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Monday, March 15, 2010

The synchronization between the Solar Inertial Motion and the Lunar Orbit

Figure 6. The main curve shows the distance of the centre-of-mass of the Solar system from the sub-Jupiter point between 1220 and 2020 A.D. The sub-Jupiter point1 is located just above the solar surface on a line joining the centre of the Sun to Jupiter. Marked above this curve are years in which the Earth experienced exceptionally strong tidal forces over the last 800 years.

Figure 6 shows that the times when Solar/Lunar tides had their greatest impact upon the Earth are closely synchronized with the times of greatest asymmetry in the Solar Inertial Motion (SIM). Over the last 800 years, the Earth has experience exceptionally strong tidal forces in the years 1247, 1433, 1610, 1787 and 1974 (Keeling and Whorf, 1997). A close inspection of Figure 6 shows that these exceptionally strong tidal forces closely correspond in time to the first peak in the asymmetry of the SIM that occurs just after a period low asymmetry. These first peaks in asymmetry in the SIM occur in the years 1251, 1432, 1611, 1791, and 1971, closely correspond the years of peak tidal force.

Thus, there appear to be periodic alignments between the lunar apsides, syzygies and lunar nodes that occur at almost exactly the same times that the SIM becomes most asymmetric for the first time after a period of low asymmetry in the SIM. It means that precession and stretching of the Lunar orbit (i.e. the factors that control the long-term variation of the lunar tides that are experienced here on Earth) are almost perfectly synchronized with the SIM.
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. When these resonances have occurred, they would have greatly amplified the effects of the planetary tidal forces upon the lunar orbit. 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.
Of course, the orbital periods of Jupiter and the other Jovian planets are responsible for the
periodicities observed in the motion of the Sun about the Solar Sytem barycentre. Hence, the apparent link between the Sun's barycentric motion and the orbit ofthe Moon may just be an artifact of the fact that both are heavily influenced by the periodicities in the motion of the Jovian planets.


  1. The following figures should be accurate to at least 6 sf. I haven’t cropped them until the end to avoid introducing further rounding errors.

    pSaros= 18.0310284658705
    days_per_year = 365.25636

    print 2/(1/pApsides+1/pSaros)

    As I noted that is very, very close to Jupiter’s sideral orbital period. (fixed stars).
    pJ= 4332.589 / days_per_year # = 11.861775658061

    Now looking at how long these cycles take to drift in phase and come back into phase:

    print 2/(1/pJ-1/pApSaros) = 21322 years
    “These two forms of ‘precession’ combine so that it takes over 21,600 years for the ellipse to revolve once relative to the vernal equinox” [Note this is the Earth's apsides (perihelion/aphelion) now, not the the lunar perigee cycle. ]

    I would guess the first relationship has already be spotted long ago but since the latter requires a very good degree of accuracy, the discrepancy may not have been linked to precession of the equinox.

  2. A fascinating set of results Greg! Thank you for your comments.

    I have not seen the link between the pApsides, pSaros and pJupiter but others may have found it.

    Have you ever noticed that:

    (1/Sjs + 1/(10*Sve)^(-1) = 8.8567 years ~ pApsidal


    Sjs = Synodic period of Jupiter/Saturn = 19.858 years
    Sve = Synodic period of Venus/Earth = 1.5986 years ?

  3. print 1/(1/pApsides-1/8.8567 )

    same ball park. I would suggest checking all your starting figures are verified and as accurate as possible. Obviously when looking at the resip. of such small differences, any errors make a huge difference.

    It's like we are measuring all this in the wrong frame of reference. Like solar vs fixed stars. Or does all this tell us something about the proper motion of the SS? Linear or rotation ?!

    I have found a lot of difficulty in getting consistent answers for these orbital 'constants' and lunar cycles.

    Lots of stuff rounded to 3 s.f. but beyond that we're into fuzzy logic.

    Do you know of reliable source for high precision astronomical data?


  4. Greg,

    You are spot-on about the fact that we are looking at the whole thing from the wrong frame of reference. I am currently writing a paper for the new PRP which will show that there is a definite long-term link between the Lunar orbit configuration and alignments of Earth and Venus. I would value your input/ideas on this paper when it get to the pre-submission stage [my email is irgeo8atbigponddotcom ifyou are interested].

    As to the precision of the orbital elements - I use the mean orbital elements when I am in the exploration stage of my analysis i.e. I use these mean elements as a rough tool to explore possible scenarios. However, I try not to jump to any conclusions until I have tested the ideas using ephemerides data at the JPL Horizon cgi web interface. The info given for planetary ephemeris data is given as follows:

    Planetary ephemerides are available using JPL's HORIZONS system. Although the HORIZONS system will be sufficient for the vast majority of ephemeris requests, JPL planetary and lunar ephemeris files (e.g. DE406) are also available. The use of these ephemeris files is recommended only for professionals whose needs are not readily met by the HORIZONS system. Alternatively, you may use the NAIF SPICE toolkit and planetary ephemerides in SPK format from JPL's NAIF web-site.

    Summary of available planetary ephemerides:
    HORIZONS (preferred solution)
    JPL ephemeris files (e.g. DE-0406)
    SPK format ephemeris files (e.g. DE-0406)
    formulae for approximate positions

    The limiting factor is the incredible complexity of the Lunar orbit. The complexity is so great that it is difficult to project the lunar orbit forward or backwards in deep-time without a great deal of care.

  5. Oddly, I've just got off the phone with someone and the last thing we discussed was using SPICE toolkit !

    Another interesting thing I've noticed is the resonant pattern between 8.85 and 9.3 gives 9.07 modulated by 356.8 years (NB years, not days).

    So apsidal precession and nodal precession slip out of phase by very close to one day per year. Again we find one of these fourth digit differences.

    Now line of apsides is an inertial perturbation of the lunar orbit by the planets (poss locked to Jupiter), so star based inertial frame reqd.

    Lunar nodal precession is currently explained as solar torque on the EM angular momentum vector and as such linked to the relative position of EMB and sol. A cycle presumably linked to the tropical year

    I find 9.051 in cross-correlation of Atl , N.Pacific SST:

    How does the 356y modulation manifest ?

    similar 9.1y result from BEST last year but with large uncertainly. They make no link to modulation pattern.

    I need a reliable value for lunar nodal period. Keeling and Whorf use 18.631 I also find 18.5993. !!

    Can you point to a definitive source for that period (preferable with at least 5 sf) ?

    Is that number available from JPL without generating a long ephemeris and digging around for nodal crossings?


  6. Sure, I'd be happy to pre-review your forth coming paper about VE alignments. I've sent you evidence of pVE in Indian Ocean SST which may be of use.

    You did not reply so I don't know whether I transcribed the email address correctly.

  7. Slight correction to the deviation from Jupiter orbital period I posted above.

    It's not the precession of equinox, circa 26ka but the combined effect of change in Earth's argument of periapsis opposing the former.

    Net effect is 21600 I stated. Sorry for incorrect description.