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Beginning of a confirmation : correlating with Schove's dates


Several readers of my W3 site quoted the work of Schove. He made analyses of old auroral reports in northern traditional sources and, plotting them on a time scale, inferred a series of dates for sunspots cycles maxima for the years -300 (before JC) to actual period.
I asked to one of these readers, Ray Tomes, author of a very interesting "Harmonic theory" and who also published on solar cycles, to send me Schove's estimated solar cycle maxima years. Here is the answer :

From: rtomes@kcbbs.gen.nz (Ray Tomes)
Subject: Years of Schove sunspot maxima
Schove dates ssmax

-293  -283  -272  -261  -249  -236  -223  -214  -205  -192 
-182  -172  -163  -149  -135  -125  -113  -104   -91   -82 
 -72   -62   -53   -42   -27   -16    -5     8    20    31  
  42    53    65    76    86    96   105   118   130   141 
 152   163   175   186   196   208   219   230   240   252 
 265   277   290   302   311   321   330   342   354   362 
 372   387   396   410   421   430   441   452   465   479 
 490   501   511   522   531   542   557   567   578   585 
 597   607   618   628   642   654   665   677   689   699 
 714   724   735   745   754   765   776   787   798   809 
 821   829   840   850   862   872   887   898   907   917 
 926   938   950   963   974   986   994  1003  1016  1027 
1038  1052  1067  1078  1088  1098  1110  1118  1129  1138 
1151  1160  1173  1185  1193  1202  1219  1228  1239  1249
1259  1276  1288  1296  1308  1316  1324  1337  1353  1362
1372  1382  1391  1402  1413  1429  1439  1449  1461  1472 
1480  1497  1505  1519  1528  1539  1548  1558  1572  1581
1591  1604  1615  1626  1639  1649  1660  1675  1685  1693
1705  1718  1727  1738  1750  1761  1769  1778  1787  1804
1816  1830  1837  1848  1860  1870  1883  1893  1905  1917
1928  1937  1947  1957  1968  1979 

I modified the "plots.pas" program to allow the plotting of Schove's dates along with the other syzygies signals. The Schove's dates are plotted as blue bars, given the same sign as the filtered syzygie quality signal.
I ran the program at first, without believing too much that it could be correlated on such a long period : the results were surprising. I present them on 700 years periods, as plots on a longer time are difficult to read on a screen.

On the 1100 - 1800 period, the correlation is very good. It seems that some auroras were a little shifted with the maximum of the syzygies signal, but never more than three years, which is excellent.
On the 400 - 1100 period, we get almost the same quality of the correlation.
On the -300 - +400 period, we see that the result is not so good. The correlation is good down to 260. Before that time, an abrupt phase shift seems to occur. At -300, there is nearly a 180 phase shift (10 years difference)

This difference could be due to several reasons :

For the first hypothese, I would like to compare with other softwares. Could somebody give me some positions (even geocentric) of Jupiter, Earth (or Sun) and Venus for some dates beetween -300 and +400 ? Precise julian or gregorian calendar. Thanks to send that by mail to jean-pierre.desmoulins@wanadoo.fr

The second hypothese is obvious. I used the actual parameters of the planets to compute the syzygies, with no secular interaction. I tried to check what difference in the angular speed of the planets was necessary to suppress the phase shift on the -300 - +400 period. For this, I included the following lines at the beginning of the "syzygies.pas" program :

        with planete [rang_venus] do LP := LP * 0.99999 ;
        with planete [rang_terre] do LP := LP * 1.00001 ;
LP being the angular velocity (degrees / days) on the orbit, this means that I slow down a little Venus of minus E-5 and that I accelerate a little Earth of plus E-5, Jupiter being supposed to stay regular. The result shows a perfect correlation on this period. It creates some problems from 400 to 1100, while the 1100 to 1800 result is nearly unchanged. This seems to show that when retro computing the position of a planet through centuries, quadratic angular acceleration terms should be used to model the secular interaction.

Now, for the third hypothese, it would be interesting to know how Schove dated his materials on the -300 - +400 period.

In conclusion, I would just say that I hope I will soon be able to confirm my ephemerids. If they are valid, being neither a specialist of secular interaction beetween planets nor of old runic texts, I cannot make my mind. What would be very helpfull would be to have records of the heliacal cycle of Venus absolutely dated, around these dates. So, if a specialist of the Mayas calendars or of the babylonian astronomic tablets could help...thanks in advance.


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