## Why Phi? – Neptune’s moon Triton and its neighbours

Posted: October 10, 2015 by oldbrew in Fibonacci, Phi, solar system dynamics
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The orbit of Triton (red) is opposite in direction and tilted −23° compared to a typical moon’s orbit (green) in the plane of Neptune’s equator [image credit: Wikipedia]

Triton is the seventh largest moon in the solar system. Not only that, it has over 99% of the mass of all Neptune’s moons combined. Its retrograde orbit makes it unique among the large moons of the solar system, and it is also the coldest known planetary body at -235° C (-391° F).

Turning to the orbit numbers, and looking at Triton’s closest ‘inner’ (nearer to Uranus) neighbour Proteus and the next two ‘outer’ moons, we find these values (in days):
1.122d Proteus
5.877d Triton
360.13d Nereid
1879.08d Halimede

We’ll treat Proteus and Triton as a pair, and the same for Nereid and Halimede.
Nereid is over fifteen times further from Uranus than Triton is, so hardly a neighbour at all.

Looking at the orbit ratios (which are also the rotation ratios, as usual with moons):
T/P = 5.877 / 1.122 = 5.238
H/N = 1879.08 / 360.13 = 5.218

The first thing to say is that the two results are very similar. One is about 99.62% of the other.

Something else can also be found here:
Phi² = 2.6180339
2xPhi² = 5.23607
So 2xPhi² equates to just over 99.96% of the observed Proteus-Triton orbit ratio.

Putting that into whole numbers for a matching period:
21 Triton = 123.417d
110 Proteus = 123.42d
Conjunctions per period = 110 – 21 = 89

Since 110 = 55 x 2, we have defined this moon pair with four Fibonacci numbers : 2,21,55 and 89.

Obviously the Nereid-Halimede numbers won’t be exactly the same because their ratio is slightly different, but a match within 0.04% of the other pair is at least interesting. The pair seem to be mimicking the orbital behaviour of their larger neighbours.

Footnote:
One theory says Halimede, the smallest of the moons listed here, could be a broken-off piece of Nereid.

Data source: Moons_of_Neptune

Other ‘Why Phi?’ posts here

Phi, or the golden ratio, and the Fibonacci sequence

1. oldbrew says:

‘So 2xPhi² equates to just over 99.96% of the observed Proteus-Triton orbit ratio.’

Neptune itself is in a similar type of orbital relationship with its inner neighbour Uranus.
N/U = 1.961408
3/4 of Phi² = 1.963525 (99.89% match with N/U)

Another way to look at it is that Neptune’s orbit is almost 165 years (55 x 3) and that of Uranus is just over 84 years (21 x 4).
55/21 (both Fibonacci numbers) is ~Phi² leaving 3/4 to finish the equation.

2. p.g.sharrow says:

I think you should consider Neptune and it’s moons to be damaged system. They are certainly not as GOD originally made them. The Earth / Luna pair demonstrates stuff happens. Uranus and Neptune systems also indicate that we exist in a dynamic place when billions of years are counted. Even Venus may not be where it originated…pg

3. oldbrew says:

pg: yes, it seems Triton barged into the Neptunian moon system and took over.

‘The mass distribution of the Neptunian moons is the most lopsided of the satellite systems of the giant planets in the Solar System. One moon, Triton, makes up nearly all of the mass of the system, with all other moons together comprising only one third of one percent. This may be because Triton was captured well after the formation of Neptune’s original satellite system, much of which would have been destroyed in the process of capture.’ – Wikipedia

Also: ‘This great perturbation may possibly be the reason why the satellite system of Neptune does not follow the 10,000:1 ratio of mass between the parent planet and all its moons seen in the satellite systems of all the other giant planets.’

4. gregole says:

Reblogged this on Alan Olee Book Report and commented:
This is somewhat, but not too terribly technical. It is extremely interesting and thought provoking.