Picking up from where we left off here…
Three well-known aspects of lunar motion are:
Lunar declination – minimum and maximum degrees
Orbital parameters – perigee and apogee distances (from Earth)
Anomalistic month – minimum and maximum days
Standstill limits due to the lunar nodal cycle
‘The major standstill limit of the moon can be reached if the lunar node is near the vernal (or autumnal) point, and with the moon at its max. distance from the equator, equal to a declination at present days of 23.44° + 5.1454°= 28.59°.
The minor standstill limit of the moon can be reached if the lunar node is near the vernal (or autumnal) point, and with the moon at its min. distance from the equator, equal to a declination at present days of 23.44°- 5.1454° = 18.29°.’
28.59 / 18.29 = 1.5631492
4th root of 1.5631492 = 1.11815
This number leads to the key to the puzzle.
Note – 23.44° is the present day tilt of the Earth:
‘Earth’s obliquity oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle; Earth’s mean obliquity is currently 23°26’12.6″ (or 23.43684°) and decreasing.’ – Wikipedia
So Earth is now near the mean of its min. and max. angles of tilt.
Perigee and Apogee
‘The Moon revolves around Earth in an elliptical orbit with a mean eccentricity of 0.0549. As a result, the Moon’s distance from Earth (center-to-center) varies with mean values of 363,396 km at perigee (closest) to 405,504 km at apogee (most distant).’
405504 / 363396 = 1.1158735
‘The anomalistic month is defined as the time it takes the Moon to make one revolution around its orbit with respect to the perigee. The length of the mean anomalistic month as calculated for the year 2000 is 27.55455 days (27d 13h 18m 33s). However, the actual duration can vary by several days due to the gravitational perturbations of the Sun on the Moon’s eccentric orbit. […] The shortest anomalistic month is 24.629 days (2.925 days shorter than the mean) while the longest anomalistic month is 28.565 days (1.011 days longer than the mean).’ – astropixels.com
27.55455 / 24.629 = 1.1187847
(28.565 / 27.55455 = 1.0366708
1.0366708³ = 1.1140959)
Phi, or the golden ratio = (√5 + 1) / 2 = 1.618034
√5 / 2 = 1.118034 = Phi – 0.5
The lunar data results above all cluster round 1.118034, which is also the square root of 5/4.
Declination – minimum:geometric mean ratio is 5:4 approx, and g. mean:maximum ratio is 4:5 approx.
So the fourth root ratio mentioned earlier (standstill limits) is the result of two square roots.
via Tallbloke’s Talkshop
November 9, 2018 at 10:07AM