John D. Cook 4/14/2026

Intersecting spheres and GPS

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This article explains the geometric principles behind GPS navigation. It describes how knowing distances to satellites creates intersecting spheres, narrowing down a location from a circle to two points and finally to a single point with three satellites. It covers how time synchronization errors are corrected with a fourth satellite, mentions relativistic effects, and notes that the nonlinear distance equations can be transformed into linear algebra problems. The content is technical and directly related to technology and satellite navigation systems.

Intersecting spheres and GPS

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