The theory of systematic atmospheric radio refraction errors affecting measurements of range and range differences (and associated time rate of change of these quantities) is developed. It is shown that the refraction errors, particularly in range difference measurements, can seriously affect the accuracy of baseline-type tracking systems. A method is derived by which the systematic portion of tL.ese errors can be removed by means of linear relationships involving the surface value of the radio refractive index; the correction process cievlsea can be used in real time if desired. Several test cases are examined where horizontally-varying profiles of the refractive index variation with height are used to calculate the errors, and the correction process based on surface refractive index values is found to be useful under these more general conditions. Approximately 98 percent of the total range or rangt difference error can be removed using this correction procedure. The problem of baseline optimization for deep-space tracking is examined briefly, and it is shown that a baseline length of about 4, 000 miles is optimal for targets more than about 6, 000 miles from the earth, and foi such a system residual atmospheric refraction errors would be only a fe\\ hundredths of a microradian, assuming the validity of ray optics and of the models of the atmosphere used in this paper
