Why Phi? – some Earth-Mars orbital harmonics

Posted: May 1, 2019 by oldbrew in Fibonacci, Lucas, Maths
Tags: ,

A simple pattern emerges when looking at the Earth-Mars synodic conjunctions.

Focussing on the numbers of Mars orbits that are equal, or almost equal, to an exact number of Earth orbits (years), the pattern can be found by subtracting the number of conjunctions from the number of Mars orbits.

The difference between the two sets of numbers follows the Fibonacci series, which is strongly related to the golden ratio.

On the right is a method for constructing the same table using Fibonacci and Lucas numbers, following their series progression.

It’s included here simply because it works.

Note that the ‘+’ numbers on the far right follow the Fibonacci series from the beginning i.e. 0.

The first two columns generate the number of Mars orbits.

  1. tallbloke says:

    Wow. I never thought we’d find a direct fibonacci relationship between Earth and Mars. Well done OB!

    Is it worth looking at other planet pairs to see if something similar emerges?

  2. oldbrew says:

    TB: neither did I, but it was hiding in plain sight.

    Certainly worth looking for more – when are you going to start ? 😆

  3. tallbloke says:

    Not today…

  4. oldbrew says:

    The numbers relate to the revolution of the conjunction position, so to speak.

    360 / 1.8808476 yrs (Mars orbit period) = 191.40306
    191.40306 * 2.13527 (Earth-Mars synod) = 408.6972 degrees

    Example 1 : 17 Mars orbits = 15 Mars-Earth synods
    408.6972 * 15 = 6130.458
    6130.458 / 17 = 360.61517 (99.83% match to 360 degrees).

    Example 2: 42 Mars orbits = 37 Mars-Earth synods
    408.6972 * 37 = 15121.796
    15121.796 / 42 = 360.04276 (99.988% match to 360 degrees).

  5. oldbrew says:

    Found a Jupiter-Saturn pattern, all Fibonacci. Probably do a post later, or tomorrow.

  6. JB says:

    Since reading through Arp’s Seeing Red I’ve had this nagging intellectual itch there is a Phi relationship embedded in the quantized steps of galactic evolution. Arp made a case for scaling of quantized behavior from the atom, to the solar system, and to the galaxy. Maybe someone else can sniff out the pattern?

  7. oldbrew says:

    JB – self-similarity should be in there.


    ‘Line segments in the golden ratio’

  8. tallbloke says:

    It’s the simplest form of fractal. No wonder nature makes diverse use of it.

  9. oldbrew says:

    As TB says…

    The golden ratio has the simplest expression (and slowest convergence) as a continued fraction expansion of any irrational number (see Alternate forms above). … This may be why angles close to the golden ratio often show up in phyllotaxis (the growth of plants).


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