A sequence of 34 photos taken from a passenger plane at about 26,000 ft captures the Earth’s shadow as a blue-grey wedge on the dawn sky. A simple geometric model treats the Sun’s rays as parallel and the shadow as a half-cylinder behind a spherical Earth; for each line of sight the point nearest the Earth’s centre (P*) determines whether that direction is in shadow. Using the sun’s position and the plane’s GPS track, the model projects directions into the camera frame and predicts the angular height α of the shadow edge above the horizon. The measured edge is extracted per image column by finding the steepest change in log(red/blue) color (the warm sunlit air versus bluish shadow), with camera geometry (4096 px width, FOV 72.4°, focal length ≈2800 px) mapping pixel heights to angles. The model ignores refraction, the solar disk, and multiple scattering, effects that shift the effective shadow surface by ~1 km.
The model matches the sharp band very well: examples include α≈2.3° predicted versus 2.4°/2.1° observed at 03:11 UTC, and a median R² of 0.97 across 14 photos; earlier frames break down because the shadow extends above eye level and the simple P*-criterion no longer captures the visible darkness. Fitting the photos for Earth’s radius yields a crude best fit of R̂ ≈ 4,000 km (mean angular error 0.09°), but uncertainties in camera pointing, grazing sunlight and scattering allow fits from roughly 3,000-6,500 km (or 4,000-7,500 km including systematic offsets); the true radius is 6,371 km.
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