Calculating Earth's Radius with Geometric Algebra: A Sunset Photo Hack
2025-03-15
This article presents a clever method for calculating the Earth's radius using a single photograph of a sunset over a calm body of water. Building upon Robert Vanderbei's elegant trigonometric analysis, the author employs the more powerful system of geometric algebra to analyze the image. By constructing vector equations and leveraging properties of geometric algebra, such as the geometric product and wedge product, a concise formula for calculating the Earth's radius is derived. The method ingeniously uses the relationship between the sun's position and its reflection on the water, and the effects of Earth's curvature, ultimately yielding a result reasonably close to the actual value.