Applications of Complex Analysis to Celestial Navigation

Abstract

Mapping points on a sphere by stereographic projection to points on the plane of complex numbers transforms the spherical trigonometry calculations performed in the course of celestial navigation into arithmetic operations on complex numbers. Rotations on spherical coordinate systems take a simple bilinear form. Relationships between circles on the sphere and circles on the complex plane are derived. The results are applied to the reduction of double altitude sights, altitude and azimuth determination, and the clearing of lunar distance sights.

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