On the mathematics of navigational calculations for meridian sailing

Abstract

Meridian sailing is actually a special case of sailing uniquely determined by relative coordinates Delta_phi, Delta_lambda. In this note we discuss explicit finding of certain navigational parameters such as loxodrome distance, rhumb line and geographic and geocentric latitude of a position on the globe surface, in terms of the inverse incomplete elliptic integral of the third kind, discussing and surveying certain traditional and recent methods of computation of this function.

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