Why Phi? – Jupiter, Saturn and the ice giants

Giant planets of the solar system [image credit: universetoday.com]

This post on the ice giants Uranus and Neptune follows on from this one:
Why Phi? – Jupiter, Saturn and the inner solar system

The main focus will be on Uranus. A planetary conjunction of three bodies (e.g. two planets and the Sun, in line) is also known as a syzygy.

Here’s the notation for the table shown below:
J-S = Jupiter-Saturn conjunctions
S-U = Saturn-Uranus conjunctions
U-N = Uranus-Neptune conjunctions

Each of the columns: U, S-U, J-S shows a Fibonacci progression.

Accuracy of best match is between 99.965% and 99.991%.

Quoting Wikipedia: ‘The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected.’
The Greek letter φ (phi) represents the golden ratio.

So what we see here is that as well as the conjunctions S-U and J-S, there is an orbital element i.e. Uranus in these evident Fibonacci patterns.

144 J-S is divisible by 9 giving this approximate formula:
7 S-U = 16 J-S (= 23 J-U)

27 U-N is divisible by 3 giving this approximate formula:
9 U-N = 34 S-U (= 43 S-N).

Turning to Neptune, since 14 Jupiter-Neptune conjunctions take 178.959 years, there is a close match with 9 Jupiter-Saturn conjunctions i.e. the solar motion cycle discussed by Gerry Pease at the Talkshop (here).

Graphic: Sun returns to solar system barycentre (~179 years)

Another Neptune link: the U-N conjunction aligns with J-S at 27 U-N = 233 J-S as shown in the data table above.

Data source: http://ssd.jpl.nasa.gov/?planet_phys_par