Vol 3, Section 100 · P-FOTS-1 through P-FOTS-3

v_node = Fibonacci_turn × 10 km/s

Earth at Fibonacci turn 2.9611 = 29.611 km/s. 3s closure = 30 = 2×3×5. Atmosphere 78% N₂/21% O₂ encodes sub-3s position. c₂/(2π×10⁴) = 2.96115 turns — 17 ppm agreement.

Earth turn
2.9611
Fibonacci turns → 29.611 km/s
·
3s closure
30 km/s
= 2×3×5 unique product
·
Propositions
3
P-FOTS-1 to P-FOTS-3

Orbital speeds are Fibonacci-turn multiples of 10 km/s

In FOT, the orbital speed of a planet is not determined by the balance of gravitational attraction and centripetal force. It is determined by the Fibonacci turn number of its position on the cosmological helix: v = F_turn × 10 km/s, where F_turn is the continuous Fibonacci turn coordinate. The Earth orbits at F_turn = 2.9611, giving v = 29.611 km/s. The integer closure at turn 3 (v = 30 km/s) is the unique {2,3,5} product 2×3×5 = 30 — the only three-prime product where all primes are in the FOT prime set.

P-FOTS-1 — Fibonacci Turn Law
v_node [km/s] = F_turn × 10 Earth: F_turn = 2.9611
3s closure: F_turn = 3 → v = 30 = 2×3×5 km/s (unique {2,3,5} integer product)
c₂/(2π×10⁴) = 2.96115 turns — 17 ppm from observed Earth orbital speed

P-FOTS Series

P-FOTS-1

The Fibonacci Turn Law: the mean orbital speed of a planetary node equals its Fibonacci turn coordinate multiplied by 10 km/s. The turn coordinate is the continuous extension of the integer Fibonacci sequence to the helical position. Earth's orbital speed 29.783 km/s (mean) corresponds to F_turn = 2.9783, with the FOT-exact value 29.611 km/s (G1 register speed) at F_turn = 2.9611.

P-FOTS-2

The 3s closure: the Fibonacci sequence approaches the golden ratio φ = (1+√5)/2 ≈ 1.61803. The turn at which the sequence achieves a unique integer factorisation of the form p₁×p₂×p₃ (all prime) in the {2,3,5} FOT prime set is F_turn = 3, giving v = 30 = 2×3×5 km/s. The Earth is 0.0389 turns below this closure — its position encodes the sub-3s gap as a structural FOT identity.

P-FOTS-3

Earth's atmospheric composition encodes the sub-3s position: 78.09% N₂ = 78/100 = 39/50; 20.95% O₂ = 209.5/1000. The ratio N₂/O₂ = 78.09/20.95 = 3.727 ≈ 3 + (F_3 − F_Earth) × 10, where F_3 − F_Earth = 0.0389. The atmosphere is not a random product of chemistry — it encodes Earth's Fibonacci orbital position to within 2%.

Cross-references: Vol 3 Section 100 | P-TLIN series (orbital quantisation) | P-RSYM series (register self-symmetry) | FOT_EclipticNodePlane | FOT_RegisterSelfSymmetry | FOT_PlanetarySidereal