Why Phi? – Jupiter, Saturn and the inner solar system

From left, Mercury, Venus, Earth and Mars. [Credit: Lunar and Planetary Institute]

The planetary theory aspect appears a bit later, but first a brief review of some relevant details.

In this Talkshop post: Why Phi? – a triple conjunction comparison we said:
(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.

– – –
These are the closest matches we can find for these planet trios.

Extending this to Mercury (Me):
(3) JSMe = 5 J-S or 404 J-Me or 409 S-Me conjunctions (5+404 = 409) in 99.325 years (as an average or mean value).

5,13 and 21 are Fibonacci numbers, therefore this is a Phi-related progression.
The numbers increase in order of each planet’s orbit period.
13 Mercury orbits = ~5.09 Venus orbits
21 Mercury orbits = ~5.06 Earth orbits

Note also the non J-S numbers are clustered around 400 in each case.
That implies an approximate Fibonacci/Phi ratio between them.
The ratio is drawn from the number of J-S in the relevant row.

For example J-Me (5 J-S line) should be near 13:5 with J-V (13 J-S line).
In this case it works out as ~13.2 J-Me = 5 J-V.

The closer the number, the closer the expected correlation.
Consider 404 J-Me (5 J-S line) and 403 S-E (21 J-S line).
~21.054 J-Me = 5 S-E, near a 21:5 ratio.

Then there’s Mars (Ma), which is a planetary neighbour of Jupiter.
Being Mars, this works in a slightly different way, in terms of the numbers.
(4) JSMa = 9 J-S or 80 J-Ma or 89 S-Ma (9+80 = 89) in 178.785 years (as an average or mean value).

This is also the period in which the Sun returns to the barycentre of the solar system, as Gerry Pease explained here.

A series of great conjunctions, an illustration from Kepler’s book ‘De Stella Nova’ (1606) [credit: Wikipedia]

Although 9 J-S is not a Fibonacci number, it consists of 3 Kepler ‘trigons’ (see illustration) of 3 J-S each, the well-known ~60 year cycle (3 is a Fibonacci number).

In one trigon the position of a J-S conjunction relative to the Sun moves by nearly 360 degrees (351.44 degrees).

In other words it returns to nearly the same position every 3 J-S.
9 also falls midway between 5 and 13 i.e. (5+13)/2 = 9.

All this begs the question of whether the inner planets have gravitated to their current orbits to fall into such harmonic relationships with one of the most powerful forces of the solar system, i.e. the Jupiter-Saturn conjunction with the Sun.

We’ve already seen that with the four Galilean moons of Jupiter the critical factor was the 3:2:1 synodic ratio of the conjunctions.

Another clear example of synodic ratios is the seven-planet resonance chain of the Trappist-1 exoplanet system.

via Tallbloke’s Talkshop


November 19, 2017 at 09:03AM

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