Lunar precession update

Posted: October 15, 2017 by oldbrew in Fibonacci, Maths, moon, Phi, solar system dynamics
Tags: ,

Credit: NASA


I found out there’s an easy way to simplify one of the lunar charts published on the Talkshop in 2015 on this post:
Why Phi? – some Moon-Earth interactions


In the chart, synodic months (SM) and apsidal cycles (LAC) are multiples of 104:
79664 / 104 = 766
728/104 = 7

The other numbers are not multiples of 104, but if 7 is added to each we get this:
86105 + 7 = 86112 = 828 * 104 (TM)
85377 + 7 = 85384 = 821 * 104 (AM)
5713 + 7 = 5720 = 55 * 104 (FMC)
6441 + 7 = 6448 = 62 * 104 (TY)

TM = tropical months
AM = anomalistic months
SM = synodic months
LAC = lunar apsidal cycles
FMC = full moon cycles
TY = tropical years


Here’s an imaginary alternative chart based on these multiples of
104. [Cross-check: 828 – 766 = 62]

In reality, 55 FMC = just over 62 TY and 7 LAC = just short of 62 TY.
For every 7 apsidal cycles (LAC), there are 766 synodic months (both chart versions).

In the real chart:
For every 104 apsidal cycles, all numbers except SM slip by -1 from being multiples of 104. So after 7*104 LAC all the other totals except SM are ‘reduced’ by 7 each.

In the case of tropical years, 6448 – 7 = 6441 = 19 * 339
19 tropical years = 1 Metonic cycle

If the period had been 6448 TY it would not have been a whole number of Metonic cycles.
Also 6441 * 4 TY (25764) is exactly one year more than 25763 synodic years i.e. the precession cycle, by definition.

Fibonacci: 104 is 13*8, and the modified FMC number is 55 (all Fibonacci numbers).

Phi: we’ve explained elsewhere that the number of full moon cycles in one lunar apsidal cycle is very close to 3*Phi².
We can see from the modified chart that the FMC:LAC ratio of 55:7 is 3 times greater than 55:21 (55/21 = ~Phi²)
– – –
Note – for more discussion of the ~62 year period, try this search:
site:tallbloke.wordpress.com 62 year
[see Google site search box in grey zone on left of this web page]

Comments
  1. J Martin says:

    62 years, so the moon drives the AMO and PDO.

  2. J Martin says:

    I can’t remember, but I thought the suns Corona had a cycle of similar 62 year length.

  3. oldbrew,

    What you have found is the 31/62/93/186 year Perigean New/Full Moon Cycle.

    [reply] yes

  4. oldbrew says:

    Three references to 62 years here.
    http://appinsys.com/globalwarming/SixtyYearCycle.htm

    Atlantic Multidecadal Oscillation (AMO)

    The following figure shows the AMO anomalies from 1850 to 2009 [http://en.wikipedia.org/wiki/File:Amo_timeseries_1856-present.svg].

    The cycle length is approximately 62 years with maxima around 1878, 1943 and 2004, and minima around 1912 and 1974.

    – – –
    The AMO cycle is very close to the global temperature cycle in terms of cycle length and occurrence of maxima / minima.
    [all from appinsys site]

  5. J Martin,

    It is actually the 59.75 year Perigean New/Full Moon cycle that drives the tri-decadal (~ 60-year) cycles that are seen in the AMO, PDO, All India Summer Monsoon rainfall and the Walker Circulation influence upon the equatorial trade winds.

    The 59.79 year lunar period associated with the Perigean New/Full Moon cycle is tied in with the orbital periods of Venus-Earth-Jupiter (VEJ) cycle that controls the level of solar activity and so the long term effect of the extreme Perigean spring tides upon the Earth’s climate are synchronized with the various cycles that are seen overall level of solar activity.

    Please see my post at:

    http://astroclimateconnection.blogspot.com.au/2017/10/world-wind-speeds-have-slowed-down-over.html

  6. oldbrew says:

    ‘For every 7 apsidal cycles (LAC), there are 766 synodic months (both chart versions).’

    That’s the ~62 year key period. All the other components have to ‘adjust’ as described above.

  7. oldbrew,

    Can you get my email off Roger so that I can contact you offline?

  8. oldbrew says:

    RE – oldbrew says: October 15, 2017 at 10:38 pm

    Three references to 62 years here.
    http://appinsys.com/globalwarming/SixtyYearCycle.htm

    The cycle length is approximately 62 years with maxima around 1878, 1943 and 2004, and minima around 1912 and 1974.
    – – –
    So the next minimum would be due around 2035-36.

  9. oldbrew says:

    766 synodic months =
    827.93269 tropical months
    820.93269 anomalistic months
    61.932689 tropical years
    54.932701 full moon cycles

    827.93269 – 820.93269 = 7 (lunar apsidal cycles in the period)
    61.932689 – 54.932701 = 7 (6.999988)

    97/104 = 0.9326923
    104 – 97 = 7

    That shows why all the numbers in the original chart that aren’t already a multiple of 104, would need 7 added to them to become so e.g.:
    61*104 plus 0.932689*104 = 6344 + 97 = 6441 trop. yrs.

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