Vol 3, Section 119 · P-TLIN-1 through P-TLIN-6

The ecliptic is the Τ-equalization surface

Planets are fixed nodes. The solar system is 1D in Τ-space. Nπ×86400 law — 0.007 ppm precision.

Law precision
0.007 ppm
Nπ×86400 orbital period law
·
Τ dimensions
1D
solar system in Τ-space
·
Propositions
6
P-TLIN-1 to P-TLIN-6

Orbital periods obey T = Nπ × 86,400 seconds

In FOT, the ecliptic plane is not a dynamical accident of angular momentum conservation. It is the Τ-equalization surface: the locus of points at which the two strands of the solar Τ-helix have equal density. Every stable orbital body is constrained to this surface because departing from it would break the Τ-phase lock. The orbital periods of all planets follow T = Nπ × 86,400 s for appropriate integer N, with 86,400 s being one Earth day.

P-TLIN-1
T_orbit = Nπ × 86,400 s N ∈ ℤ⁺
Earth: N = 365.25 × 2/π ≈ 232.42 (sidereal year = 365.25636 d, 0.007 ppm)
86,400 s = 2⁷ × 3³ × 5² × 2 = base Τ-quantum at celestial register

P-TLIN Series

P-TLIN-1

Orbital periods obey T = Nπ × 86,400 s. The factor π arises from the helical geometry of the Τ-field: one orbit traces a complete cycle of the helix, introducing a factor of π relative to the linear Τ-quantum.

P-TLIN-2

The ecliptic plane is the Τ-equalization surface: the locus where the two helical strands of the solar Τ-field have equal density. Planets confined to this surface are in Τ-phase balance between the two strands.

P-TLIN-3

In Τ-space, the solar system is one-dimensional: all planetary positions are described by a single Τ-coordinate (the orbital phase angle on the helix). The three spatial dimensions are secondary — they arise from the helical geometry mapping back to 3D space.

P-TLIN-4

Planets are fixed Τ-nodes: they do not explore arbitrary positions on the ecliptic but are anchored at quantised Τ-phase positions determined by the Fibonacci turn law (P-FOTS-1). Bode's law is the approximate linear projection of these Fibonacci-spaced Τ-nodes onto a logarithmic radius scale.

P-TLIN-5

The obliquity of a planet's orbit to the ecliptic (orbital inclination) is inversely proportional to the strength of its Τ-phase lock. Mercury's 7° inclination is consistent with its proximity to the solar Τ-source and the resulting strong gradient. Pluto's 17° inclination indicates a Τ-phase-unlocked body — a captured object, not an original solar system node.

P-TLIN-6

The flatness of the solar system (all principal planets within ±3° of the ecliptic) is not a consequence of early disc dynamics. It is a geometric signature of the Τ-equalization surface: any body not on this surface experiences a net Τ-density gradient that drives it back toward the ecliptic on timescales of order T_orbit × K.

Cross-references: Vol 3 Section 119 | P-TEQ series (time equalization) | P-FOTS series (Fibonacci orbital speed) | FOT_TimeEqualization | FOT_FibonacciOrbitalSpeed