The Sagnac Effect: Measuring the Earth's Rotation with Light
🔄 Rotation & tilt
Question
How does an aircraft know the Earth is rotating?
Send two light beams around a loop in opposite directions: on a rotating platform they return at different times, because the loop moves while the light is in flight. The time difference depends on the rotation rate and the area of the loop. Ring-laser gyros and fibre-optic gyros (FOGs) use this to measure the Earth's rotation rate continuously - aircraft inertial navigation systems do it in flight, all the time.
The math
Fringe shift ΔN = 4Aω / (λc). For A = 1 m² and λ = 1,550 nm: ΔN = 4 × 1 × 7.292×10⁻⁵ / (1.55×10⁻⁶ × 3×10⁸) ≈ 0.63 fringes. The Earth's rotation rate is 7.292×10⁻⁵ rad/s = 15.04° per hour. GPS receivers apply a Sagnac correction of up to ~207 ns.
Why it matters
This is the same 15° per hour that the flat-earth community's $20,000 fibre-optic gyroscope 'could not accept' in 2017 - measured in real time, every hour, by the navigation systems of every aircraft. The rotation rate is constant globally, which is exactly what a rotating sphere predicts.