Linking the Orbital Configuration of Jupiter, Saturn, Venus & Earth to Lunar Tides & Climate

Planetary Near-Resonances and The Precession of the Lunar Line-of-Nodes

A SUMMARY OF THE CONCLUSIONS

Since:

5/4×DY = (1/10)×T_J

and

S_JS – T_J = 5×S_VE

then

12 ½×DY = S_JS – 5×S_VE

therefore

            Earth's climate     Moon        Jupiter       Venus/Earth & Jupiter/Saturn

                   2×CW = QBO = 2 ½×DY = (2/10)×T_J = (2/10)×S_JS – S_VE

where  

DY = the lunar draconic year

T_J = Sidereal orbital period of Jupiter

S_{JS =} Synodic period of Jupiter/Saturn                 

S_VE = Syndoic period of Venus/Earth

CW = the period of the Chandler Wobble

QBO = the mean period of the Quasi-Biennial Oscillation

THE MAIN ARGUMENT 

The following appeared in the ABSTRACT of my 2010 paper:

Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation

Rate Externally Driven and Do They Affect Climate?

The General Science Journal, Dec 2011, 3811.

http://gsjournal.net/Science-Journals/Essays/View/3811

"We know that the strongest planetary tidal forces acting on the lunar orbit come from the planets Venus, Mars and Jupiter. In addition, we known that, over the last 4.6 billion years, the Moon has slowly receded from the Earth. During the course of this lunar recession, there have been times when the orbital periods of Venus, Mars and Jupiter have been in resonance(s) with the precession rate for the line-of-nodes the lunar orbit (Cuk 2007). When these resonances have occurred, they would have greatly amplified the effects of the planetary tidal forces upon the lunar orbit (Cuk 2007). Hence, the observed synchronization between the precession rate of the line-of-nodes of the lunar orbit and the orbital periods of Venus, Earth, Mars and Jupiter, could simply be a cumulative fossil record left behind by these historical resonances."

This conjecture was based upon the following two observations:

1. Synchronization of the Draconic year with the Jupiter's orbital period.

The line of nodes of the lunar orbit appears to rotate around the Earth, with respect to the Sun, once every Draconic Year (DY = 346.620076 days). This means that the Earth experiences a transition from maximum to minimum meridional tidal stress (or vice-versa), at times separated by:

¼ DY______________ = 86.65002 days  
5 ×  ¼ DY = 1 ¼ DY__= 433.275095 days _= 1.18622 years  
5 ×  1 ¼ DY = 6 ¼ DY = 2166.375474 days = 5.93111 years

Remarkably, these time intervals are precise sub-multiples of the sidereal orbital period of Jupiter (T_J) = 4332.82 days = 11.8624 sidereal years, such that:

1/50 ×  T_J = 86.6564 days

1/10 × T_J = 433.282 days

  ½ × T_J = 5.93120 years

[N.B. The sidereal orbital period is the time for the planet to complete one orbit of the Sun with respect to the stars.]

2. The source of excitation for the Chandler Wobble is extra-terrestrial.

The Earth has two distinct short-term wobbles. The first is the annual wobble which is a forced motion caused by the seasonal variations in the Earth’s atmosphere, oceans and hydrosphere. The second is a periodic wobble of the Earth’s polar axis with an average period of 433 days known as the Chandler Wobble (Gross 2000). This wobble is thought to be a free oscillation of the Earth’s rotation axis caused by the fact that the Earth does not rotate about its figure axis.


Dissipation processes associated with wobble-induced deformations of the solid Earth should cause the Chandler wobble to freely decay on a timescale of about 30-100 years (Plag et. al. 2005), unless some force is acting to reinvigorate it. The fact that there has been no noticeable decay in the Chandler Wobble has raised questions about the source of excitation for the wobble. Gross (2000) proposed that the wobble was excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean-bottom pressure fluctuations.

The Chandler Wobble also suffers from a sinusoidal variation in its amplitude that has a period of roughly 6.4 years (Kosek 2005). It is generally believed that the 6.4 year amplitude modulation period is most likely just a beat period produced by the interaction the annual oscillation and Chandler Wobble (Kosek 2005) but what if the source of excitation for the Chandler Wobble had an extra-terrestrial origin?

