## Why Phi? – a Neptune-Pluto-Eris model

Posted: June 3, 2015 by oldbrew in Fibonacci, Phi, solar system dynamics
Tags: ,

Comparison of the eight brightest TNOs [credit: Wikipedia]

As Pluto is getting some media attention due to the impending ‘fly-by’ of a NASA space probe, let’s take a look at its orbital relationship with its neighbours.

Pluto and its neighbours

So-called dwarf planet Eris is rarely mentioned in the media but is about the same size as Pluto. At its furthest point from the Sun (aphelion) it’s over three times as far away as Neptune in a highly elliptical orbit.

In the diagram each ‘triangle’ of figures is self-consistent e.g. 149-99 = 50.
The conjunction ratios of 50:55:105 reduce to 10:11:21, close to 1:1:2. (2,5,21 and 55 are Fibonacci numbers).

The well-known 3:2 Neptune-Pluto orbital ratio is closely reflected by the 149:99 figures (150:100 = 3:2).

Note also the Pluto:Eris orbital ratio of 44:99 = 4:9 = 2²:3²

JPL orbital data:
Neptune 164.79132y
Pluto 247.92065y
Eris 558.04y

44 Eris = 24553.76y
99 Pluto = 24544.144y
149 Neptune = 24553.906y

Model accuracy: greater than 99.95%.

Pluto orbit graphics: http://en.wikipedia.org/wiki/Pluto#Orbit_and_rotation

1. oldbrew says:

FWIW the long period of 24550y (+/- a few) is about 21:20 with Earth’s precession ‘wobble’.

Wikipedia gives a figure for general precession of around 25771.4 years (current epoch).
http://en.wikipedia.org/wiki/Axial_precession#Values

25771.4 x (20/21) = 24544.19y (= 99 Pluto – see above)

NB the precession figure is 144 Jose cycles or 144 x 14 Jupiter-Neptune conjunctions, but that’s probably another story…

Prolonged minima and the 179-yr cycle of the solar inertial motion
– Rhodes W. Fairbridge, James H. Shirley

(144 x 179y = 25776y)

2. Paul Vaughan says:

Phi Knot?

https://tallbloke.wordpress.com/2014/10/29/why-phi-giant-planets-update-part-2/comment-page-1/#comment-91733

836, 418, 209 …

Jupiter axis slip on the “60 year” cycle:

(6.104648218)*(5.9313075) / (6.104648218 – 5.9313075) = 208.886557
(6.104648218)*(5.9313075) / (6.104648218 + 5.9313075) = 3.00836482
(6.104648218)*(5.9313075) / ( (6.104648218 + 5.9313075) / 2 ) = 6.01672964

Analogous Saturn slip:

(15.26162054)*(14.723749) / (15.26162054 – 14.723749) = 417.773114
(15.26162054)*(14.723749) / (15.26162054 + 14.723749) = 7.493930328
(15.26162054)*(14.723749) / ( (15.26162054 + 14.723749) / 2 ) = 14.98786066

Together:

(10.05201076)*(9.932517933) / (10.05201076 – 9.932517933) = 835.5462281
(10.05201076)*(9.932517933) / (10.05201076 + 9.932517933) = 4.995953552
(10.05201076)*(9.932517933) / ( (10.05201076 + 9.932517933) / 2 ) = 9.991907104

a well-aged brew….

3. Paul Vaughan says:

appendix:

(14.723749)*(11.862615) / (14.723749 – 11.862615) = 61.04648218
(29.447498)*(19.86503587) / (29.447498 – 19.86503587) = 61.04648218
(11.862615)*(9.932517933) / (11.862615 – 9.932517933) = 61.04648218

harmonic nearest S/2 = 4th = 61.04648218 / 4 = 15.26162054
harmonic nearest (J-S)/2 = 6th = 61.04648218 / 6 = 10.05201076
harmonic nearest J/2 = 10th = 61.04648218 / 10 = 6.104648218

4. Paul Vaughan says:

Note well: negative sidebands near subharmonics of terrestrial year (e.g. 6, 10, 15)
…and note how those resonances break with progressive halvings….
(tip: annual, semi-annual….)

5. oldbrew says:

PV: that 61.04648218 figure looks suspiciously like this result:

126 Jupiter-Saturn = 2503 years = 41 x 360 degrees of rotation (i.e. exact return to start point)
2503 / 41 = 61.04878y = time taken for J-S to move 360 degrees retrograde (once).

The other figures represent multiples of the de Vries cycle: 126 J-S = 12 de Vries.
2503 / 12 = 208.58333y = 1 de Vries (mean value).
2 de V = 417.1666, 4 de V = 834.333 etc.

126 J-S is also 211 Jupiter and 85 Saturn orbits (211 – 85 = 126), so that should repeat more or less as it’s almost exactly a whole number of orbits of both planets. [NB 211 is a prime number].

Since the number of conjunctions (J-S, J-E, S-E) in 2503 years is in each case a multiple of 6 it follows that 21 J-S (126 / 6) is at the heart of the repeating de Vries cycle/period.

6. oldbrew says:

Forgot to mention that whereas the Neptune:Pluto orbit ratio is 3:2, the Pluto:Eris ratio is 3²:2².
(99 Pluto:44 Eris = 9:4 ratio).
That gives the equation: 4 Eris = 5 Pluto-Eris conjunctions = 9 Pluto (about 99.97% true with current data).

The square roots of 4,5 and 9 are 2, 2.23607~ and 3 which can be the sides of a Pythagoras triangle.
The square root of 5 is also used to derive the golden ratio value:
((square root of 5) + 1) / 2 = Phi

7. NikFromNYC says:

Fun artistic take on planetary paths here:

http://www.grasshopper3d.com/photo/planetary-positions?context=latest

-=NikFromNYC=-