IX.8 - GREAT CIRCLE PLOTTING

Abstract

This chapter describes the great circle plotting. A great circle comprises those points common to a sphere, and a plane, the latter passing through the formers center. Great circles partition a sphere into equal hemispheres, and form geodesies and lines of minimal length spanning two points on the spheres surface. The properties make them ubiquitous to charts, and other applications involving spherical coordinates. Examples include the instantaneous ground track of a satellite, the Earths present day/night terminator, and the way followed by a long-haul airline route, or a radio wave. By deriving the equations for a great circle in analytic form, the equations of projection or algorithms for plotting can be created easily. A simple chart illustrates the great circles forming the day/night terminators on consecutive months during fall in the Northern Hemisphere. Plotting great circles is especially difficult when the track passes near a pole and pronounced shifts in instantaneous heading arise.