## Why Phi? – Earth’s secret neighbours

Posted: January 22, 2014 by oldbrew in Celestial Mechanics, Fibonacci, Phi, Solar physics, solar system dynamics
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1685 Toro and 1866 Sisyphus may be names you haven’t heard of but they’re
orbiting the Sun in the neighbourhood of our planet. What are they and what
exactly are they doing?

They are known as Apollo asteroids (see footnote) – two of several dozen in fact.

‘They are Earth-crosser asteroids that have orbital semi-major axes greater
than that of the Earth (more than 1 AU) but perihelion distances less than
the Earth’s aphelion distance (which is 1.017 AU).’

http://en.wikipedia.org/wiki/List_of_Apollo_asteroids

What they are doing is orbiting the Earth in interesting synodic relationships
with it. Toro completes 5 orbits of the Sun every 8 Earth years/orbits while 5
Sisyphus orbits take 13 Earth years/orbits, thus 8 Sisyphus = 13 Toro orbits
(as very close approximations). On a longer time scale the figures are:
825 Toro = 1319 Earth orbits (825:1320 = 5:8) and
100 Sisyphus = 163 Toro orbits (100:162.5 = 8:13).

## A new way to calculate the value of Pi?

Posted: April 21, 2013 by tallbloke in Analysis, Measurement, methodology, Philosophy
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Barbury Crop Circle represents Pi

Update: I made a dumb algebra mis-step – back to the drawing board. :)

I believe I’ve found a new way to calculate the value of Pi. Before anyone starts shouting at me, the value I’ve arrived at is Pi, not some new number I’m claiming to be the circumference of a circle divided by its diameter.

So, what is the equation I’ve come up with which can calculate the value of Pi?

Here it is:

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

Posted: February 20, 2013 by tallbloke in Analysis, Astronomy, Astrophysics, climate, Cycles, data, Gravity, Natural Variation, Ocean dynamics, Solar physics, solar system dynamics, Tides
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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: an = an-1 + an-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.