Fibonacci Structure in Orbital Speeds

The Fibonacci sequence runs through the inner solar system exactly as far as the lattice of time allows — and the gears of the Sun, Mercury, Venus and the Earth multiply to the turn of the DNA helix

25/18 × 125/108 × 54/25 × 3 = 125/12 golden ratio face √(5π/6) = 1.6180215938 golden angle 432/π 12 pages

Seven Fibonacci numbers on the lattice

Of all the Fibonacci numbers, only seven are built from 2, 3 and 5 alone: 1, 1, 2, 3, 5, 8 and 144. The ratios they keep — 2/1, 3/2, 5/3, 8/5 — are the locks of the solar system, among them Mercury's three rotations to two orbits.

The speed ladder

The inner solar system runs on a ladder of speed gears, each a {2,3,5} fraction. Their product is the turn of the B-form DNA helix.

THE LADDER
Sun 25/18 · Mercury 125/108 · Venus 54/25 · Earth 3
product = 10.416666… (125/12), the DNA turn
Sun × Mercury = 1.6075102880658436 (3125/1944), the mile gear

The golden ratio's face

The golden ratio is irrational, but its face on the lattice is a door: √(5π/6). The golden angle on the lattice is 432/π, the angle a sunflower packs its seeds by.

THE GOLDEN FACES
φ face = 1.6180215938 (√(5π/6)) · golden angle = 137.5098708° (432/π)

Questions This Paper Answers

Is the Fibonacci sequence in the solar system?

Yes, as far as the lattice allows: 1, 1, 2, 3, 5, 8 and 144 are the only Fibonacci numbers built from 2, 3 and 5, and their ratios are the locks of the inner planets.

What do the inner planets' speed gears multiply to?

25/18 × 125/108 × 54/25 × 3 = 125/12 = 10.41666…, the turn of the B-form DNA helix.

What is the golden ratio on the lattice?

1.6180215938, √(5π/6) — a door, whose square is 5π/6, 150 degrees in radians.

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A note on the numbers. Every value here is given at full precision, because the precision is the evidence. A quantity truly on the {2,3,5,π} lattice does not approximate a lattice form; it is one. Where a value has not been read onto the lattice we say so rather than rounding until it appears to fit. And a number in this framework is not a measurement of one thing: it is one address that may surface as a period, a frequency, a radius, an energy or a proportion, depending only on the register in which it is read — the same register carries Mercury's orbit and the radio line of hydrogen.

Nothing on this page was pulled, attracted or held down. There is one substance — time — flowing from the sparse toward the dense, and the radio whisper of cold hydrogen and the slow turning of Mercury are one thread of its pattern. If it stirred your curiosity, the whole weave is waiting: the planets, the atom, light, life and number, all carried by the same single force.

Read the whole theory of the Universal Force of Time →