The effect of tropospheric refraction on the Doppler shift of a satellite signal

An expression for the contribution made by tropospheric refraction to the Doppler shift of a satellite signal is derived. It is assumed that the troposphere is horizontally stratified and does not vary during the time of a pass; a two-parameter quadratic expression is used as an approximation to the refractivity profile. The qualitative effect of the troposphere during any satellite pass is to steepen the slope of the Doppler shift versus time curve, making the tracking station appear slightly closer to the orbit than it actually is. When Doppler data from several passes are used for orbit computation, the resultant effect of the troposphere in general is not zero; thus it may bias the orbit slightly, the amount depending on the geometry of the selected passes. Conversely, if the orbit is assumed to be known, the station position as determined by a single satellite pass may be shifted toward the orbit by 50 meters or more. Such errors are not negligible if precise geodetic work is to be done with satellites. The residual tropospheric error in the Doppler shift can probably be reduced by an order of magnitude by using a computed tropospheric correction of the type described here. Some Doppler data from observed satellite passes are presented in corroboration of the theory.