is x +1 = 1/X = with 1/x the generalized value of Phi.
    Here Fibb(0) = 1, Fibb (-1) = 0.618 = 1/Fibb(1), Fibb(1) = 1.618 = 1/Fibb(-1), Fibb(2) = (Fibb(1))^2 = 1/Fibb(-2), FibB(3) = (Fibb(1))^3 = Fibb(1) x Fibb(2) = 1/Fibb(-3) etc, etc!
    The ratios of any triplet are always the GSR or Phi. All from Miles Mathis!

  12. oldbrew says:

    Will: this may or may not answer the question, but 89/34 is very slightly less than phi².

    Another way of looking at it is the position of the synod. Every 21 conjunctions is about 60 degrees away from the starting point (21 is a Fibonacci number).

    After 21 x 6 conjunctions the cycle is complete (6 x 60 = 360 degrees). That’s also a near-exact number of Saturn (85) and Jupiter (211) orbits.

  13. oldbrew says:
    October 27, 2014 at 10:21 am

    “Will: this may or may not answer the question, but 89/34 is very slightly less than phi².
    Another way of looking at it is the position of the synod. Every 21 conjunctions is about 60 degrees away from the starting point (21 is a Fibonacci number).
    After 21 x 6 conjunctions the cycle is complete (6 x 60 = 360 degrees). That’s also a near-exact number of Saturn (85) and Jupiter (211) orbits.”

    No not really, but thanks. Do you want me to calculate the Fibbs to +211? The larger ones are close to integers. I will need to do the real Phi, not the approximation.

  14. oldbrew says:

    OK Will, no harm in trying it if you want to run some numbers.

  15. oldbrew says: October 27, 2014 at 12:16 pm

    “OK Will, no harm in trying it if you want to run some numbers.”

    I see that you also use the factors of the Fibonacci Series integers that are not prime.
    If I normalize the Fibb(0) to Fib(23) = 28657, or Fib(29) = 514229, (All primes), the results of x Phi, increasing, or x 1/Phi, decreasing, rounded to integers are the series.
    The exact values are still irrational as Phi is irrational. I was using Phi = 1.6180344 as I have nothing now that can handle 1.6180339887498948482. The slight differences may tell if the Solar system is Fibonacci or Phi.
    Now I must re-learn how to do a spreadsheet, lotsa numbers!

  16. oldbrew says:

    We have to use whatever numbers the planets dictate – can’t have our own facts😉

    NB ‘I was using Phi = 1.6180344’ – the second ‘4’ is redundant.

  17. oldbrew says: October 27, 2014 at 7:21 pm

    “We have to use whatever numbers the planets dictate – can’t have our own facts”😉

    Yea, just trying to be helpful!

    “NB ‘I was using Phi = 1.6180344′ – the second ‘4’ is redundant”.
    Thank you, not redundant “wrong’ to 4 decimal places, sorry! 1.61803400005

  18. […] formula we’re now able to see the link between Jupiter and Saturn orbits. As in the original giant planets update post the numbers are quite large but easily connected to the ‘Why Phi’ […]

  19. oldbrew says:

    ’89 Jupiter-Saturn conjunctions = almost 1768 years’

    Links to the inner system of rocky planets, Mars being the nearest:

    9 Jupiter-Saturn conjunctions = 80 J-Mars = 89 S-Mars
    (9 J-S is often described as the solar-related Jose cycle of just under 179 years)
    ‘http://articles.adsabs.harvard.edu/full/1965AJ…..70..193J/’

    89 J-S = 880 (55 x 16) S-Mars (1768.075y) = 791 J-Mars (880 – 89)

  20. […] good a match it is – or not. This post follows on from two recent posts which can be found here and […]

  21. […] period of 1092 years can be compared to the earlier giant planets post where a period of 1768 years was analysed: 1768 = 34 x 13 x 4 years 1092 = 21 x 13 x 4 […]