Why Phi? – Jupiter, Saturn and the de Vries cycle

By far the two largest bodies in our solar system are Jupiter and Saturn. In terms of angular momentum: ‘That of Jupiter contributes the bulk of the Solar System’s angular momentum, 60.3%. Then comes Saturn at 24.5%, Neptune at 7.9%, and Uranus at 5.3%’ (source), leaving only 2% for everything else. Jupiter and Saturn together account for nearly 85% of the total.

The data tell us that for every 21 Jupiter-Saturn (J-S) conjunctions there are 382 Jupiter-Earth (J-E) conjunctions and 403 Saturn-Earth (S-E) conjunctions (21 + 382 = 403).

Since one J-S conjunction moves 117.14703 degrees retrograde from the position of the previous one, the movement of 21 will be 21 x 117.14703 = 2460.0876, or 2460 degrees as a round number.

The nearest multiple of a full rotation of 360 degrees to 2460 is 2520 (= 7 x 360).
Therefore 21 J-S has a net movement of almost 60 degrees (2520 – 2460) from its start position.

It follows that 6 x 21 J-S has a net movement of 6 x 60 = 360 degrees (just under) relative to its start position, giving us a full cycle of 126 J-S conjunctions. This necessarily requires a whole number of orbits of Jupiter and Saturn, and the numbers in question for this 126 J-S cycle are 85 for Saturn and 211 for Jupiter (211 – 85 = 126). The whole number of Earth orbits is 2503 (years). With these 3 sets of orbits we can create a chart (below, right):

The synodic periods all occur in multiples of six, and one sixth of 2503 years is 417.1666 years which is 21 J-S, 382 J-E, 403 S-E and two de Vries cycles. Since 382 is an even number, there will also be a J-E conjunction at the ‘half-period’ (averaging 208.58333 years) i.e. every de Vries cycle (191 J-E), while Saturn will be in opposition so J-S and S-E (odd numbers: 21 and 403) will also be oppositions, not conjunctions.

Thus the de Vries cycle has in theory two alternating configurations: one a triple conjunction of Jupiter, Saturn and Earth, and the other a Jupiter-Earth conjunction with a Saturn opposition. That would work if conjunction periods were uniform, but as they vary around a mean (due to known speed variations of the individual planets in their elliptical orbits) things will not necessarily be quite as exact.

The effects of these types of planetary conjunctions are found in numerous studies, some discussed here at the Talkshop. Other possible mechanisms are analysed and these may suggest ways of identifying the factors behind when a de Vries cycle starts/ends.

Another study noted: “the de Vries cycle has been found to occur not only during the last millennia but also in earlier epochs, up to hundreds of millions [of] years ago.” So there is little question that such a cycle is a genuine phenomenon.

Looking more closely at the numbers we find:
21 is a Fibonacci number
382 = 1000/Phi²
403 = 13 (Fib.no.) x 31

This puts the period itself in a Phi relationship with other significant Fibonacci multiples of J-S conjunctions, e.g. 89 (see here) and 233 J-S = ~27 Uranus-Neptune conjunctions.
For example the number of J-E in 89 J-S is 1619 (1000 x Phi = ~1618).

Below are some graphical illustrations (here restricted to the giant planets plus Earth) using a solar simulator :
[click to enlarge]

Whether these dates were markers of a particular de Vries cycle starting/ending is uncertain, but the pattern is there. A study by German scientists said the de Vries cycle was at a maximum in the late 20th century:
http://notrickszone.com/2013/12/03/german-scientists-show-climate-driven-by-natural-cycles-global-temperature-to-drop-to-1870-levels-by-2100/

‘The spectrum Fig. 2 (Fig. 1d of [2]) shows clearly a 208-year period as the strongest variation of the solar activity’ – see graphic here. They also refer to ‘the last AMO/PDO minimum of 1940′, which is the year mentioned above where there was a strong Jupiter-Saturn-Earth conjunction. There may or may not be a better candidate for the start of the current 2503-year planetary cycle.

Note also that 2503 years minus half a de Vries cycle (~104.3 years) closely matches 14 Uranus-Neptune conjunctions (2399.7 years).