Why Phi? Simplified: A brief Fibonacci tour of the Solar System

A couple of years ago I made my original discovery that all the planets of the solar system are connected by golden section or phi relationships between their orbits, spin rates, conjunction periods and conjunction cycle precession periods and expressed in the Fibonacci series. I’ve been searching for a way to present the findings in a simple, clear way that anyone can easily understand. Last week, during a sleepless night of back pain, I hit on a nice solution.

All the commensurabilities in the following layout are pretty accurate for an overview of the system. Mars is a special case, being a small body getting shoved around between gas giant Jupiter and Earth. It has power series numerics relating it to a near neighbour reminiscent of the dwarf planets Pluto and Eris, which are beyond the main system, and further from the Sun’s gravitational pull. They relate more to Neptune’s orbital period.

A remarkable discovery: All Solar system periods fit the Fibonacci series and the Golden Ratio. Why Phi?

Many other people have noticed Phi relationships in the solar system in the past, from Kepler onwards, and there are several websites which cover this interesting topic. But up until now, so far as I know,  no-one has been able to find a single simple scheme linking all the planets and the Sun into a harmonious whole system described by the basic Fibonacci series. A couple of weeks ago while I was on holiday, I had a few long ‘brainstorming sessions’ with Tim Cullen, and decided to roll my sleeves up and get the calculator hot to test my ideas. What I discovered is laid out below in the style of a simple ‘paper’. Encouraged by an opinion from a PhD astrophysicist that this is “a remarkable discovery”, I will be rewriting this for submission to a journal with the more speculative elements removed and some extra number theory added to give it a sporting chance of acceptance. For now, this post establishes the basics, but there is much more I have discovered, and I will be using some of that extra material in more posts soon.

Relations between the Fibonacci Series and Solar System Orbits

Roger Tattersall – February 13 2013

Abstract

The linear recurrence equation: a_n = a_n-1 + a_n-2 with the starting conditions: a₁ = a₂ = 1 generates the familiar Fibonacci series: 1,1,2,3,5,8,13… This paper will use the first twenty terms of the sequence to demonstrate a close match between the Fibonacci series and the dynamic relationships between all the planets, and two dwarf planets in the Solar System. The average error across the twenty eight data points is demonstrated to be under 2.75%. The scientific implication of the result is discussed.

Introduction

Since it was noticed that five synodic conjunctions occur as Earth orbits the Sun eight times while Venus orbits thirteen times, many attempts have been made to connect the Fibonacci series and it’s convergent ‘golden ratio’ of 1.618:1 to the structure of the solar system. Most of these attempts have concentrated on the radial distances or semi-major axes of the planet’s orbits, in the style of Bode’s Law, and have foundered in the inner solar system.