Ian Wilson: Connecting the Planetary Periodicities to Changes in the Earth’s Length of Day

Posted: October 15, 2013 by tallbloke in Astrophysics, Celestial Mechanics, Cycles, Fibonacci, LOD, Natural Variation, solar system dynamics

This guest post by Ian Wilson is very timely in the wake f the Wyatt-Curry paper currently under discussion here at the talkshop. Thanks Ian for the recognition of our independent work, although you are one of the ‘collaborators’ yourself! (that sounds very ‘conspiratorial’ 🙂 ).

Connecting the Planetary Periodicities to Changes in the Earth’s Length of Day
Ian Wilson – 15th Oct 2013

[(*) Some of the findings in this blog post concerning the connection between the Earth’s rotation rate and the planetary configurations have also been independently discovered by Rog “Tallbloke” Tattersall and his collaborators]

A. The Connection Between Extreme Pergiean Spring Tides and Long-term Changes in the Earth’s Rotation Rate as Measured by the Rate-of-Change of its Length-of-Day (LOD). (*)

If you plot the rate of change of the Earth’s Length of Day (LOD) [with the short-term atmospheric component removed] against time [starting in 1962] you find that there is a ~ 6 year periodicity that is phase-locked with the 6 year period that it takes the lunar line-of-nodes  to re-align with the lunar line-of-apse [see the first note directly below].

NB: The pro-grade precession of the lunar line-of-apse once around the Earth with respect to the stars takes 8.8504 Julian years (J2000) while the retrograde precession of the lunar line-of-apse once around the Earth with respect to the stars takes 18.6000 Julian years (J2000). Hence, the lunar line-of-apse and the ascending node of the lunar line-of-nodes will realign once every:
(18.6000 x 8.8504) / (18.6000 + 8.8504)  = 5.9969 Julian years

Figure 1

[NB: that in the case of figure 1 the line-of-nodes and line-of-apse are just re-aligning with each other. They do not necessarily realign with the Sun – see figure 2].

A much better alignment between the lunar orbital configuration and the rate of change of the Earth’s LOD is achieved if we re-plot figure 1 below and superimpose the times when solar/lunar eclipses occur at or near the times of lunar perigee. These events occur at or very near to the times when both the lunar line-of-apse and lunar line-of-nodes point directly towards or away from the Sun. When the Moon is in this particular configuration with respect to the Sun and the Earth (marked by vertical red lines in figure 2), our planet experiences extremely strong luni-solar tidal forces known as Perigean Spring Tides. Figure 2 (top graph below) shows whenever this occurs, the rate of change of the Earth’s LOD undergoes an inflection in its value.

Figure 2

The tight relationship between the configuration of the lunar orbit and the rate of change of LOD is further reinforced by the lower graph in figure 2. This shows lowest velocity (in km/sec) of the Moon its orbit, when perigee occurs at or near the First/Last Quarter of the Moon. This is a reasonable proxy for the actual strength of global lunar tides impacting the Earth (see note below).

[NB: Keeling and Whorf (1997) indicate that an: “approximate relative measure of the global tide raising forces of individual strong tidal events is given by the angular velocity of orbital motion of the Moon with respect to the perturbed motion of perigee, in degrees of arc per day at the moment of maximum forcing. They go on to say that: “The tide raising forces define a hypothetical equilibrium tide which approximates the global average strength of the actual tides.”]

Hence, figure 1 and 2 firmly establish that there is a direct connection between the conditions that produce extreme Perigean Spring Tides and long-term changes in the rate-of-change in the Earth’s Length-of-Day (LOD).

Now, if we can show that the other planets of the Solar System have an effect upon setting the rates of precession of the line-of-nodes and line-of-apse of the lunar orbit then we can plausibly claim that the spatio-temporal configuration of the planets plays a role in producing changes in the Earth rotation rate on decadal to inter-decadal time scales.

B. Evidence that the Precession of the Lunar Line-of-Nodes and the Lunar Line-of-Apse are linked to the orbital period of the planets.

NB: The following arguments use these mean planetary orbital periods:

V = 224.70069 days = 0.615186 sidereal years
E = 365.256363004 days = 1.0000 sidereal year
J = 4332.75 days = 11.862216 sidereal years
Sa = 10759.39 days = 29.4571 sidereal years

1) The Lunar Lines-of-Apse

If we look at the realignment period between the half pro-grade synodic period of Jupiter and Saturn (1/2 JS cycle) with the retrograde realignment cycle of the inferior-conjunctions of Venus and Earth with the Terrestrial year (VE cycle) i.e.

