Radio Doppler shifts between a lander on Mars' surface and an orbiter are modeled through a linearized analytical formulation. This simplified formulation allows us to understand the signature and interplay of the different geophysical parameters (nutations, polar motion, and rotation rate variations) on the lander-orbiter observable. The frequency band of the investigated periodic phenomena goes from some months to about one Martian year in their respective frames. Long-term effects like precession are taken into account but are not investigated. The satellite orbit is modeled as a precessing orbit because of the oblateness of Mars. We show that we are able to see the signature of a possible liquid core after less than 50 weeks of observation for a given precision of 0.1 mm/s for the Doppler tracking. We are also able to monitor the rotation rate variation and polar motion at a level of 5 mas over the same period. This study was done in the frame of the preparation of the Netlander Ionosphere and Geodesy Experiment (NEIGE).