Jupiter, Earth and Venus’ tropical alignments point to the mean solar cycle length

Precession of Earth’s axis [image credit: NASA, Mysid @ Wikipedia]

Introduction:
A number of researchers have hypothesised that the relative motions of Jupiter, Earth and Venus are connected to the length of solar cycles. In this post we will show that cyclic periods of 83 years (Gleissberg), 166 years (Landscheidt, Wilson), and 996 years (Eddy, Stefani et al) are found not just in the syzygies and synodic periods between these planets, but also in their heliocentric orientations with respect to a frame of reference rotating at the rate of Earth’s axial precession. This discovery has implications for our understanding of the forces driving that axial precession, and opens some new avenues for hypothesising about the links between planetary motion and solar activity variations.

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We propose that not only amplitude, but the mean period of the solar cycle itself derives from planetary influence in a specific manner.

Planetary theorists have from time to time alighted on an 83-year cycle, often attributed to the work of W. Gleissberg. In reality this is a half cycle, with the full one being 2*83 = 166 years. A notable study of this is in Ian Wilson’s PRP paper: The Venus–Earth–Jupiter spin–orbit coupling model (2013).

Figure 6 shows the smoothed torque curve from Fig. 5, replotted to highlight its long-term modulation (Horizons OnLine Ephemeris System, 2008). Superimposed on the torque are two sinusoidal envelopes with periods of 166.0 yr.

Figure 7 (from Wilson, 2011) shows that the variations in the heliocentric latitude of Venus essentially mimic the variations in the mean distance of Jupiter from the Sun, provided these variables are measured at the times when Jupiter aligns with either the inferior or superior conjunctions of Venus and the Earth. What this indicates is that the long-term net tangential torque should be weakest when Venus is at its greatest positive (most northerly) heliocentric latitude, and Jupiter is at its greatest distance from the Sun (˜5.44 A.U.). Figure 7 shows that this condition reoccurs roughly once every 166 yr and that they correspond in time with periods of low solar activity known as Grand Solar Minimum. [NB with one exception, noted in the paper].

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What we find is that Arnholm’s Solar Simulator tool gives us clear indication of the 166-year cycle, as these screenshots indicate. Moving the date by exactly 166 years shows the orientation of Jupiter (and Earth, as expected) in the same direction relative to the rotating frame of reference. When we vary the date by exactly 996 years (166*6), Venus is also in the same orientation as it was before.

In 166 tropical years (see below re. orbital data):
Jupiter tropical orbits (J) = 14
Proposed number of mean solar cycles (SC) in the period:
J orbits + 1 = 15

(Obviously solar cycle length varies, but we’re talking about mean values here.)

Using those numbers:
SC-J = 1 by our definition (using mean values), in one full cycle in 166 tropical years. The half cycle of 83 years has the same orientation, but with opposite positions of the two bodies.

This formula returns a mean SC period of 166/15 = 11.066 years. Converting from the tropical to sidereal frame of reference, this yields the same value other researchers (e.g. Wilson, Scafetta, Stefani, to name a few – see below) have found and/or discussed in published papers, of approximately 11.07 years.

14 sidereal Jupiter orbits of 11.8624 years (Seidelmann) divided by 15 = 11.0716 sidereal years.

Earth can be added to this test, e.g. at a time of conjunction with Jupiter, and both planets will maintain the same orientation as before. The mean period of 76 J-E conjunctions is 83 tropical years. However, 7 Jupiter sidereal orbits take slightly longer: 83.038305 years. This strongly suggests the alignments are related to Jupiter’s tropical year, which is about 2 days less than the sidereal one.

On the assumption of 7 Jupiter tropical orbits taking 83 Earth tropical years, as appears to be the case when using the solar simulator, we propose a cycle where:
2071 J(sidereal) = 2072 J(tropical) orbits in 24568 tropical years.
2071 = 148*14,-1
2072 = 148*14
24568 = 148*166 TY

If the mean solar cycle (MSC) occurs once more than the number of Jupiter sidereal orbits in 166 TY, then in 148 of those we should get:
MSC in 24568 TY = 2071+148 = 2219 (148*15,-1)
Check: 24568/2219 = 11.071654
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The simulator follows the 25771.5 year precession of Earth’s axis.

