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How did I choose the "quality" function of the syzygies ?

My research started with the reading of a paper, in "La Recherche", which was intended to fight against astrology. The paper quoted the work of Michel Trellis on the influence of planetary positions on sunspots. Interested, I found the papers of Trellis in the "Compte rendus de l'academie des sciences", and tried to imagine the possible link beetween the position of planets and the birth of active centers. I tried to compute tidal coefficients with the equations of Trellis but didn't find anything in the results, perhaps because my program was bugged, I don't know. I had to wait around 15 hours for each run (on a PC XT) : imagine my satisfaction one day when mother in law put her feet in the power supply cable of the computer just before I got results...

I made another program which calculated the dates of the syzygies, which were supposed to be the maximum of the tidal coefficients. I choosed 10 degres, for the first runs, to validate syzygies. Using it, I found that the VeEaJu syzygie occured every 594 days, in bursts, separated by a time without syzygie, which intrigated me. Increasing this angle, I saw the bursts spreading into time and interpenetrating each other like the teeth of a pair of gears. Looking at the heliocentric longitudes of the three planets at the syzygie, I saw that the syzygie was good at the middle of the burst, bad on the edges. Plotting the syzygies on a time scale (by hand), with a little bar at each syzygie, I had the idea to put a tall bar for a "good" syzygie, a smaller bar for a "bad" one.

Choosing a sector of 15 degres was the good value to have the two bursts just touch each other. So, I decided to give a value of 15 to a perfect syzygie, 10 to a syzygie in a sector of 5 degres, 5 to a syzygie in a sector of 10 degres, and 0 to all syzygies in a sector greater than 15 degres, with a linear decreasing function beetween these points.

Added december 2007 this sketch. It shows how the q function is computed from the "orb" : angle beetween the three planets axis. I tried also a "r" function which is the integral of q over the time. Gives approximately the same results.

I plotted the syzygies and saw a signal looking like the output of a rectifier bridge : archs of sinusoids. Calculating the period of the signal, I found around 11 years, which made me think of the solar cycle, as it was the starting point of my reasonning. Drawing the sunspot numbers curve on the same diagram as the VeEaJu syzygie, I found them in phase for 3 centuries.

From there, looking for data on the solar cycles, I found various papers, including those of Bracewell and Ribes which induced me to think that the main (and more stable) cycle in the sun was the magnetic cycle. I followed Bracewell in his way of plotting positively or negatively the sunspot numbers and did the same with the syzygies. I was surprised to see that in one burst we had Ve-Ea syzygies and in the following VeEa oppositions. That is the reason which made me give signs to the syzygies depending on the longitude difference beetween Earth and Venus, as I have absolutely no idea of the physical difference that could exist beetween the two situations.

And the fact is that, when you plot on the same diagram(fig 3) the quality signal and the signed wolf number, looking to it with a systems engineer's eye, you see the input-output diagram of a dynamic system.

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