Posts Tagged ‘phi’

[image credit: imagineeringezine.com]

[image credit: imagineeringezine.com]

Only two questions are needed here:

(1) What is the period of a Jupiter(J)-Saturn(S)-Earth(E) (JSE) triple conjunction?
JSE = 21 J-S or 382 J-E or 403 S-E conjunctions (21+382 = 403) in 417.166 years (as an average or mean value).

(2) What is the period of a Jupiter(J)-Saturn(S)-Venus(V) (JSV) triple conjunction?
JSV = 13 J-S or 398 J-V or 411 S-V conjunctions (13+398 = 411) in 258.245 years (as an average or mean value).

Since JSV = 13 J-S and JSE = 21 J-S, the ratio of JSV:JSE is 13:21 exactly (in theory).

As these are consecutive Fibonacci numbers, the ratio is almost 1:Phi or the golden ratio.
Golden ratio: relationship to Fibonacci sequence

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Jupiter dominates the solar system

Jupiter dominates the solar system

By far the two largest bodies in our solar system are Jupiter and Saturn. In terms of angular momentum: ‘That of Jupiter contributes the bulk of the Solar System’s angular momentum, 60.3%. Then comes Saturn at 24.5%, Neptune at 7.9%, and Uranus at 5.3%’ (source), leaving only 2% for everything else. Jupiter and Saturn together account for nearly 85% of the total.

The data tell us that for every 21 Jupiter-Saturn (J-S) conjunctions there are 382 Jupiter-Earth (J-E) conjunctions and 403 Saturn-Earth (S-E) conjunctions (21 + 382 = 403).

Since one J-S conjunction moves 117.14703 degrees retrograde from the position of the previous one, the movement of 21 will be 21 x 117.14703 = 2460.0876, or 2460 degrees as a round number.

The nearest multiple of a full rotation of 360 degrees to 2460 is 2520 (= 7 x 360).
Therefore 21 J-S has a net movement of almost 60 degrees (2520 – 2460) from its start position.

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Click on image to enlarge

Click on image to enlarge

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

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The model is ~99.78% accurate

The model is ~99.78% accurate


The model is in the diagram, so here’s the explanation.
Divide the orbit period of Venus by that of Mercury:
0.61519726 years / 0.2408467 years = 2.554310522

To get to whole numbers, round the result up to 2.56 then:
2.56 x 5 = 12.8
12.8 x 5 = 64
64 / 25 = 2.56

64 = 8² and 25 = 5²
Therefore the approximate ratio of Mercury:Venus orbit periods is 8²:5².
The number of conjunctions in the period is the difference in orbit numbers:
8² – 5² = 64 – 25 = 39 = 13 x 3

Phi link: 2,3,5,8, and 13 are all Fibonacci numbers.

2.554310522 / 2.56 = 0.99777755~ so the accuracy of the model is around 99.78%.

An even more accurate model would be:
626 Venus = 1599 Mercury.
1599 / 626 = 2.554313 i.e. almost the same as 2.554310522 = the true ratio.

Note that 1600 / 625 = 2.56 which is the same as 8² / 5².
So there’s one more Venus (626) and one less Mercury orbit (1599) in reality, every 385.11 years, compared to our model.

Footnote:
1600 = 8² x 5²
625 = 5² x 5²
(The common 5² is redundant in the ratio, leaving 8²:5²)

18 Inex cycles = 521 years [click to enlarge]

18 Inex cycles = 521 years
[click to enlarge]

In the wake of today’s solar eclipse and following an earlier post on the same topic, we have another perspective on the 521 year period that corresponds exactly to 18 Inex eclipse cycles.

An Inex corresponds to:
358 lunations (synodic months) = 28.94444 years
388.50011 draconic months
30.50011 eclipse years
Source: http://en.wikipedia.org/wiki/Inex

This means two Inex = 716 synodic months (358×2) and 777 draconic months (388.5×2).
This period will also be 61 eclipse or draconic years (777 – 716 or 30.5 x 2).

Each number in the diagram (below the top line) is derived from the numbers above it. Note that 18 Inex is the same period as 28 lunar nodal cycles. Both periods end at the lunar node they started at.

We can build on this, first by looking at data from a well-known science paper by Keeling & Whorf titled:
‘The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change’

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Kepler Space Telescope [NASA]

Kepler Space Telescope [NASA]


A very interesting report of a new science paper has appeared in the New Scientist:

‘William Ditto and his colleagues at the University of Hawaii, Manoa, compared the two strongest oscillations, or tones, made by the variable star KIC 5520878, using observations by NASA’s Kepler space telescope. They noticed that dividing the frequency of the secondary note by that of the primary, or lowest, note gives a value near the “golden ratio” – a number that shows up often in art and nature and is close to 1.618′

So is it real or did they perhaps just imagine it?
Let’s start with the abstract :

‘The unprecedented light curves of the Kepler space telescope document how the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean, the most irrational number.’

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Santorini_moon2
What is a Saros? Quoting Wikipedia:
‘One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur’

‘It takes between 1226 and 1550 years for the members of a saros series to traverse the Earth’s surface from north to south (or vice-versa)’

Only a few lines to go … (more…)

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).

toro-orbit

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Barbury-Castle-Wiltshire-01-06-08

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:

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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.

planet_orbits-sideview

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.

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