Here's the calculation: https://upload.wikimedia.org/wikipedia/commons/2/21/GeometricDistanceToHorizon.png https://upload.wikimedia.org/wikipedia/commons/2/21/

Here's the calculation: https://upload.wikimedia.org/wikipedia/commons/2/21/GeometricDistanceToHorizon.png https://upload.wikimedia.org/wikipedia/commons/2/21/Geometri... R ≈ 6.4E6 h = 0.3 d = √(2Rh + h²) ≈ 2.0E3 γ ≈ sin γ = d/(R + h) ≈ 3.1E-4 extra rope length = 2 × (d − γR) = 2R × (tan γ − γ) ≈ 2R × γ³/3 ≈ 0.13E-3