‘Pluto’s orbital period is 248 Earth years. Its orbital characteristics are substantially different from those of the planets, which follow nearly circular orbits around the Sun close to a flat reference plane called the ecliptic. In contrast, Pluto’s orbit is moderately inclined relative to the ecliptic (over 17°) and moderately eccentric (elliptical). This eccentricity means a small region of Pluto’s orbit lies nearer the Sun than Neptune’s.’ – Wikipedia

## Posts Tagged ‘phi’

## Why Phi? – Pluto’s eccentric orbit

Posted: March 27, 2016 by**oldbrew**in Phi, solar system dynamics

Tags: phi, planetary theory

## Why Phi? – lunar eclipses at Stonehenge

Posted: February 19, 2016 by**oldbrew**in Celestial Mechanics, Cycles, moon, Phi

Tags: moon, phi

Stonehenge Visitors Guide – under ‘Eclipse Cycles’ – says:

*‘Now, it’s widely accepted that Stonehenge was used to predict eclipses. The inner “horseshoe” of 19 stones at the very heart of Stonehenge actually acted as a long-term calculator that could predict lunar eclipses. By moving one of Stonehenge’s markers along the 30 markers of the outer circle, it’s discovered that the cycle of the moon can be predicted. Moving this marker one lunar month at a time – as opposed to one lunar day the others were moved – made it possible for them to mark when a lunar eclipse was going to occur in the typical 47-month lunar eclipse cycle. The marker would go around the circle 38 times [2 x 19] and halfway through its next circle, on the 47th full moon, a lunar eclipse would occur.’*

## Why Phi? – a unified precession model

Posted: February 1, 2016 by**oldbrew**in Cycles, Fibonacci, Phi, solar system dynamics

Tags: phi, precession

*‘Because of apsidal precession the Earth’s argument of periapsis slowly increases; it takes about 112000 years for the ellipse to revolve once relative to the fixed stars. The Earth’s polar axis, and hence the solstices and equinoxes, precess with a period of about 26000 years in relation to the fixed stars. These two forms of ‘precession’ combine so that it takes about 21000 years for the ellipse to revolve once relative to the vernal equinox, that is, for the perihelion to return to the same date (given a calendar that tracks the seasons perfectly).’*– Wikipedia

Here we’ll fit the three precession cycles into one model and briefly examine its workings.

## Why Phi? – an orbital parameters test

Posted: December 21, 2015 by**oldbrew**in Analysis, Fibonacci, solar system dynamics

Tags: phi, planetary

## Why Phi? – the resonance of Jupiter’s Galilean moons

Posted: November 26, 2015 by**oldbrew**in Fibonacci, Phi, solar system dynamics

Tags: phi, resonance

The resonance of three of the four Galilean moons of Jupiter is well-known. Or is it?

We’re usually told there’s a 1:2:4 orbital ratio between Ganymede, Europa and Io, but while this is not far from the truth, a closer look shows something else.

## Phi and the Great Pyramid of Khufu

Posted: November 19, 2015 by**oldbrew**in Maths, Measurement, Phi

Tags: phi

*Let’s have a look at some numbers for the Great Pyramid.*

Source: Building the Great Pyramid (aka Cheops)

Copyright 2006 Franz Löhner and Teresa Zuberbühler

Dimensions as designed (in Egyptian royal cubits):

Length: 440

Height: 280

Slope: 356

Original dimensions as built (a,h and c in the pyramid diagram below):

Length: 230.36m (half = 115.18m)

Height: 146.59m

Slope: 186.42m

## Why Phi? – some Moon-Earth interactions

Posted: November 9, 2015 by**oldbrew**in Celestial Mechanics, Fibonacci, moon, Phi

Tags: phi, planetary theory, resonance

Tallbloke writes: *Stuart ‘Oldbrew’ has been getting his calculator warm to discover the congruences in various aspects of the Lunar orbit around Earth, and its relationship to Earth-Moon orbit around the Sun. Emerging from this study are some useful insights into longer periods, such as the ‘precession of the equinoxes‘.*

Some matching periods of lunar numbers:

86105 tropical months (TM) @ 27.321582 days = 2352524.8 days

85377 anomalistic months (AM) @ 27.55455 days = 2352524.8 days

79664 synodic months (SM) @ 29.530589 days = 2352524.8 days

These identical values are used in the chart on the right (top row). The second row numbers are the difference between the numbers in the first row (TM – AM and AM – SM).

The derivation of the third row number (6441) is shown on the chart itself [click on the chart to enlarge it].

**The period of 6441 tropical years (6440.75 sidereal years) is one quarter of the Earth’s ‘precession of the equinox’.**

Multiplying by 4: 25764 tropical years = 25763 sidereal years.

The difference of 1 is due to precession.

