We have found really good evidence that the orbits of planets are intimately linked with the solar cycle and influence solar activity levels. Jupiter and Saturn are the two biggest planets in the solar system. They both have strong magnetospheres which exhibit immense aurorae at their poles. Their orbital distances and velocities are such that the timings generated by their interaction match timings derived from spectrographic analysis of the Sun’s activity as demonstrated below. What is the probability that these relationships are due to mere chance or coincidence? In our view – vanishingly small. So are we claiming that the planets cause the Sun’s activity cycles? We believe this is the wrong question. The question we should be asking is:
What are the feedback mechanisms which bring about these relationships, how are they maintained, and what is their physical basis?
But first things first, what have we found?
Over on Bart’s thread, we’ve been looking at a Power Spectral Density (PSD) analysis of the Sunspot data from 1749. After the application of some clever signal processing techniques, Bart says:
The sunspot count appears to reflect the energy of these combined processes at around 20 and 23.6 years, which necessarily has apparent periods of 0.5*T1, 0.5*T2, T1*T2/(T2+T1), and T1*T2/(T2-T1) years, or 10 years, 11.8 years, 10.8 years, and 131 years.
The 11.8 year period is very close to 11.86 years, the orbital period of Jupiter.
The 10 year period is very close to 9.93 years, half the synodic period of Jupiter and Saturn.
(Conjunction and opposition of these two planets are both effective tidally)
So if we hypothesise that these are the two planetary frequencies which are combining to govern the solar cycle, we are left with the 10.8 year period and 131 year period to explain in terms of their appearance in the spectral analysis.
But our solar physicist disputant Leif Svalgaard says the opposite. He maintains the 10.8 year period is the fundamental oscillation period of the so called ‘Solar Dynamo’ theory still favoured by the mainstream solar scientists, and coupled with the longer period, can then reproduce the periods which only coincidentally tally with the orbits and conjunctions of Jupiter and Saturn. Both interpretations are equivalent, and so we are left needing more evidence to settle the matter one way or the other.
Yesterday on the Hale cycle thread, regular contributor Tenuc put up a link to a graph he had found on the net claiming to show a strong correlation between Jupiters changing distance from the Sun and the average sunspot number. I traced this back to the original thread it had come from on Bautforum.com and there I found a link to a 1984 paper by Schwentek and Elling of the Max Planck Institute for Aeronomy. Here’s the Abstract:
And there in the last sentence of the paragraph is a big clue:
The clearly dominant spectral band in sunspot number, the solar cycle of 10.8 years. is given by the configuration period of Jupiter and Saturn (19.859 yr) times the ratio of their distances from the Sun (0.545)
This is in fact equivalent to Bart’s third formula for ‘necessarily apparent periods'; T1*T2/(T2+T1)
i.e. 23.72 (twice Jupiters orbital period) times 19.85 (the J-S synodic period) all divided by 23.72 plus 19.85, which equals 10.806.
Kepler’s third law states: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
So for the orbits of Jupiter(11.86 years) and Saturn(29.46 years) we find that the squares (multiplication by itself) of the orbital periods are 140.67 and 867.3. The cube roots of these values are 5.2 and 9.54. The ratio of these values (one divided by the other) is 0.545. Jupiter’s orbit is a little over half the size of Saturn’s.
As Jupiter passes Saturn at conjunction it then takes just under 20 years for Jupiter to catch up with Saturn again. We can calculate this using a law discovered by Kepler’s mentor Copernicus:
The Synodic period is given by the inverse of the inverse of the orbital period of the slower moving body minus the inverse of the orbital period of the faster moving body:
Synodic period of Jupiter and Saturn is 1/(1/11.86 – 1/29.46)=19.852 years
We can then multiply that result by the orbital distance ratio of 0.545 we calculated to obtain 10.819
The mismatch of 0.013 between Bart’s theoretical result (10.806) and this celestial mechanic’s result is due to the imperfection of Keplers law (discovered 1619), which in fact applies only to single bodies of zero mass, but it’s near enough for farmwork. :)
So all three periods around the length of the solar cycle which are observed in the spectral analysis of the sunspot numbers derive from the related orbital motions of Saturn and Jupiter. The fourth ‘necessarily apparent’ period of ~131 years is given by Bart’s equation T1*T2/(T2-T1) years. When we use the actual orbital periods rather than the DSP analysis estimates this works out at 122 years, which is within error for the spectral analysis, which reaches limits of useability as the frequency of the period’s appearance in the length of the dataset approaches zero.
The half period of 122 is 61 years and this also turns out to be related to Jupiter and Saturn another way. The 61-year cycle is given by 1/(1/9.93 – 1/11.86), where 9.93 is half the time between conjunctions of Saturn and Jupiter (half, because tides are raised also on the other side of the sun), and 11.86 is Jupiter’s orbital period, as was suggested long ago by Brown [MNRAS, vol 60, pages 599-606, 1900] – My thanks to Leif Svalgaard for this excellent reference!
Furthermore, if we consider the fact that Jupiter’s orbital period is itself close to the average length of the solar cycle, and the fact that the alternating magnetic polarity of the solar cycles means that the Hale cycle of double the length can be considered as a solar cycle in it’s own right, then we can also take a look at what we get by doubling Jupiters orbital period in the above equation. 1/(1/9.93 – 1/23.72)=17.01 years, the period Leif Svalgaard claims for the “true solar cycle length” due to the continuing appearance of ‘old polarity’ sunspots after the new ~11 year Schwabe cycle has begun and ‘new polarity’ spots start to appear before it finishes.
Five out of five solar periods now accounted for by Jupiter and Saturn:
Kerrrching – JACKPOT!
We hypothesise that Saturn and Jupiter provide the background drumbeat which governs the solar cycle. The modulation of that beat by the other heavy gas giant planets and magnetically active inner planets is the subject of further investigation which has been taking place on this blog and others. We are getting closer to solving the puzzle and being able to predict the future evolution of solar activity levels with a high degree of confidence. That will revolutionise climate science, because once we can confidently predict solar activity, climatologists will ‘rediscover’ the Sun as an important climate driver. Watch this space.