Four Planets, Four Pure Lattice Speeds
In the Universal Force of Time framework each inner body carries a spacetime dimensional speed — a pure {2,3,5} rational number that governs its role in the Tau time field. Reading outward from the Sun:
| Body | Speed (decimal) | Exact Fraction | Prime Lattice Form |
|---|---|---|---|
| Sun | 1.388888... | 25/18 | 5² / (2×3²) |
| Mercury | 1.157407... | 125/108 | 5³ / (2²×3³) |
| Venus | 2.160000 | 54/25 | 2×3³ / 5² |
| Earth | 3.000000 | 3/1 | 3 |
Sun × Mercury = km/miles Conversion Factor
The product of the Sun and Mercury dimensional speeds gives the FOT kilometre-to-mile conversion exactly — this is not a numerical coincidence but an algebraic identity:
Inverse: (1/Sun) × (1/Mercury) × km_miles = 1 [exact]
The Cascade to DNA Helical Turns
Each additional planet multiplies the running product by its dimensional speed, revealing a cascade of physically meaningful quantities:
Sun × Mercury: 3125/1944 = 1.607510... (km/miles)
Sun × Merc × Venus: 3375/900 = 3.75000...
The final four-body product 125/12 = 5³/(2²×3) links directly to the fine structure constant. The three DNA geometric parameters 12, 10π²/9, and 125/12 multiply to give 10/α.
Key Results
Each inner body (Sun, Mercury, Venus, Earth) carries a pure {2,3,5} spacetime dimensional speed: 25/18, 125/108, 54/25, and 3 respectively.
Sun × Mercury = 3125/1944 = 5⁵/(2³×3⁵) = FOT km/miles conversion factor (1.607510288...) exactly. The inverse identity (1/Sun)(1/Mercury)(km_miles) = 1.
The consecutive product cascade terminates at Sun×Mercury×Venus×Earth = 125/12, the FOT DNA helical turns ratio.
The product 125/12 is the third DNA geometric parameter. Together with 12 (base pairs per helical turn) and 10π²/9 (pitch geometry), the product 12 × (10π²/9) × (125/12) = 1250π²/9 = 10/α gives the fine structure constant: 1/α = 125π²/9.
The Sun speed 25/18 and Mercury speed 125/108 are consecutive terms in the pure-5 power series divided by the pure-{2,3} denominator lattice: 5ⁿ/(2×3ⁿ), 5ⁿ⁺¹/(2²×3ⁿ⁺¹).
The free-fall derivation chain uses km/miles = Sun×Mercury as the unit bridge: AU(million miles) × (Sun×Mercury) → AU(million km) → g. Planetary dimensional speeds are therefore embedded in Earth surface gravity.