Earth radius from a single sunrise image: a classroom-ready activity

Abstract

Using a photograph of the shadow of Mont Blanc taken from Geneva at sunrise, we derive an upper limit for the Earth radius. After presenting the observational context and the model underlying assumptions, we determine the direction of the solar rays relative to the local vertical. This direction constrains the Earth maximum diameter which -- once corrected for atmospheric refraction -- amounts to roughly 1.7 times its presently accepted value. This work illustrates a pedagogical approach to scientific inquiry, showing how simple observations, combined with reasoning and elementary mathematical and geometrical tools, can yield meaningful physical estimates.

Figures (9)

• Figure 1: The shadows of Mont Blanc and its neighbor, Mont Maudit, projected above their summits onto a cloud layer illuminated by the rising Sun. The sunlight arrives from below the local horizon, as illustrated in the drawing below.
• Figure 2: Map showing the orientation of the location from which the photo was taken (Geneva) in relation to Mont Blanc.
• Figure 3: Cropped section of the photograph in Fig. 1 showing key details for measurements.
• Figure 4: Schematic illustrating the image formation on the camera’s CCD sensor.
• Figure 5: Schematic illustration of the situation. The dimensions are not drawn to scale, as the horizontal distance $d$ is more than ten times greater than the height of the cloud layer.