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.
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References
Breit, G., and Tuve, M. A., Phys. Rev., 28, 554 (1926).
Appleton, E. V., and Beynon, W. J. G., D.S.I.R. Rad. Res. Spec. Rep. No. 18 (1948).
Shearman, E. D. R., Proc. Inst. Elec. Eng., 103, B, 210 (1956).
Forsterling, K., and Lassen, H., Z. tech. Phys., 12, 502 (1931).
McCue, C. G., Austral. J. Phys., 9, 454 (1956).
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GETHING, P. Relation between Oblique and Ground Path-lengths in Ionospheric Propagation over a Curved Earth. Nature 193, 260–261 (1962). https://doi.org/10.1038/193260a0
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DOI: https://doi.org/10.1038/193260a0
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