**Minor Updates: 12/Oct/2015**

**SUMMARY**

**The two periods that control the precession of the tilt (i.e. the Draconic year = DY) and elongation (i.e. the Full Moon Cycle = FMC) of the lunar orbit are directly related synodic period of Venus and the Earth (T (VE)) via the formula.**

**4.0 DY x 1.0 FMC / (4.0 DY - 1.0 FMC) = T (VE)**

**This shows that there is a direct connection between the relative planetary orbital periods of Venus and the Earth and factors which control level of tidal stresses upon the Earth's atmosphere and oceans, namely the rates of precession of the lunar line-of-nodes and the lunar line-of-apse.**

**BLOG POST**

From the previous blog post I have found that:

if the minimum period between peaks in the rate of change in tidal stresses upon the Earth caused by the change in strength of the lunar tides (i.e. 10.14686 tropical years)

**amplitude modulates**the minimum period between of the rate of changes in tidal stresses upon the Earth caused by the change in direction of the lunar tides (i.e. 1.89803 tropical years), you find that the 1.89803 year tidal forcing term is split into a positive and a negative side-lobe, such that:
Positive side-lobe

[10.1469 x 1.89803] / [10.1469 – 1.89803] = 2.334(7) tropical yrs = 28.0 months

Negative side-lobe

[10.1469 x 1.89803] / [10.1469 + 1.89803] = 1.598(9) tropical yrs

The time period of the positive side-lobe is almost exactly the same as that of the Quasi-Biennial Oscillation (QBO). The QBO is a quasi-periodic oscillation in the equatorial stratospheric zonal winds that has an average period of oscillation of 28 months, although it can vary between 24 and 30 months (Giorgetta and Doege 2004).

[10.1469 x 1.89803] / [10.1469 – 1.89803] = 2.334(7) tropical yrs = 28.0 months

Negative side-lobe

[10.1469 x 1.89803] / [10.1469 + 1.89803] = 1.598(9) tropical yrs

However, the important period that is discussed in this post is the 1.589(9) tropical year negative side-lobe period. This just happens to be synodic period of Venus and the Earth = 583.92063 days = 1.5987 tropical years, to within an error of ~ 1.8 hours).

Interestingly, the negative side-lobe period can also be obtained by the beat period between 4.0 Draconic years = 4.0 DY = 3.79606 tropical years and 1.0 Full Moon Cycles = 1.0 FMC = 411.78445 days = 1.1274 tropical years.

4.0 DY x 1.0 FMC / (4.0 DY - 1.0 FMC) = 585.7530 days = 1.6037 tropical years

Where 1.0 Draconic years is the time it takes the lunar line-of-nodes to re-synchronize with the lunar phase (synodic) cycle.

This beat period differs from the Venus Earth Synodic period by 0.005 tropical years = 1.84 days.

[N.B. The 3.79606 tropical year period is part of the 19.0 year Metonic Cycle with the Moon's phase returning to new moon at a node after 1387.481264 days (=3.79606 tropical years). This happens because 47 Synodic months = 1387.937678 days and 51 Draconic months = 1387.82322 days. With this cycle, the synodic lunar cycle realigns with the seasonal calendar once every 4 tropical years, 4 + 4 = 8 tropical years, 4 + 4 + 3 = 11 tropical years, 4 + 4 + 3 + 4 = 15 tropical years and 4 + 4 + 3 + 4 + 4 = 19.0 tropical years. to give and average spacing of roughly (4 + 4 + 3 + 4 + 4)/5 = 3.8 years.]

This beat period differs from the Venus Earth Synodic period by 0.005 tropical years = 1.84 days.

[N.B. The 3.79606 tropical year period is part of the 19.0 year Metonic Cycle with the Moon's phase returning to new moon at a node after 1387.481264 days (=3.79606 tropical years). This happens because 47 Synodic months = 1387.937678 days and 51 Draconic months = 1387.82322 days. With this cycle, the synodic lunar cycle realigns with the seasonal calendar once every 4 tropical years, 4 + 4 = 8 tropical years, 4 + 4 + 3 = 11 tropical years, 4 + 4 + 3 + 4 = 15 tropical years and 4 + 4 + 3 + 4 + 4 = 19.0 tropical years. to give and average spacing of roughly (4 + 4 + 3 + 4 + 4)/5 = 3.8 years.]

1.0 Full Moon Cycles is the time it takes for the lunar line-of-apse to re-synchronize with the lunar phase (synodic) cycle.

A Full Moon Cycle (FMC) is the time required for the Perigean end of the lunar line-of-apse to re-align with the Sun close to a new moon:

**1.0 Full Moon Cycle = 1.0 FMC = 411.78445 days = 1.1274 tropical years (1)**

The Moon almost returns to being New at perigee after 1.0 FMC because 14 Synodic months = 413.42824 days and 15 anomalistic months = 413.31825 days.

Hence, the two periods that control the precession of the tilt (i.e. the Draconic year) and elongation (i.e. the Full Moon Cycle) of the lunar orbit are directly related synodic period of Venus and the Earth (T(VE)) via the formula.

4.0 DY x 1.0 FMC / (4.0 DY - 1.0 FMC) = T(VE)

This shows that there is a direct connection between the relative planetary orbital periods of Venus and the Earth and factors which control level of tidal stresses upon the Earth's atmosphere and oceans, namely the rates of precession of the lunar line-of-nodes and the lunar line-of-apse.

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Updated 12/Oct/2015

[NB: The lunar and planetary periods used in this post:

Lunar J2000.0 (1 January 2000 12:00 TT) values:

Synodic month = 29.5305889 days

Anomalistic month = 27.554550 days

Draconic month = 27.212221 days

Tropical Year = 365.242189 days

Planetary Values:

Updated 12/Oct/2015

[NB: The lunar and planetary periods used in this post:

Lunar J2000.0 (1 January 2000 12:00 TT) values:

Synodic month = 29.5305889 days

Anomalistic month = 27.554550 days

Draconic month = 27.212221 days

Tropical Year = 365.242189 days

Planetary Values:

Sidereal orbital period of the Earth = 365.256363 days

Sidereal orbital period of Venus = 224.70069 days

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