Why Phi? – a Mars-Earth model and more

The Mars-Earth model is based on 34 Mars orbits. This equates to 64 years, which is 8². Since Venus makes 13 orbits of Earth in 8 years, we can easily add it to the model.
2,3,5,8,13 and 34 are Fibonacci numbers.

The story doesn’t end there, because as the diagram shows this results in a 3:4:7 relationship between the 3 sets of synodic periods. This was analysed in detail in a paper by astrophysicist Ian Wilson, featured at the Talkshop in 2013:

Ian Wilson: Connecting the Planetary Periodicities to Changes in the Earth’s Length of Day

Wilson notes: ‘A remarkable near-resonance condition exists between the orbital motions of the three largest terrestrial planets with:

4 x sVe = 6.3946 years where sVe = synodic period of Venus and Earth
3 x seM = 6.4059 years seM = synodic period of Earth and Mars
7 x sVM = 6.3995 years and sVM = synodic period of Venus and Mars

This means that these three planets return to the same relative orbital configuration at a whole multiple of 6.40 years.’

The Mars-Earth model above reflects that near-resonance and shows a strong link to whole numbers of planetary orbits.
A close link also occurs with the long Inex period (521 years) that was recently discussed here:

https://tallbloke.wordpress.com/2015/03/20/why-phi-the-inex-eclipse-cycle-part-2/

…where we find with reference to Keeling and Whorf’s tidal cycles:
‘Figure 2 in the [K&W] paper shows two long tidal cycle periods of 1823 years each…
By adding these two periods together, plus one year, we get 7 sets of 18 Inex cycles (3647 years = 521y x 7)’

A quick check shows that 57 x 64 years = 3648 while 7 x 521 years = 3647 — i.e. one year less.

We now find that:
1939 (34 x 57, +1) Mars orbits = 3646.96 years
5928 (13 x 8 x 57) Venus orbits = 3646.89 years
3647 (64 x 57, -1) Earth orbits = 3647 years
— so we have strong matches to the 3647 years (7 x 521 years) Inex period there.

In this analysis Mars ‘gains’ one orbit and Earth ‘loses’ one compared to the model over the 3647 year period, while Venus orbits are ‘on target’. This shows how small the difference is between the original model (graphic above) and the likely reality.

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Planetary data source: http://ssd.jpl.nasa.gov/?planet_phys_par