There is a remarkable near-resonance condition that exists between the orbital motions of the three largest terrestrial planets with:

4 ×  S_VE = 6.3946 years 

3 × S_EM = 6.4059 years 

7 × S_VM = 6.3995 years 

where:

S_VE = synodic period of Venus/Earth = 583.9214 days

S_EM = synodic period of Earth/Mars = 799.9359 days

S_VM = synodic period of Venus/Mars = 333.9215 days

[N.B. The synodic period is the time required for a faster inner planet to catch up to a slower outer planet.]

and

T_V = sidereal orbital period of Venus = 224.70080 days

T_E = sidereal orbital period of Earth = 365.256363 days

T_M = sidereal orbital period of Mars = 686.9800 days

T_J = sidereal orbital period of Jupiter = 4332.820 days

Source: JPL ephemeris http://ssd.jpl.nasa.gov/horizons.cgi?s_body=1#top

[N.B. the point in the Earth’s orbit that is 1 ¼ DY's after the position of the Earth on January 1st, subsequently 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].

In addition:

28 × S_VE = 44.763 years

69 × S_VJ = 44.770 years 

41 × S_EJ = 44.774 years 

20 × S_MJ = 44.704 years 

where:

S_VJ  = synodic period of Venus/Jupiter

S_EJ  = synodic period of Earth/Jupiter

S_MJ = synodic period of Mars/Jupiter

This means that these four planets return to the same relative orbital configuration once every 44.77 years.

There is a possibility that the 6.40 year realignment period for the terrestrial planets has interacted with the sidereal orbital period of the Earth/Moon system over the eons, to produce a side-lobe modulation that it has slowly nudged the precession rate of the line-of-nodes of the lunar orbit towards its current value. Hence, we now have a precession rate that varies on a time scale of 1 ¼ TD = 433.2751 days = 1.18622 years. The fact this so close to the nominal 433 day period of the Chandler Wobble, suggests that the variations in lunar tides produced by the precession of the line-of-nodes of the lunar orbit could, in fact, be the source of the ocean-bottom pressure fluctuations that are thought to be responsible for the excitation of the Chandler Wobble.

[N.B. This means that Venus, Earth and Jupiter, in particular, form alignments at sub-multiples of the 179 year Jose cycle i.e.:

½ × 179 yrs     = 89.50 yrs 
¼ × 179 yrs     = 44.75 yrs
1/8 × 179 yrs   = 22.38 yrs 
1/16 × 179 yrs = 11.19 yrs

These alignments only change slowly over hundreds of years and they closely match the well known Schwabe (~ 11.1 yrs), Hale (~ 22.2 yrs) and Gleissberg (~ 90 years) solar cycles.]

FINALLY 

Wilson (2011) showed that the following relationship links the rate of procession of the lunar line-of-node to the sidereal orbital period of Jupiter:

5/4 × DY = 1/10 × T_J

It can also be shown that the sidereal orbital period of Jupiter and Saturn can be linked to the sidereal orbital periods of Venus and the Earth through the following near-resonance relationship: 

S_JS – T_J = 5 × S_VE

If we combine these two relationships, we get the following expression which links the rate of precession of the line-of-nodes of the lunar orbit with the orbital periods of Venus, the Earth and Jupiter:

12 ½ × DY = S_JS – 5 × S_VE

Finally, it can be shown that this implies that to a high degree of precision:

2 × CW = QBO = 2 ½ × DY = 2/10 × T_J 

These last two relationships indicate that there may be a link between the relative orbital configurations of Jupiter, Venus and the Earth and variations in the terrestrial lunar tides. They also indicate the tidal variations could be responsible for setting the periods for the Chandler Wobble and the QBO.

References:

Cuk, M. 2007, Excitation of Lunar Eccentricity by Planetary Resonances, Science, 318, 244.

Gross, R.S., 2000, The excitation of the Chandler wobble, Geophysical Research Letters, Volume 27, Issue 15, p. 2329-2332.


JPL ephemeris: http://ssd.jpl.nasa.gov/horizons.cgi?s_body=1#top

Kosek W., 2005, Excitation of the Chandler wobble by the geophysical annual cycle, Proc. ECGS Chandler Workshop, ed. H.-P. Plag, European Center for Geodynamics and Seismology, Luxembourg-city, 2005.

Plag, H.-P., Chao, B.F., Gross, R.S., and Van Dam T., 2005, Forcing of Polar Motion in the Chandler Frequency Band: An Opportunity to Evaluate Inter-annual Climate Variations, Eos, Transactions American Geophysical Union, Volume 86, Issue 3, p. 26-26.

Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation Rate Externally Driven and Do They Affect Climate? The General Science Journal, Dec 2011, p. 3811.