For the Jupiter-Venus-Mercury (JVMe) model, we start with this basic synodic conjunction relationship:
61 Jupiter-Venus (J-V) = 100 Venus-Mercury (V-Me) = 161 Jupiter-Mercury (J-Me) conjunctions in 39.58 years.
Orbit numbers per 39.58y: 64.337~ Venus, 164.337~ Mercury, 3.3365~ Jupiter
Since the ratio 61:100:161 is only one conjunction different from 60:100:160 (= 3:5:8), there is a very close match to a Fibonacci-based ratio as 3,5 and 8 are all Fibonacci numbers.
In the model we convert the orbits to whole numbers using a multiple of 3, to obtain a triple conjunction period where there are (very close to) a whole number of orbits of the relevant planets, as per the chart [right].
Solar Simulator graphics (right) show a long term JVMe solar pattern using snapshots averaging 118.74 years apart.
Over nearly 3000 years and 25 occurrences the apparent position of the triple conjunction relative to that of the Sun itself changes only very gradually, in an anti-clockwise manner roughly following a line that’s one solar diameter from the barycentre of the solar system (the red circle on the graphic – click on it to enlarge).
N.B. 442 AD (top row, centre) looks slightly different due to the effect of the three opposing giant planets Saturn, Uranus and Neptune – see graphic [below, right].
In the Why Phi? – a Mars-Earth model and more post we found a Mars-Earth-Venus period of ~64 years.
Note that 64 / 39.58 (basic JVMe period) = ~1.617
Therefore a near-Phi ratio also exists between these J-V-Me and Ma-E-V conjunction periods (Phi = 1.618~).
We can observe that the JVMe period of 118.74 years is almost two-thirds of the Jose cycle (~3:2 ratio) of repeating solar inertial motion (~179 years). This could help to explain its near-repeating pattern of conjunctions as shown in the graphic above.
Every 179 years or so, the sun embarks on a new cycle of orbits.
Note also that 3 Venus-Mercury conjunctions = just under 433.7 days which is well within the estimated average period (430-435 days) of the Chandler wobble:
‘The Chandler Wobble may be a natural harmonic resonance’:
For example a frequency of 54 Chandler wobbles in 64 years (Mars-Earth-Venus period as above) equates to 1 CW = 432.888 days [as an average].
Ian Wilson: Solar System Timings Evolved Lunar Orbital Elements Linked to Earth’s Chandler Wobble
‘The century-old mystery of Earth’s “Chandler wobble” has been solved by a scientist at NASA’s Jet Propulsion Laboratory in Pasadena, Calif.’
Reference data: http://solarsystem.nasa.gov/planets/charchart.cfm/
Related Talkshop posts: https://tallbloke.wordpress.com/?s=Why+Phi