1/2 JS cycle = 1/2 x 19.859 years = 9.9295 sidereal years [pro-grade]
VE Cycle___= 7.9933 sidereal years [retro-grade]

we find that:

(9.9295 x 7.9933) / (9.9295 + 7.9933) = 8.8568 sidereal years

This is extremely close to the time of precession time of the lunar line-of-apse with respect to the stars, which is 8.8501 sidereal years – error = 0.007 years or 2.56 days

2) The Lunar Line-of-Nodes

The line-of-nodes of the lunar orbit appears to rotate around the Earth, with respect to the Sun, once every Draconitic Year (TD = 346.620 075 883 days). This means if we start with the Earth and Jupiter aligned on the same side of the Sun and with the ascending node of the lunar line-of-nodes pointing at the Sun, then the ascending node of the lunar line-of-nodes will move from pointing along the Earth-Sun line to pointing at right-angles to the Earth-Sun line (or vice versa), at times separated by:

¼ TD = 86.65002 days 1st tidal harmonic
5 x ¼ TD = 1 ¼ TD = 433.275095 days = 1.18622 years 2nd tidal harmonic
5 x 1 ¼ TD = 6 ¼ TD = 2166.375474 days = 5.93111 years 3rd tidal harmonic

The first point that needs to be made about this is that there appears to be an almost perfect synchronization between the three tidal harmonic intervals and sub-multiples of the sidereal orbital period of Jupiter (TJ = 4332.82 days = 11.8624 sidereal years – note this is slightly different from the adopted value):

(1/50) x TJ = 86.6564 days
(1/10) x TJ = 433.282 days
(1/2) x TJ = 5.93120 years

The synchronization between the orbital period of Jupiter and the rate of precession of the lunar nodes is significant. However, this synchronization could be dismissed as just a coincidence, if it were not for one further piece of evidence that links the nodal precession of the lunar orbit with the orbital motion of the planets. A remarkable near-resonance condition exists between the orbital motions of the three
largest terrestrial planets with:

4 x SVE = 6.3946 years    where SVE = synodic period of Venus and Earth
3 x SEM = 6.4059 years             SEM = synodic period of Earth and Mars
7 x SVM = 6.3995 years   and    SVM = synodic period of Venus and Mars

This means that these three planets return to the same relative orbital configuration at a whole multiple of 6.40 years. Amazingly, the point in the Earth’s orbit where the 2nd tidal harmonic occurs (i.e. 1 ¼ TD), rotates around the Sun (with respect to the stars) once every 6.3699 years. This is just over three hundredths of year less than the time required for the realignment of the positions of the three largest terrestrial planets.

Thus, the realignment time for the positions of the three largest terrestrial planets and the orbital period of Jupiter appear to be closely synchronized with the time period over which the Earth experiences a maximum change in the tidal stress caused by the precession of the line-of-nodes of the lunar orbit.

CONCLUSION

The periods of precession of the line-of-nodes and line-of-apse of the lunar orbit (when measured with respect to the stars).appear to be synchronized with the relative orbital periods of Jupiter and the three largest terrestrial planets.

In addition, long-term changes in the rate of change of the Earth’s LOD [excluding short-term changes (less than a couple of years) cause by the exchanges of angular momentum between the atmosphere, oceans and the Earth’s crust] appear to be synchronized with the conditions that produce extreme Perigean Spring Tides.

This implies that the spatio-temporal configuration of the planets must play a role in producing changes in the Earth rotation rate that we see on decadal to inter-decadal time scales.

Comments
  1. tallbloke says:

    And the system isn’t just connected by the sidereal timings Ian elucidates in this post. The Timings of the Moon’s phase cycle, the time between successive full or new Moons which relates to the rate of Earth’s orbit round the Sun appears to be linked to the rest of the planets and their long term interaction timings too, via the solar system connected Fibonacci series Oldbrew and I have been working with:

    Here’s a set of Fibonacci numbers connected obs I wrote down last week which tie this back to the Sun and include all the planets:

    1 Full Moon is close to the average Solar surface rotation period
    2 Full Moons is 0.4 days more than the Mercury rotation period
    3 Full moons is 0.62 days more than the Mercury orbital period
    5 Full Moons is 3.1 days more than the Venus-Mercury synodic period
    8 Full Moons falls at the phi ratio between Venus’ orbital and rotation periods
    Earth’s orbital period falls at the phi ratio between 12 and 13 full Moons
    13 Full Moons is half a Moon less than the Earth-Jupiter synodic period
    20 Full Moons is a quarter Moon more than The Venus-Earth synodic period and is 1.617 years.
    23 Full Moons is a quarter Moon less than Mars Orbital period
    55 Full Moons is 4% more than 2 Earth-Mars synodic periods
    144 Full Moons is 2% less than the Jupiter orbital period
    233 Full Moons is 5% less than the Jupiter-Saturn synodic period
    987 Full Moons is 5% less than the Uranus orbital period
    2584 Full Moons is 0.3% more than the 208 year De Vries Cycle (208.79y)
    28657 Full Moons is 0.08% more than the 2313.5yr average Halstatt cycle length

    Those last two are real eye-openers for me.

