IMPORTANT SUMMARY:

The stresses caused by lunar tides in the Earth's atmosphere and oceans should be a maximum when the tidal forces of the Moon acting upon the Earth change by the largest amount in either strength or direction over a relative short period in time.

There are two such conditions where this takes place:

When a new/full moon occurs at or near the times when the lunar line-of-apse (see figure 1) is pointing towards the Sun. This is true because a new/full moon at closest perigee produces the strongest lunar tidal forces upon the Earth while a new/full moon at apogee produces the weakest lunar tidal forces upon the Earth (see figure 2). Thus, when the new/full moon takes place very close to perigee it will be followed roughly 14 days later by a full/new moon not far from apogee. Similarly, when the new/full moon takes place very close to apogee it will be followed roughly 14 days later by a full/new moon not far from perigee.

Figure 1.

Figure 2.

We are looking for the times when the stresses caused by lunar tides in the Earth's atmosphere and oceans will be a maximum because the direction of the tidal forces of the Moon acting upon the Earth are changing by the largest amount over a relative short period in time.

When a new/full moon occurs at or near the time when the lunar line-of-nodes is at a right angle to the Earth-Sun line (see figure 3 and 4). This is true because a new/full moon at a major lunar standstill produces the largest changes in the meridional (north-south) lunar tidal forces upon the Earth (see figure 4).

Hence, when the new/full moon takes place very close to a time when the lunar line-of nodes is at a right angle to the Earth-Sun line (i.e. the new/full moon is at a major lunar standstill) it will be located at a declination of roughly 28 degrees in one hemisphere, followed roughly 14 days later by a full/new moon located at a declination of roughly 28 degrees in the other hemisphere.

Figure 3.

Figure 4.

a) the rate of change in the stresses caused by lunar tides in the Earth's atmosphere and oceans, as a result of a change in the

b) the rate of change in the stresses caused by lunar tides in the Earth's atmosphere and oceans, as a result of a change in the

Now if the period of the rate of change in stresses caused by the change in strength of the lunar tides (i.e. 10.14686 tropical years)

Interestingly, 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). Of even more interest is the 1.589(9) tropical year negative side-lobe period, which just happens to be synodic period of Venus and the Earth = 583.92063 days = 1.5987 years, to within an error of ~ 1.8 hours).

**strength**of the lunar tidal forces, should reach a maximum every**0.563714**tropical years (= 205.89223 days = 0.5 FMCs) and**10.14686**topical years (= 9.0 FMC's). [Note: the longer time period is the more precise alignment of the two and FMC = Full Moon Cycles]b) the rate of change in the stresses caused by lunar tides in the Earth's atmosphere and oceans, as a result of a change in the

**direction**of the lunar tidal forces, should reach a maximum every**1.89803**tropical years (= 2.0 Draconic year).**amplitude modulates**the period for the rate of changes in stresses caused by the change in direction of the lunar tides (i.e. 1.89803 tropical years), you would expect that the 1.89803 year tidal forcing term would split into two spectral peaks i.e. 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**

**REWRITTEN BLOG POST - UPDATED: 05/10/2015**

**1. The rate of change of the Moon's tidal stresses upon the Earth's atmosphere and oceans - When is it maximized?**

The stresses caused by lunar tides in the Earth's atmosphere and oceans should be a maximum when the tidal forces of the Moon acting upon the Earth change by the largest amount in either strength or direction over a relative short period in time.

There are two such conditions where this takes place:

**a) Changes in lunar tidal strength.**When a new/full moon occurs at or near the times when the lunar line-of-apse (see figure 1) is pointing towards the Sun. This is true because a new/full moon at closest perigee produces the strongest lunar tidal forces upon the Earth while a new/full moon at apogee produces the weakest lunar tidal forces upon the Earth (see figure 2). Thus, when the new/full moon takes place very close to perigee it will be followed roughly 14 days later by a full/new moon not far from apogee. Similarly, when the new/full moon takes place very close to apogee it will be followed roughly 14 days later by a full/new moon not far from perigee.

Figure 1.

A time when a new moon exerts maximal tidal forces upon

the Earth because of its distance from Earth (i..e it is at closest

perigee). Approximately 14 days later, a full moon will exert

minimal tidal forces upon the Earth because of its distance (i.e.

it is at apogee).

**b) Changes in lunar tidal direction**We are looking for the times when the stresses caused by lunar tides in the Earth's atmosphere and oceans will be a maximum because the direction of the tidal forces of the Moon acting upon the Earth are changing by the largest amount over a relative short period in time.

When a new/full moon occurs at or near the time when the lunar line-of-nodes is at a right angle to the Earth-Sun line (see figure 3 and 4). This is true because a new/full moon at a major lunar standstill produces the largest changes in the meridional (north-south) lunar tidal forces upon the Earth (see figure 4).

Hence, when the new/full moon takes place very close to a time when the lunar line-of nodes is at a right angle to the Earth-Sun line (i.e. the new/full moon is at a major lunar standstill) it will be located at a declination of roughly 28 degrees in one hemisphere, followed roughly 14 days later by a full/new moon located at a declination of roughly 28 degrees in the other hemisphere.

