## Re-visiting one of the PRP papers

Posted: January 15, 2017 by oldbrew in Cycles, modelling, research, solar system dynamics
Tags: ,

Jupiter-Saturn-Earth orbits chart

Browsing through some of the PRP papers I came across this at the end of the introduction to R.J. Salvador’s paper – A mathematical model of the sunspot cycle for the past 1000 yr:

Another well-known oscillation found in solar records is
the de Vries cycle of 208 yr (see McCracken et al., 2013).
The frequency of 1253 yr, together with the Jose frequency of
178.8 yr, produces a beat of 208 yr and is used in the model.

Looking back at this Talkshop post from 2014 I wondered if these numbers could be linked to it.

From the chart [top line: ‘2503 E’] I’d suggest the ‘frequency of 1253 years’ could be the half-period of the 2503 year cycle i.e. 1251.5 years, a difference of only 0.0012%.

With the ‘Jose frequency of 178.8 years’ being the mean period of 9 Jupiter-Saturn conjunctions (by definition), we see from the chart that 1251.5 years would be 63 J-S, since it’s half the full period of 2503 years or 126 J-S [= 63 * 2].

Therefore the two periods would be in a simple ratio of 1:7.

To obtain the de Vries period:
(63 * 9)/(63 – 9) = 567 / 54 = 10.5 J-S = 208.583 years
10.5 = 21/2 J-S

As we see on the chart, 21 J-S is a fundamental period of it [since 21 * 6 = 126], representing 2 notional de Vries cycles.
Apart from mean duration, the 2 cycles are not identical since 10.5 is obviously not a whole number, but are a pair.

One of the points about the 2503 year period is that it represents a more or less exact number (41) of retrograde revolutions of the Jupiter-Saturn conjunction position.
1 J-S = 117.14703 degrees of retrograde movement
126 * 117.14703 = 14760.525 degrees
14760 = 360 * 41

So after 1251.5 years the J-S conjunction would be directly opposite its ‘starting position’.
(With Kepler’s ‘trigon‘, 3 J-S returns to about 8.5 degrees from its initial position.)

Another reason for the 2503 year period is that it contains almost exact whole numbers of Jupiter, Saturn and Earth orbits (see chart), with conjunctions of all three occurring at twice the notional de Vries interval (illustration graphic below).

[Caption: the repeating conjunction orientation of the three planets (J,S,E) every 417.16~ years or 2 de Vries cycles – using Arnholm’s solar simulator]