IONOSPHERIC CONTRIBUTIONS TO THE DOPPLER SHIFT AT VHF FROM NEAR-EARTH SATELLITES

Abstract : The ionospheric contributions to the non-relativistic Doppler shift at VHF from satellites above the ionosphere are considered to 0(1/f sub s to the 3rd power) where f sub s is the satellite transmitter frequency and the vacuum Doppler shift is considered of 0(f sub s). Boundary conditions are imposed on the solution to the wave equation containing the ionosphere electron contribution to the refractive index such that the solution to 0(1/f sub s to the 3rd power) in the phase is obtained. It is shown that to this order Fermat's principle can still be applied if the index of refraction is modified by terms containing gradients of the electron density. This generalized Fermat's principle is used to obtain the ionospheric contributions to the Doppler shift to 0(1/f sub s to the 3rd power) at VHF. Upper bounds for the various terms are estimated. It is shown that: (1) additional terms not given by the geometrical optics approximation are negligible so that geometrical optics theory is valid at VHF to 0(1/f sub s to the 3rd power), and (2) except for very disturbed conditions in the ionosphere, the use of the two frequency doppler data to eliminate the first order refraction contribution should yield negligible higher order refraction errors so long as the lower of the two frequencies in above 100 mc/s.