    It seems that the Moon gets little near-to-resonant pushes by every Body and their neighbour from the Sun to Neptune. There are other mechanism possibilities which Hans Jelbring will be able to tell us about before too long as well.

  2. Brian H says:

    Edit: “They do not necessarily realigned with the Sun” is kinda gummy crammar.

    [Reply] Thanks Brian; fixed. -TB

  3. timspence10 says:

    Very interesting read Ian, I’m not sure if we’re phase lock looped or phase loop locked, but there’s defninitely a phase there.

  4. oldbrew says:

    ‘A remarkable near-resonance condition exists between the orbital motions of the three
    largest terrestrial planets’

    Does that mean the time period is remarkable? Any three planets will sum their synodics to whole numbers somewhere along the line (allowing for very slight time differences). It’s a mathematical inevitability.

  5. tallbloke says:

    OB: The shorter the period, the more remarkable the congruence, given the numbers aren’t recognised as being those which would normally produce a phase lock.

  6. Ian Wilson says:

    Oldbrew,

    You are correct in pointing out that it is not remarkable that synodic periods eventually agree in whole number ratios. In addition, Rog and I are not correct in claiming that it is somehow remarkable that the ratios involve low whole numbers. The following example shows why.

    Lets take three hypothetical planets with the following randomly selected orbital periods between 0.0 and 2.0 years. The rand() excel function was used to generate the periods of planets A and C. Let the middle distance planet B, have an orbital period of 1.000.

    Period A = 0.44417 years
    Period B = 1.00000 years
    Period C = 1.929216 years

    Synodic(AB) = 0.799111239 years ~ 0.8 years
    Synodic(BC) = 2.0761760452 years ~ 2.1 years
    Synodic(AC) = 0.57701908 years ~ 0.6 years

    13 x Synodic(AB) = 10.3884461 years ~ 10.388 years They all differ by less than 0.007 years
    5 x Synodic(BC) = 10.3808802 years ~ 10.381 years
    18 x Synodic(AC) = 10.3863434 year ~ 10.386 years

    As you can see, the first set of random number that I came up with produce a “remarkable” set of low number ratios between these three synodic periods. Hence, Oldbrew is correct in pointing out that
    “remarkable” synchronizations like this between the synodic products are a mathematical certainty.

    However, what would be truly remarkable is if one of these three planets has a Moon going around it which had one of its orbital elements (e.g. either the period of precession of its line-of-nodes or line-of-apse with respect to the stars) which was also a perfect sub-multiple of 10.38 years.

    If this occurred, it would indicate that the orbit of the Moon had been influenced by the repetitive alignment of the three planets.

  7. Ian Wilson says:

    Oldbrew,

    Of course the same would be true if the rotation period of one of the planets in the hypothetical example given in the previous post was a perfect (whole) sub-multiple of 10.38 years.

    Let’s look at a real life example.

    Here is the “not-so-remarkable” synchronization between the synodic periods of the three largest Terrestrial planets:

    4 x SVE = 6.3946 years where SVE = synodic period of Venus and Earth
    3 x SEM = 6.4059 years SEM = synodic period of Earth and Mars
    7 x SVM = 6.3995 years and SVM = synodic period of Venus and Mars

    However, the beat period between the Earth’s Chandler wobble (i.e. 1.18622 years) and it sidereal year (i.e. the length of its orbital period about the Sun with respect to the stars) is:

    (1.18622 X 1.00000) / (1.18622 – 1.0000) = 6.36999 years ~ 6.37 years

    which is remarkably close synchronization time of the three largest Terrestrial planets – strongly hinting that the period of the Chandler wobble has been set by by the periodic alignments of the three planets.

  8. oldbrew says:

    @ IW – thanks for the detailed response and for being willing to re-visit your analysis.

    I wonder if this could amount to anything – I offer no rationale but here it is:

    (Earth-Mars synodic period divided by Venus-Mercury s.p.) x Chandler 1.18622y = 6.3995

  9. oldbrew says:

    IW says: ‘strongly hinting that the period of the Chandler wobble has been set by by the periodic alignments of the three planets.’

    It’s certainly very close, but I’m a bit puzzled to find the Chandler wobble period is variable.

