Why Phi? – giant planets: a Jupiter-Uranus model

Posted: November 21, 2014 by oldbrew in solar system dynamics

Jupiter and Uranus [image credit: Jimmy Eubanks / NBC News]

Jupiter and Uranus (as seen from Earth)
[image credit: Jimmy Eubanks / NBC News]

This brief look at Jupiter-Uranus synodic patterns follows the style of the Saturn-Uranus model post, where details of the method are given.

Here we’ll run through the relevant model details then compare with planetary data, as in the other post. It should be straightforward as it’s mostly based on just two Fibonacci numbers: 13 and 21.

For Uranus the notional orbit period will be 84 years (JPL value: 84.016846y).
13 Uranus orbits @ 84y x 13 = 1092 years (84 = 21 x 4).
This will be the full period of the model.

Since it’s known that one Jupiter-Earth (J-E) conjunction takes around 1.092 years, we can add to the model:
1000 J-E = 1092 years.

Now the rest of the model can be built:
13 U = 1092 years = 21 x 13 x 4 years
92 J (1092 – 1000) = 7 x 13,+1 J = 1092y
79 J-U (92 – 13) = 6 x 13,+1 J-U = 1092y
1079 U-E (1092 – 13) = 83 x 13 U-E = 1092y
1000 J-E (1092 – 92) = 77 x 13,-1 J-E = 1092y

Let’s see how that compares with the JPL-derived orbital data:
13 Uranus = 1092.219y
92 Jupiter = 1091.36y
79 J-U = 1091.219y
1079 U-E = 1091.997y
1000 J-E = 1092.06y

All the numbers match to within at least 99.94%, and U-E is almost 100%.

The 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 years

The ratio of the periods is obviously 34:21 or ~phi.
Note also: 13 x 4y (52y) divided by 1 Jupiter-Saturn synod = 2.61766 (~phi²).
2.61766 x 34 = 89 (13, 21, 34 and 89 are Fibonacci numbers).

As mentioned in one of the earlier posts, the ‘x 4’ in effect means the unit of currency is 1461 days i.e. a whole number of Earth rotations as well as a whole number of years. Of course in Fibonacci terms 4 = 2 x 2 or 2².

Conclusion: the phi-related pattern of Fibonacci numbers can be detected in the Jupiter-Uranus orbital data at this timeframe, using a simple model.

To view any of the earlier related posts, see ‘Related’ links below or click here.
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Reference data: http://ssd.jpl.nasa.gov/?planet_phys_par

Comments
  1. Sparks says:

    Hi guys,

    That image of Jupiter and Uranus scale is way off, it’s laughable tbh.

  2. tallbloke says:

    This is beautiful work. Well done OB.
    Working towards a fibonacci-phi integration is demanding work as the myriad branches of sequences hide the central tree.

  3. oldbrew says:

    Another phi relationship is Uranus’ orbit with the Jupiter-Saturn synodic period.

    That works out close to 1:phi³ and even closer in Fibonacci terms as a 13:55 ratio, so it links to the model:
    13 Uranus = 1092.219y
    55 J-S = 1092.57y

  4. oldbrew says:

    Thanks Rog. This might be apt for a post about 13 Uranus😉

  5. tallbloke says:

    34 x 2² V-E cycles is quite close to your 1092yrs as well. Out by around 1/2 a V-E cycle

    You said:
    1768 = 34 x 13 x 4 years
    1092 = 21 x 13 x 4 years

    And 13 x 13 x 4 = 676 years, which is very close to 1:Phi with 1092

    Maybe the 676 year period is worth analysing too? It is 34 J-S, this is obvious and falls straight out of the maths. But what other conjunction periods and/or precession cycles fit?

    676 is 132 x 4

  6. oldbrew says:

    ‘And 13 x 13 x 4 = 676 years, which is very close to 1:Phi with 1092’

    It’s 13:21 by definition if you’re comparing 13 x 52 with 21 x 52😉
    I’ll have a look at the shorter period anyway.

    The other thing is the 1000 J-E. If we treat that as 1 x 1000, then as the number of corresponding J-S goes up the Fibonacci scale, the 1 goes up in a phi-related way:

    If 55 J-S = 1 [x 1000 J-E], 89 will be ~1.618 [etc], 144 will be ~2.618 [etc.]…
    In fact they don’t quite align so at 233 J-S it’s 4237 J-E instead of 4236 (phi³ = 4.2360679), i.e. one ‘extra’ J-E per 233 J-S compared to the theoretical scale.

    You covered this in one of the PRP papers.

  7. oldbrew says:

    TB: ‘Maybe the 676 year period is worth analysing too? It is 34 J-S’

    89 x 13 J-S = 676y x 34 (another way of saying 89 J-S = 1768y)
    57 Jupiter = 676.17y
    619 J-E = 675.985y