Reference:
Given that:
DT = the lunar Draconic year ________= 0.9490 sidereal yrs = 346.620076 days
DP = lunar nodal precession _________= 18.599 sidereal yrs
AT = the lunar Full Moon Cycle______= 1.1274 sidereal yrs = 411.784430 days
AP= lunar apsidal precession________ = 8.851 sidereal yrs
AD = alignment period of the lunar line-of-apse and the lunar line-of-nodes = 5.9971 sidereal yrs
where 1 -- 1/AT = 1/AP , 1/DT -- 1 = 1/DP* and 1/AD = 1/DP + 1/AP***
and
TJ = Sidereal orbital period of Jupiter __= 11.8622 sidereal yrs = 4332.75 days
SJS = Synodic period of Jupiter/Saturn _= 19.859 sidereal yrs
SVE = Synodic period of Venus/Earth__= 1.5987 sidereal yrs
It can be shown that the apsidal precession period of the lunar orbit is linked to the synodic periods of Venus/Earth and Jupiter/Saturn by the following relationship:
AP ≈ [SJS×10SVE] / [SJS + 10SVE] = 8.857 yrs
[with an error of 0.006 sidereal yrs = 2.2 days]
and that the lunar nodal precession period is linked to the sidereal orbital period of Jupiter by:
5/4×DT = (1/10)×TJ**
See the following link:
Now this last equation can be rearranged using the relationships (*) and (**) to give:
DP = TJ / [25/2 -- TJ] = 18.599 yrs
Hence, using the relationship (***), we can see that the six year re-alignment period between the lunar line-of-apse and the lunar line-of-nodes is synchronized with the synodic periods of Venus/Earth and Jupiter/Saturn and the orbital period of Jupiter.
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