1. The Defacto 13 year Lunar
tidal cycle
There is a defacto 13 year lunar
tidal cycle created by the difference
between 31 perigee/syzygy cycle and the
18 year Saros cycle, such that:
13 years = 31 – 18
years
Now the reason for
the 18.03 sidereal year Saros cycle is:
223 Synodic
months______= 18.02931 sidereal years
239 anomalistic
months___ = 18.02990 sidereal years
242 Draconic
months______= 18.02941 sidereal years
[with closest
alignment between Synodic and Draconic cycles,
though the
anomalistic cycle is not far off]
while the reason for
the 31 year cycle is:
383.5 Synodic
months______= 31.005568 sidereal years
411.0 anomalistic
months___ = 31.005401 sidereal years
416.0 Draconic
months_____= 30.992708 sidereal years
[with closest
alignment between Synodic and anomalistic cycles]
hence, the defacto
13 year cycle possibly comes about because:
160.5 Synodic
months______= 12.976254 sidereal years
172.0 anomalistic
months___= 12.9754963 sidereal years
174.0 Draconic
months_____= 12.9632963 sidereal years
[with closest alignment
between Synodic and anomalistic cycles]
2.
The 208 year de Vries Cycle
Now
16 x 13 years = 208 years
Thus, this would indicate that a possible
reason for the ~ 208 de Vries cycle is:
16 x 160.5 = 2568.0 Synodic
cycles________= 207.6200718 sidereal years
16 x 172.0 = 2752.0 anomalistic cycles_____= 207.6079414 sidereal years
16 x 174.0 = 2784.0 Draconic cycles_______= 207.4127406 sidereal years
or with a drift of 3.0 Draconic cycles in roughly 208 years you get:
2787.0 Draconic cycles___= 207.6362457 sidereal years
[with closest alignment between Synodic
and anomalistic cycles]
Finally, if you allow for a slight drift
of 4.5 Synodic cycles and 5.0 anomalistic and
Draconic cycles you get:
2572.5 Synodic cycles___= 207.98389
sidereal yrs_____= 207.99196 tropical yrs
2757.0 anomalistic cycles_= 207.98514 sidereal yrs____= 207.99321 tropical yrs
2792.0 Draconic cycles___= 208.00875 sidereal yrs____= 208.01682 tropical yrs
Of course, the drift required to realign
the sidereal/tropical reference frame
with the seasonal year of 4.5 synodic = 5.0 anomalistic = 5.0
Draconic cycles
over 208 tropical years is not arbitrary since this is equivalent
to:
132.887 days in 75970.375 days = 0.0017492
of a full cycle in 208 tropical years.
which for the Earth’s orbit is 0.6297133
degrees in 208.0 tropical years
or 10.90 ~ 11 arc second per tropical year!
This is just the (pro-grade) rate of
precession of the perihelion of the Earth’s orbit
which is
currently about:
11.45 arc seconds per year – theoretical
11.62 arc seconds per year – observed epoch 2000.
CONCLUSION
Hence, If we look at times where the perigee of the lunar orbit
points at the
Sun, they will realign with the seasons in (almost) precisely 208.0 tropical
years or one de Vries Cycle, if you measure the alignment in a
reference
frame that is fixed with the Earth’s orbit (i.e. a frame that is
tracking the
perihelion precession of the Earth’s orbit).