The currently accepted value of Earth’s axial precession period 25771.5 +/- 0.1 yr. is divisible by 83/2 (41.5) years.

The Earth’s axial precession doesn’t drive the orbit period of major solar system bodies such as Jupiter and Venus. Our finding shows the reverse; that Earth’s axial precession is driven by Jupiter and Venus’ entrainment of the Lunar orbit, which is the proximate cause of precession by its tidal action on Earth’s equatorial bulge.

Summary.

Our formula for a mean solar cycle in the tropical reference frame is: 15 SC = 14 J in 166 tropical years, where J = the Jupiter tropical orbit period. This confirms the empirically derived average solar cycle period of 11.07 years.

In our next post in this series, we’ll see how looking at the numerics of Jupiter and Saturn syzygy cycles also gets a lot simpler in the tropical frame of reference too. It’s almost as if the solar system was designed that way.

Notes and quotes:

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Quote 1: The precise physical origin of solar cycles is still poorly known and dynamo models are debated, but recent literature has strengthened the hypothesis of a correlation with planetary harmonics.
The planetary theory of solar activity variability: a review – Nicola Scafetta and Antonio Bianchini (2022).

Quote 2: The Sun’s magnetic activity varies cyclically over a period of about 11 years. An analysis of a new, temporally extended proxy record of this activity hints at a possible planetary influence on the amplitude of the cycle.
The planetary hypothesis revived – Paul Charbonneau (2013)

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Other papers re 83 years…

New Little Ice Age Instead of Global Warming? (c.2003)
– Theodor Landscheidt

It is shown that minima in the 80 to 90-year Gleissberg cycle of solar activity, coinciding with periods of cool climate on Earth, are consistently linked to an 83-year cycle in the change of the rotary force driving the sun’s oscillatory motion about the centre of mass of the solar system.
. . .
7. 166-year cycle in variations of the rotary force driving the sun’s orbital motion

The dynamics of the sun’s motion about the centre of mass can be defined quantitatively by the change in its orbital angular momentum L. The time rate of change in L is measured by its first derivative dL/dt. It defines the rotary force, the torque T driving the sun’s motion about the CM. Variations in the rotary force defined by the derivative dT/dt are a key quantity in this connection as they make it possible to forecast Gleissberg extrema for hundreds of years and even millennia.

A cycle of 166 years and its second harmonic of 83 years emerge when the time rate of change in the torque dT/dt is subjected to frequency analysis (Landscheidt, 1983).
. . .
The next secular minimum, indicated by an empty triangle, is to be expected around 2030. The following minima should occur around 2122 and 2201. The figure [Fig. 10] shows that the Gleissberg cycle behaves like a bistable oscillator. The current phase should last at least through 2500. Because of the link between Gleissberg cycle and climate, future periods of warmer or cooler climate can be predicted for hundreds of years. The next cool phase is to be expected around 2030.
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THE SOLAR WOLF-GLEISSBERG CYCLE AND ITS INFLUENCE ON THE EARTH (2000)
Shahinaz M. Yousef

Click to access THE_SOLAR_WOLF-GLEISSBERG_CYCLE_AND_ITS_INFLUENCE_ON_THE_EARTH_cli267_293.pdf

When Rudolf Wolf reconstructed solar activity based on historical observations of sunspots, he found an 11-year cycle going back to at least 1700. In 1853, Wolf also claimed that there is a 83-year sunspot
cycle. This longer term variation becomes evident simply by smoothing the data. Wolf’s original discovery of an 83-year cycle was forgotten, but the long cycle was rediscovered by H.H. Tuner , W. Schmidt, H.H. Clayton and probably others. After W. Gleissberg also discovered this 80 to 90 year cycle around 1938, he published so much material on the subject that ever since, it was called Gleissberg cycle (Hoyt and Schatten 1997).
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The Cause of the Gleissberg Cycle: A Working Hypothesis (2015)
– Sebastián Martín Ruiz

