Prediction of Apparent Elevation Angle from Specified Position for an Object in the Troposphere

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Abstract
A method is presented for calculating the apparent elevation angle to be expected for an object situated in the troposphere at specified values of geometrical elevation angle and height. The assumptions are made that the troposphere is spherically stratified and that the index of refraction decreases exponentially with height above a spherical earth. The method also allows for a direct application of the ray-tracing formulae for computing the corresponding optical path length (also termed radio range or electrical range) and ray path length. Results based on the method are compared with calculations made by the National Bureau of Standards for a source of radio waves and for the same space points and atmosphere. The comparison indicates that the new method is intrinsically more accurate. It is applicable to both the optical and radio frequency portions of the spectrum and the accuracy is limited only by the degree of approximation used to evaluate the integrals involved.

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