Refraction of radio waves in the atmosphere is becoming a topic of increasing concern to space scientists as tracking systems of extremely high precision are put into operation. Already ray bending and retardation of signal are many times greater than instrumental inaccuracies in measuring arrival time and elevation angle at the various tracking sites.

A number of methods are presently in use for computation of the effects of atmospheric refraction on tracker measurements but all which have come to the writer's attention involve interpolation from tables, double precision methods on digital computers, or needlessly involved formulation.

In this paper the mathematics of earthquake seismology are used to derive new analytic expressions for the effects of atmospheric refraction on the measurements of conventional radio frequency tracking devices. These expressions are concise, accurate, and rapidly evaluated in single precision. Expressions are also derived for the effects of refraction on time derivatives of the measurements, a subject which is virtually ignored in the literature.

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