2. PHASE SHIFT DUE TO PLANETARY IONOSPHERES

2.1 Principle Of The Phase Shift Due To Plasma

The phase shift due to plasma is

......(1)

where x is the distance along the ray path, is the wave length of the radio wave, and is the refractive index of plasma. The refractive index of unmagnetized plasma is expressed as (11) in Appendix A. Substituting (11) into (1), we get

......(2)

where I is the total electron content along the ray path in units of m,^-2 c is the light velocity in m s^-1 and fuso represents the nominal frequency of the radio wave from the spacecraft in Hz. I is expressed as

......(3)

where Ne is the electron density of plasma. The frequency shift is the derivative of with respect to time t, thus it is proportional to dI/dt. Since dI/dt is proportional to the spacecraft velocity, the frequency shift is proportional to the spacecraft velocity as well as the electron content.

To evaluate the typical phase shifts due to the Martian ionosphere and the lunar ionosphere, we calculate the total electron content I along the ray path in the model Martian ionosphere and the model lunar ionosphere assuming that the spacecraft moves in a direction perpendicular to the ray path. By substituting the calculated I into (2), the phase and frequency shifts can be evaluated. We also evaluate the phase shifts due to the fluctuation of the terrestrial ionosphere from GPS data in typical cases to compare them with the phase shifts by the Martian ionosphere and the lunar ionosphere.