Why Phi? – Pluto’s eccentric orbit

Posted: March 27, 2016 by oldbrew in Phi, solar system dynamics
Tags: ,
Pluto's non-standard orbit [credit: Wikipedia]

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

Comments
  1. Bloke down the pub says:

    If their orbits cross, what is the chance of Pluto being recaptured by Neptune?

  2. oldbrew says:

    Pluto was last in the same part of its orbit as it is now, in about 1768.

  3. oldbrew says:

    The sum of Uranus and Neptune’s semi major axes (average distance from the Sun) is almost the same as Pluto’s aphelion (furthest distance from the Sun). The amount by which it falls short is about the same as the difference between Pluto and Neptune’s perihelion distances.

    Also, the sum of Uranus and Neptune’s orbit periods (248.81y) is very similar to Pluto’s orbit period (247.92y).

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