Tropical timings – a 193-year solar magnetic cycle

NASA image of the day: Sun’s quiet corona [credit: NASA/SDO]

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Using planetary data from our tropical timings posts we offer a slightly recalculated version of this cycle, based on Ian Wilson’s PRP paper formula, numbered (1) in the document:
(22.137 × 19.859)/(22.137 − 19.859) = 192.98 yr.

Figure 12 in the PRP paper refers to a 193-year period.

We use a tropical years version of the Jupiter-Saturn (J-S) conjunction cycle of 19.860714 TY (83*67/280). Based on our calculation that 14 Jupiter orbits = 15 mean solar cycles per 166 tropical years (see this post), the mean Hale cycle is 2* 166 TY/15 = 22.13333 TY. We substitute this for Ian Wilson’s ‘VEJ torquing cycle’ of 22.137 years (see the PRP paper), as follows:
(22.13333 * 19.860714)/(22.13333 – 19.860714) = 193.42608 TY.

On a longer time scale, we find 201 Hale cycles = 224 J-S = 23 solar magnetic cycles (224 – 201) in 4448.8 TY.

Note that almost the same period (~4450 years) is found by researcher Prof. Harald Yndestad, by a different route, in this 2022 planetary science paper:
‘The mean envelope time period of JSUN cycle phase coincidences is 4449.28 years.’
(JSUN = the 4 giant planets of the solar system, by their initial letters).

A broader explanation of this cycle can be found at the start of the Discussion section of the paper.
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This 2021 press release by the German research centre HZDR has a section headed:
Rosette-shaped movement of the sun can produce a 193-year cycle

Researcher Frank Stefani of HZDR on Ian Wilson’s formula:

Mathematically, the 193 years arise as what is known as a beat period between the 19.86-year cycle and the twofold Schwabe cycle, also called the Hale cycle. The Suess-de Vries cycle would thus be the result of a combination of two external “clocks”: the planets’ tidal forces and the sun’s own movement in the solar system’s gravitational field.

(NB it’s not the de Vries cycle in our opinion. We believe the de Vries cycle occurs as a pair every 21 J-S, so one would be 10.5 * 19.860714 = 208.5375 TY. Other researchers have pegged that cycle at around 208 years in various papers e.g. Ian Wilson, here. Wikipedia says it’s ‘a cycle present in radiocarbon proxies of solar activity with a period of about 210 years’.)

The actual 193-year solar magnetic cycle arises from the calculation referred to in the related HZDR paper:

Still, it is the dominant 19.86-year cycle which has the capacity to produce, in concert with the 22.14-year Hale cycle, a beat period of 19.86 × 22.14/(22.14 − 19.86) = 193 years, as worked out in the above-mentioned paper by Wilson (2013) and also by Solheim (2013).

The ratio of that to the 208~ year de Vries cycle would be 69:64.

The 193-year cycle appears again in this 2024 press release by HZDR for another paper by Stefani et al, which says:
‘And the model even predicts long-term fluctuations of the sun because the movement of the sun around the solar system’s center of gravity causes a so-called beat period of 193 years on the basis of the Schwabe cycle.’

More on that can be found in this Talkshop post – The sun’s clock: New calculations support and expand planetary hypothesis (2021).
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Image: Sun [credit: NASA/SDO]

Source: https://tallbloke.wordpress.com/2026/03/27/tropical-timings-a-193-year-solar-magnetic-cycle/