## Why Phi? – a Jupiter-Neptune model

Posted: September 15, 2015 by**oldbrew**in Fibonacci, Phi, solar system dynamics

Tags: phi, planetary theory, resonance

Continuing our long-term series researching Fibonacci and/or Phi based ratios in planetary conjunction periods, it’s time for a look at the inner- and outer-most gas giants of our solar system: Jupiter and Neptune.

Initial analysis shows the period of 14 Jupiter orbits is close to that of one Neptune orbit of the Sun, and even closer to the period of 13 (14 less 1) Jupiter-Neptune (J-N) conjunctions.

It also turns out that there’s a multiple of 13 J-N that equates to a whole number of Earth orbits:

Jupiter-Neptune(J-N) average conjunction period = 12.782793 years

221 J-N = ~2825 years (2824.9972y)

(221 = 13 x 17)

But this period is not a whole number of either Jupiter or Neptune orbits.

This is resolved by multiplying by a factor of 7.

## Why Phi? – a Jupiter-Uranus-Neptune model

Posted: August 20, 2015 by**oldbrew**in Fibonacci, Phi, solar system dynamics

Tags: phi, planetary

Continuing our quest to understand more about planetary frequencies, we turn to links between the largest planet Jupiter and the two ‘outer’ giant planets, Uranus and Neptune.

This model is based on a match of synodic periods, which is found to be:

22 Uranus-Neptune (U-N) = 273 Jupiter-Uranus (J-U) = 295 Jupiter-Neptune (J-N)

The period is just under 3771 years (~3770.93y).

To find a link to Fibonacci numbers we can look first at Jupiter-Uranus:

273 J-U = 13 x 21 (13 and 21 are Fibonacci numbers)

## Why Phi? – Moons of Pluto

Posted: July 26, 2015 by**oldbrew**in Fibonacci, Phi, solar system dynamics

Tags: phi, planetary theory

*In this extract from Wikipedia we’ve highlighted the relevant part in bold, so without more ado:*

**Resonances**

Styx, Nix, and Hydra are in a 3-body orbital resonance with orbital periods in a ratio of 18:22:33. The ratios are exact when orbital precession is taken into account. This means that in a recurring cycle there are 11 orbits of Styx for every 9 of Nix and 6 of Hydra. Nix and Hydra are in a simple 2:3 resonance. **The ratios of synodic periods are such that there are 5 Styx–Hydra conjunctions and 3 Nix–Hydra conjunctions for every 2 conjunctions of Styx and Nix.**

## Why Phi? – a Venus transit cycle model

Posted: July 3, 2015 by**oldbrew**in Fibonacci, Phi, solar system dynamics

Tags: phi, planetary

NASA: 2004 AND 2012 TRANSITS OF VENUS – Introduction says:

*‘Transits of Venus across the disk of the Sun are among the rarest of planetary alignments. Indeed, only six such events have occurred since the invention of the telescope (1631, 1639, 1761, 1769, 1874 and 1882). The next two transits of Venus will occur on 2004 June 08 and 2012 June 06.’*

Obviously there are three pairs of transits (eight years apart per pair) shown in the brackets, plus the fourth pair that occurred in 2004 and 2012. The model we use here is structured as per this graphic:

This is where it gets a little bit tricky perhaps.

## Why Phi? – a triple conjunction comparison

Posted: June 14, 2015 by**oldbrew**in Fibonacci, Phi, solar system dynamics

Tags: phi, planetary, resonance

**(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

## Why Phi? – Jupiter, Saturn and the de Vries cycle

Posted: April 17, 2015 by**oldbrew**in Cycles, Fibonacci, solar system dynamics

Tags: phi, solar - planetary theory, 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.

## Why Phi? – a Mars-Earth model and more

Posted: March 27, 2015 by**oldbrew**in Celestial Mechanics, Cycles, Fibonacci, Phi, solar system dynamics

Tags: phi, resonance

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

## Why Phi? – a simple Venus-Mercury model

Posted: March 22, 2015 by**oldbrew**in Fibonacci, Phi, solar system dynamics

Tags: phi, planetary theory

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)

## Why Phi? – the Inex eclipse cycle, part 2

Posted: March 20, 2015 by**oldbrew**in Cycles, Fibonacci, modelling, moon, Phi, solar system dynamics

Tags: phi

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’

## Why Phi? – ‘Fractals seen in throbs of pulsating golden stars’

Posted: January 28, 2015 by**oldbrew**in Astronomy, Astrophysics, Fibonacci, Phi

Tags: exoplanets, phi

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.’

## Why Phi? – the Saros connection

Posted: January 3, 2015 by**oldbrew**in Celestial Mechanics, Cycles, Fibonacci, Maths, moon, Phi

Tags: equations, moon, phi

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…)

## Why Phi? – Earth’s secret neighbours

Posted: January 22, 2014 by**oldbrew**in Celestial Mechanics, Fibonacci, Phi, Solar physics, solar system dynamics

Tags: phi, planetary, solar system

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

Tags: calculation, definition, mathematics, phi, 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: