Why Phi? – a Jupiter-Neptune model

Continuing our long-term series researching Fibonacci and/or Phi based ratios in planetary conjunction periods, it’s time for a look at the inner- and outer-most gas giants of our solar system: Jupiter and Neptune.

Initial analysis shows the period of 14 Jupiter orbits is close to that of one Neptune orbit of the Sun, and even closer to the period of 13 (14 less 1) Jupiter-Neptune (J-N) conjunctions.

It also turns out that there’s a multiple of 13 J-N that equates to a whole number of Earth orbits:
Jupiter-Neptune(J-N) average conjunction period = 12.782793 years
221 J-N = ~2825 years (2824.9972y)
(221 = 13 x 17)

But this period is not a whole number of either Jupiter or Neptune orbits.
This is resolved by multiplying by a factor of 7.

We can now produce the Jupiter-Neptune synodic chart(1) below.

Note: the number of conjunctions = the difference between orbit numbers where both time periods are the same, e.g.:
1667 J orbits – 120 N orbits = 1547 J-N conjunctions

It can be seen in Chart 1 that a common factor of 119 ties the numbers together within +/- 1 of the actual values, and the J-N number is also an exact multiple of 13.

Since we’re looking for Fibonacci numbers we need to take it one stage further, and multiply the Chart 1 values by 6, as shown in Chart 2.

Now we have 720 N (144 x 5) and 9282 J-N (34 x 21 x 13).

So: 144 x 5 Neptune orbits = 34 x 21 x 13 Jupiter-Neptune conjunctions.
5,13,21, 34 and 144 are all Fibonacci numbers.

This may seem a complex outcome but it’s what the data tell us and the Fibonacci match is at least interesting, maybe even surprising.

Results can be checked using JPL data (i.e. the ‘sidereal orbit period’ column) in this link:
http://ssd.jpl.nasa.gov/?planet_phys_par
720 x 164.79132y (N) = 118649.75y
10002 x 11.862615y (J) = 118649.87y
(19775y (E) x 6 = 118650y)

Footnotes:
24 Neptune = ~3955y (3954.9916)
24 is 1/5th of 120 (see chart 1).

J*N / J+N = 1954.8559 / 176.65393 = 11.06602y
(whereas the conjunction period formula is J*N / J-N = 12.782793y)

42 x 118650 y = 1470y x 565
(1470 years is the long period of Jupiter-Saturn-Neptune-Earth multiple conjunction)
Since 42 = 21 x 2 and these are both Fibonacci numbers, the Fibonacci link is maintained – over a period of nearly 5 million years.

While all these numbers can only be regarded as a guide – hence the term ‘model’ – the accuracy of the NASA data is considered to be high.