    Wikipedia: ‘This wobble, which is a nutation, combines with another wobble with a period of one year, so that the total polar motion varies with a period of about 7 years.’

    Of course the 7 years is not a lot more than the 6.4 years…the plot thickens?

    Also from Wiki: ‘The wobble’s amplitude has varied since its discovery, reaching its largest size in 1910 and fluctuating noticeably from one decade to another.’

    Could that be linked to the differing positions of the inner planets, if so what was happening in 1910?

  10. tallbloke says:

    There was a deepish minimum in LOD around 1910. So, faster spin – bigger wobble. Paul Vaughan did some Chandler wobble work. His graph label acronyms and glyphs are a bit hard to remember though.

  11. tallbloke says:

    OB: It’s certainly very close, but I’m a bit puzzled to find the Chandler wobble period is variable….”This wobble, which is a nutation, combines with another wobble with a period of one year”

    Or is it 398.8 days? J-E synod

    Time to do a Jupiter hunt and work in the LOD.

  12. tallbloke says:

    Looking now at the Earth and Mars rotation:orbit ratios:
    Earth 1/365.256 = 0.0027
    Mars 1.0275/686.98= 0.0015 The ratio of these numbers is:
    0.0027: 0.0015 = 0.546 (Note: the ratio of Jupiter and Saturn’s distances from the Sun is 0.545)

    Earth completes 1.092 orbits between synodic conjunctions with Jupiter, while
    Mars completes 1.18844. The ratio of these numbers is:
    1.092: 1.18844 = 1: 1.088
    The ratio of the ratios (1.088:0.546) is 2:1 (99.6%)

    The reason for the 2:1 ratio becomes apparent when we observe that the Mars-Jupiter synodic conjunction period is in a 2:1 ratio with the Earth-Jupiter synodic period (98%).

    There are just under 9 Mars-Jupiter synods in the same period as the Jupiter-Saturn synodic period (-1%)
    There are just over 18 Earth-Jupiter synods in the same period as the Jupiter-Saturn synodic period (+1%)

    Once again there appears to be a quantisation and spin-orbit coupling occurring involving the largest planet in the system and its inner planet neighbours.

  13. oldbrew says:

    TB: I think we’ve been here before. I recall saying that 1.092 / 0.546 = 2 exactly 😉

  14. oldbrew says:

    1/2 JS cycle = 1/2 x 19.859 years = 9.9295 sidereal years [pro-grade]
    VE Cycle___= 7.9933 sidereal years [retro-grade]
    (9.9295 x 7.9933) / (9.9295 + 7.9933) = 8.8568 sidereal years

    An interesting equation. Slightly OT perhaps but note also that:

    102 J-S = 1267 V-E = 2025.6 years
    (V-E = 1266/1267 x 8/5 years)
    1267 – 102 = 1165 (233 x 5)
    (J-S x V-E) / (J-S – V-E) x 1165 = 2025.6 years

  15. tallbloke says:

    Every 14 orbits of Jupiter there are:
    1.007 Neptune orbits
    15.001 Average solar cycles of 11.07 years
    166.06 sidereal Earth orbits
    174.99 Draconic years
    2054.014 synodic months
    2220.079 sidereal months
    2229.007 draconic months

    Note that the difference between the number of Earth years and lunar draconic years at this interval is close to the period of the lunar apsidal precession of around 8.85 years (difference = 0.08 years = 1 synodic lunar month) .

    Note also that the Earth-Jupiter synodic period divided by the lunar evection-in-latitude oscillation period is
    398.9/32.3 = 12.34984
    Which is close to the number of draconic months in a draconic year = 12.36826
    And the average of that figure and synodic months in sidereal years is
    (12.73791+12.36826)/2 = 12.553
    Intriguingly, the Earth-Jupiter synodic period divided by the lunar evection oscillation period is
    398.9/31.8 = 12.544
    I don’t think anyone ever made sense of those evection figures before now, just some armwaving saying “it’s the Sun wot dunnit”.

    Looks more like a gravitational-spin-orbit-precession-electromagnetic-luni-solar-Jovian-Terrestrial coupling to me. 🙂

  16. oldbrew says:

    The period of time from perigee to perigee in the Moon’s orbit is called the “Anomalistic Month”.

    An anomalistic month (A.M.) has an average length of 27.554551 days.
    http://en.wikipedia.org/wiki/Anomalistic_month#Anomalistic_month

    1193 A.M. = exactly 90 Earth orbits / years

  17. tallbloke says:

    OB: Good spot! So that’s another J-S link, via a 3:2 to the triple conjunction period around 60 years. Converges in a 2:1 at the Jose cycle length too.