Every 83 years, Jupiter and the Earth are in the same relative position in the Solar System and this way Jupiter is seen against the same background of stars.
. . .
In conclusion, we think that the influence of Jupiter’s magnetic field on cosmic rays reaching the Earth and its relationship to Earth’s climate should be investigated.
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A Holocene North Atlantic SST record and regional climate variability (2011)
– Sejrup et al

A detailed correlation of the oxygen isotope record with solar proxies for the last 1 ka was not apparent for the whole 8 ka record. However, a statistically significant (>95%) spectral peak at c. 83 yr may represent the so-called Gleissberg solar cycle.
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A Model of a Tidally Synchronized Solar Dynamo
– Stefani et al (2019)

Specifically, we focus on the 11.07-years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14-years period or pulsating with a 11.07-years period, but also quadrupolar fields with corresponding periodicities.
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The Greenland Climate Clock (2022)
– Harald Yndestad

“The Little Ice Age” covers the six deepest Uranus-Neptune minima coincidences in period distances of 166 years.
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See also: Jovian Planets and Lunar Nodal Cycles in the Earth’s Climate Variability (2022)
– Harald Yndestad

…mean period coincidences of Tun-mco = [166.42, 332.83, 499.70, 998.49]…etc.
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Article @ space.com: Planetary Orbits May Explain Mystery of Sun’s 11-Year Cycle (Apr. 2022)

The orbits of Venus, Earth and Jupiter may explain the sun’s regular 11-year cycle, a new study suggests.

A team of researchers from Helmholtz-Zentrum Dresden-Rossendorf (HZDR), a research institute in Dresden, Germany, showed that the tidal forces of those three planets influence the cycle of solar activity, resolving one of the bigger questions in solar physics.

“Everything points to a clocked process,” Frank Stefani, a researcher at HZDR and lead author of the new study, said in a statement. “What we see is complete parallelism with the planets over the course of 90 cycles.”

What the team found is that the tidal forces are strongest when Earth, Venus, and Jupiter align, and that this alignment occurs every 11.07 years – falling at the same time as the solar minimum.

Link to study here.
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Comment on the 2022 Stefani study: That looks like the 996 year JEV period on the solar simulator screenshots of J-E-V triple conjunctions 1993 and +/- 996y.
996/11.06666 tropical years (mean solar cycle) = 90 SC.

Stefani’s team spoke of the planetary aspects, which are shown in our earlier four-part graphic. We have 12 occurrences of any given J-Sun orientation in that period (12*83 = 996), and 6*166 years, so 6 Jupiter-MSC (mean solar cycle) beats. The number of tropical Jupiter orbits in 996 years is 7 per 83 years, so 7*12 = 84 (and 90-84 = 6).

In an article at Science Alert: Our Sun’s Mysterious 11-Year Cycle Appears to Be Driven by Alignment of The Planets (2019), Dr. Stefani says his team used 1000 years of data (or 1000-2009 AD).
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New paper (pre-print): No evidence for absence of solar dynamo synchronization (March 2023)
– F. Stefani, J. Beer, T. Weier

ABSTRACT
Context. The old question of whether the solar dynamo is synchronized by the tidal forces of the orbiting planets has recently received renewed interest, both from the viewpoint of historical data analysis and in terms of theoretical and numerical modelling.

Aims. We aim to contribute to the solution of this longstanding puzzle by analyzing cosmogenic radionuclide data from the last millennium.

Methods. We reconsider a recent time-series of 14C-inferred sunspot data and compare the resulting cycle minima and maxima with the corresponding conventional series down to 1610 A.D., enhanced by Schove’s data before that time.

Results. We find that, despite recent claims to the contrary, the 14C-inferred sunspot data are well compatible with a synchronized solar dynamo, exhibiting a relatively phase-stable period of 11.07 years, which points to a synchronizing role of the spring tides of the Venus-Earth-Jupiter system.

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Planetary data from JPL: https://ssd.jpl.nasa.gov/planets/phys_par.html
Also:
‘4,333 days – the length of a year on Jupiter, in Earth days (4,332.82 days).’
— https://historyinnumbers.com/places/space/solar-system/planet-jupiter/

Mean solar cycle discussion at the Talkshop:
— https://tallbloke.wordpress.com/2021/10/30/orbital-resonance-and-the-celestial-origins-of-earths-climatic-changes-why-phi/