Now that all the relevant material has been brought forward we are ready to do a comparison of absolute barycentre cycle periods and Sunspot cycle periods.

(1) In post Explaining Planetary Alignments Relationship to the Sunspot Cycle http://ray.tomes.biz/barycentre-periods.png shows the barycentre periods found.

(2) Periods derived from long solar system motions over longer periods and these are known far more accurately. The barycentre periods will approach these values if longer periods are used. However it was desired to use a historical period for comparison with historical sunspots.

(3) Sunspot periods determined by Olvera as mentioned in my previous post.

(4) Sunspot periods determined by me as mentioned in the previous post. This is just as a cross check on the periods near 11 years which are slightly tricky to separate. The other periods are less influenced by each other.

Note that for longer periods the cycles analysis cannot determine the period anywhere near as accurately because there are so few cycles present.

Code:

   (1)         (2)         (3)       (4)
Barycentre  Planetary   - Sunspot Period -
Periods       Period     (Olvera)  (Tomes)
(years)       (years)    (years)   (years)

170      / 164.8   N    ~200
         \ 171.4  U-N
85          84.0   U    ~106 
57?         55.6  U+N     55.4
46          45.4  S-U     44.3
36          35.9  S-N     38.0
30          29.46  S      29.0
25?         25.00 S+N     24.1
23?         21.81 S+U     21.8
19.8        19.86 J-S     19.2
13.8        13.81 J-U     14.17     14.06
12.8        12.78 J-N     13.18     13.08
11.9        11.86  J      12.03     11.96
11.1        11.07 J+N     11.06     11.00
10.4        10.40 J+U     10.56     10.52
9.9          9.93 (J-S)/2 10.06     10.04
8.45         8.46 J+S      8.50      8.48
5.9          5.93 J/2

Conclusions

We see that the figures are generally similar. The weaker peaks in the spectra have generally been omitted or labeled with "?" above. The differences are small considering the period of data available. For example if we compare 11.86 years to (12.03 to 11.96) years we note that in 306 years there are 25.8 cycles, so that a discrepancy of 0.10 to 0.17 years represents just 0.22 to 0.36 cycles difference over that period which is about as good as can be hoped for.

The very longest cycles are not very good fits. When you only have 1.5 or 3 cycles in the data it is not possible to get an accurate fix (this incidentally is the same as the uncertainty principle).