Why Phi? – Pluto’s eccentric orbit

Pluto’s non-standard orbit [credit: Wikipedia]

‘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

A planet’s perihelion occurs at its nearest position to the Sun during its orbit.
Conversely aphelion occurs at its furthest position from the Sun.
The difference between Pluto’s perihelion and aphelion is nearly 3 billion kilometres.
Phi is the golden ratio.

Phi = (1 + √5) / 2 = ~1.618034
Uranus:Pluto perihelion ratio = 1:1.6185094
Neptune:Pluto perihelion ratio = 1:1 (99.82% match)
Uranus:Neptune perihelion ratio = 1:1.6212928
Neptune:Pluto aphelion ratio = 1:1.6226276

The figures speak for themselves but the 1:1 Neptune:Pluto perihelion ratio is worth a mention.
It could mean that Pluto was once a moon of Neptune, as its perihelion is ‘inside’ that of Neptune.
The difference in perihelion distance of 763,000 km. would be a plausible orbital distance for Pluto from Neptune.
Various theories exist as to Pluto’s orbital history.

The fact that the Uranus:Pluto perihelion ratio is almost the same as the Neptune:Pluto aphelion ratio, both being almost the golden ratio, seems unlikely to be a coincidence.

Note also that the well-known 3:2 Neptune:Pluto orbital period ratio is closely related to the golden ratio:
Neptune:Pluto semi-major axis ratio = 1:1.31397
Phi²/2 = 1.309017 (99.62% match)
Using Kepler’s third law: √(1.31397³) = 1.50618 or just over 3/2.

Uranus:Pluto semi-major axis ratio = 1:2.05621
2.05621 is 99.9% of √(Phi³) = 2.05817

Data from NASA’s Planetary Fact Sheets