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

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