Doppler shifts and Faraday rotation of radio signals in a time-varying, inhomogeneous ionosphere: Part II. Two-signal case

Following procedures applied in Part I [Kelso, 1960a] to a single radio signal transmitted to the ground from a space vehicle in or above the ionosphere, equations are obtained in Part II for the time rate of change of the phase difference between two signals whose refractive indices are slightly different. These results are applied to the frequency shifts experienced in a two-frequency Doppler experiment of the Seddon-Jackson type, and to the determination of the rate of Faraday rotation of the plane of polarization. The principal restriction on the generality of the results is that the ionosphere is treated as quasi-isotropic; i.e., the ray paths are obtained by methods that would be exact in a slowly varying isotropic medium, but the refractive index is permitted to be a function of ray direction (implying an anisotropic ionosphere). The following conditions prevail: (a) the (slowly varying) ionosphere may be a general function of three spatial co-ordinates and of time; (b) the vehicle may follow an arbitrary (nonrelativistic) trajectory; (c) the magnetic field, which characterizes the dependence of the refractive index on direction, may have arbitrary form.