Figure 3.

Figure 4.

This file is available under Creative Commons CC0 1.0 Universal Public Domain Dedication

*Hence, the maximal rate of change in the strength of the lunar tidal forces acting upon the Earth should vary with a period set by**the minimum time required for the lunar line-of-apse to realign with the Sun, at the same time as a new/full moon is taking place.*

*In addition, the maximum rate of change in the direction of the lunar tidal forces acting upon the Earth should vary with a period set by the minimum time required for the perpendicular to the the lunar line-of-nodes to re-align with the Earth-Sun line, at the same time as a new/full moon is taking place.***2. Minimum Realignment Times for the Lunar Line-of-Apse**

**Starting out with a new moon at perigee with the Perigee end of lunar line-of-nodes pointing at the Sun (see figure 5).**

Figure 5

The time required for the Perigean end of the lunar line-of-apse to point back at the Sun close to New Moon is (see figure 6):

**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.

[NB: There is a slight miss-match of 0.110 days between these two alignments which means that the new Moon occurs ~ 1.3 degrees away from actual lunar perigee.]

Figure 6.

This means that minimum time required for the lunar line-of-apse to realign with the Sun when there is new/full moon is (see figure 7):

**0.5 FMC = 205.89222(5) days = 0.56371(4) tropical years (2)**

The Moon almost returns to being New at apogee after 0.5 FMC because 7 Synodic months = 206.714122 days and 7.5 Anomalistic months = 206.659125 days. [NB: producing an error of ~ 0.8 days between 7 Synodic months and the length of 0.5 FMC.]

Figure 7.

The next shortest time required for the lunar line-of-apse to re-align with the Sun when there is a new/full moon (in this case a Full Moon) is at:

**9.0 FMC = 3,706.06005 days = 10.1468(6) tropical years (3)**

The Moon almost returns to Full Moon at apogee after this period because 125.5 synodic months = 3706.08891 days and 134.5 anomalistic months = 3706.08698 days. Note that there is a mismatch of only 0.029 days between 125.5 Synodic months and 9.0 FMC which means that this realignment period is about four times more precise than that at 0.5 FMC realignment period.

**3. Minimum Realignment Times for the Perpendicular to the Lunar Line-of-Nodes**

**Starting out with a New Moon at a major lunar standstill (i.e. the line-of-nodes is at right angles to the Earth-Sun direction).**

**Figure 8.**

**The lunar line-of-nodes return to being perpendicular to the Earth-Sun direction after 0.5 Draconic Year (DY), where:**

**0.5 DY = 173.310038 days = 0.47450(7) tropical years (4)**

**[NOTE: 1.0 Draconic Year (DY) = 346.620076 days = 0.94901(4) tropical years]**

Figure 9,

Unfortunately, 173.310038 days is 5.869 Synodic months and 6.369 Draconic months and so the Moon phase is not new or full.

It turns out that the minimum time required for the Moon to return to a major standstill (i.e. the time required for the perpendicular to the lunar line-of-nodes to realign with the Sun), when there is a new/full moon is:

**2.0 DY = 4 x 0.5 DY = 693.24015(2) days = 1.8980(3) tropical years (5)**

The Moon almost returns to being Full after 2.0 DY because 23.5 Synodic months = 693.96884 days and 25.5 Draconic months = 693.91161 days. [NB: producing an error of ~ 0.73 days between the 23.5 Synodic months and 2.0 DY.]

The 1.89803 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 3.79606 tropical yrs = 1387.481264 days (since 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 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.

**3. Discussion**

The above analysis tells us that:

a) the rate of change in the stresses caused by lunar tides in the Earth's atmosphere and oceans, as a result of a change in the

is the more precise alignment of the two.]

b) the rate of change in the stresses caused by lunar tides in the Earth's atmosphere and oceans, as a result of a change in the

Now if the period of the rate of change in stresses caused by the change in strength of the lunar tides (i.e. 10.14686 tropical years) amplitude modulates the period of the rate of changes in stresses caused by the change in direction of the lunar tides (i.e. 1.89803 tropical years), you would expect that the 1.89803 year tidal forcing term would 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

Interestingly, 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).

a) the rate of change in the stresses caused by lunar tides in the Earth's atmosphere and oceans, as a result of a change in the

**strength**of the lunar tidal forces, should reach a maximum every 0.563714 tropical years (= 0.5 FMCs) and 10.14686 topical years (= 9.0 FMC's). [Note: the longer time periodis the more precise alignment of the two.]

b) the rate of change in the stresses caused by lunar tides in the Earth's atmosphere and oceans, as a result of a change in the

**direction**of the lunar tidal forces, should reach a maximum every 1.89803 tropical years (= 2.0 DYs).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

Even more interesting, is the 1.589(9) tropical year negative side-lobe period, which 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).

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

Synodic month = 29.5305889 days

Anomalistic month = 27.55455 days

Draconic month = 27.21222 days

Tropical Year = 365.242189 days

Sidereal orbital period of the Earth = 365.256363 days

Sidereal orbital period of Venus = 224.70069 days