A dip into solar-planetary theory

Posted: February 12, 2017 by oldbrew in solar system dynamics

Solar system [credit: BBC]

Solar system [credit: BBC]

The details of interest here are:
Jupiter’s orbit period (J): 11.862615 years
Jupiter-Saturn conjunction period (J-S): 19.865036 years (mean value)
Solar Hale cycle (HC): ~22.14 years (estimated mean value)

Looking for a solar-planetary beat frequency (BF):
28 J = 332.15322 years
15 HC = 332.1 years
28 – 15 = 13 = number of beats in the period

Since Jupiter’s orbit period is a known value:
BF (approx.) = 332.15322 / 13 = 25.550247 y

Turning to J-S, consider the ‘Jose cycle‘ of 9 J-S:
9 J-S = 178.78532 y
7 BF = 178.85172 y
The value of BF using J-S known value:
178.78532 / 7 = 25.54076 y

Percent match of the two BF values = > 99.96%

Result – on the basis of the selected Hale cycle period:
Jupiter’s orbit matches the calculated solar-planetary beat frequency in the ratio 28:13.
For the Jose cycle (9 J-S conjunctions) the equivalent ratio is 9:7.
The Hale cycle ratio is 13 BF:15 HC by the above definitions.

Conclusion: this beat frequency connects the three items of interest as described.

(Note: 9 J-S figure updated 14/02/17 due to a typo).

  1. Sparks says:

    You know there’s a relativistic effect in the timing “beat” that’s why my own graphs are slightly off, for example;

    When I take the mean anomaly of both Jupiter and Uranus at a specific date and time and subtract one from the other, there is a gravitational time delay between the two planets, I think it works out at one third of the distance (could be phi) but changes in gravitational focal points between the planets account for the relative space/time shift between the sunspot record and planetary orbits…

    I’ve worked out a way to correct this by offsetting each of the planets mentioned above in time with a value related to their distance from the sun.

    For example; the mean anomaly’s of both Jupiter and Uranus were sampled at [D/M/Y] 1-1-1615 and with the correction, Jupiter is delayed (as it moves forward in time faster) relative to Uranus therefor the sample rates work out something like [Uranus: 1-1-1615] and [Jupiter 30-12-1614] then the mean anomaly values with the offset are subtracted to give the gravitational focal point.

    If there’s an easier way I’m all ears…

  2. oldbrew says:

    Hi Sparks.

    What can be said is that 8 Jupiter-Uranus conjunctions and 5 Hale cycles (using their average or estimated periods) would be around the same period i.e. ~110.5 years. The ratio of that period to the Jose cycle (178.785~ y) is about 1.618:1 i.e. Phi:1. (I think there was a Talkshop post about this a few years ago, I’ll try and find it.)

    Note also that the ratio of the Hale cycle to the Jupiter orbit period is 15:28 and 15 is 3 x 5.
    In fact 24 J-U (3 x 8) is about 99.8% of 28 J.

    Working with actual dates is obviously tricky when planets are travelling at variable speeds in their slightly elliptical orbits. I’ll have to leave the mechanics of it to you I’m afraid 😦

  3. oldbrew says:

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    By Steve Spaleta | February 13, 2017
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  4. oldbrew says:

    This can be modelled at the level of the Hallstatt cycle:

    9 J-S * 13 (117) = 7 BF * 13 (91) = 2324.21 y
    28 J * 7 (196) = 196 J = 2325.07 y
    (79 Saturn = 2326.35 y)
    15 * 7 Hale cycles (105) = 105 * 22.14 y(approx) = 2324.7 y

    These numbers all fall on or close to multiples of 13:
    91 BF = 7 * 13
    105 Hale = 8 * 13, +1
    117 J-S = 9 * 13
    196 J = 15 * 13, +1
    79 S = 6 * 13, +1

    The mean Hallstatt cycle could therefore be expressed as:
    13 Jose cycles = 21 * 5 Hale cycles
    – where 5,13 and 21 are Fibonacci numbers
    – – –
    ‘An oscillation with a period of about 2100–2500 years, the Hallstatt cycle, is found in cosmogenic radioisotopes (14C and 10Be) and in paleoclimate records throughout the Holocene. This oscillation is typically associated with solar variations, but its primary physical origin remains uncertain. Herein we show strong evidences for an astronomical origin of this cycle. Namely, this oscillation is coherent to a repeating pattern in the periodic revolution of the planets around the Sun: the major stable resonance involving the four Jovian planets – Jupiter, Saturn, Uranus and Neptune – which has a period of about p = 2318 years.’ – N. Scafetta

    Link to paper: https://tallbloke.wordpress.com/2016/09/22/nicola-scafetta-on-the-astronomical-origin-of-the-hallstatt-oscillation-found-in-radiocarbon-and-climate-records-throughout-the-holocene/

    NB 13.5 Uranus-Neptune conjunctions = ~2314 years
    179 * 13 = 2327 y

  5. oldbrew says:

    Going one step further – I’ve called the Hale cycle beat frequency with Jupiter ‘BF’ but it should be JBF.
    JBF per Hallstatt cycle = 91 = 7 * 13

    For the Saturn BF there are 105 Hale in the same period and 79 Saturn orbits:
    SBF per Hallstatt cycle = 105 – 79 = 26 = 2 * 13

    Therefore 2 SBF = 7 JBF
    We already know 7 JBF = 9 J-S conjunctions
    So 2 SBF = 9 J-S conjunctions

    7 + 2 = 9
    Therefore the axial period of JBF+SBF is the Jupiter-Saturn conjunction period (19.865~ years).
    J-S / JBF (7/9) + J-S / SBF (2/9) = 9/9 = 1 J-S
    – – –
    NB Landscheidt’s 35.76 year period would be about 9 J-S / 5.
    7 – 2 = 5 = the beat frequency of JBF and SBF per 9 J-S (Jose cycle).

    A complete five-fingered hand covers a period of 178.8 years, the fundamental cycle in the sun’s motion discovered by Jose (1965) and studied by Fairbridge, Sanders, and Shirley (Fairbridge and Sanders 1987; Fairbridge and Shirley 1987). Dansgaard (Dansgaard et al. 1969) has derived a cycle of just 180 years in climate from the Camp Century ice core drilled from the Greenland Ice Sheet. This correspondence begs for investigation of a possible relationship of climate features with the complex pattern of the five-fingered hand, which reflects both variations in impulses of the torque in the sun’s motion and secular sunspot activity.

    The mean interval between fingers of the hand is 35.76 years, and the average distance from the peaks of fingers —major maxima in the running variance of IOT (KMAX)-to the deepest points between two neighboring fingers — major minima in the running variance of IOT (KMIN) — cover; 17.88 years.
    [bold added]

    35.76 / 22.14 (Hale) = 21 / 13 approx.

  6. […] is an extended re-write of the earlier post on this topic. The purpose is to explain the Jose cycle chart shown below (in blue). – […]

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