Relation between Oblique and Ground Path-lengths in Ionospheric Propagation over a Curved Earth

Abstract

FOR a plane Earth and horizontally stratified ionosphere, Breit and Tuve's theorem¹ gives the relation between the effective oblique path-length P′ travelled by a radio-wave packet and the corresponding ground-range D as: P′ = D sec Δ where Δ is the angle of elevation of the ray path relative to the ground. Provided that the electron density within the layer is a function of height only and that there is no imposed magnetic field, this relation is rigorously true for any density–height profile.