Tuesday, May 5, 2015

The six year re-alignment period between the lunar line-of-apse and line-of-nodes is set by the planets.


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/DPand  1/AD = 1/DP + 1/AP*** 

and

T= 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.