The Martian global-scale CO2 seasonal cycle implies temporal variations in both the zonal gravity coefficients, such as $bar{C}$20, and in the rotation rate. To estimate the ability to detect simultaneously these two main geodetic signatures, a new approach based on a Network Science Experiment is investigated. We have numerically simulated the two types of Doppler signals involved, accurate orbiter tracking from the Earth and Martian lander tracking from the orbiter, by using a model of both the rotation variations and the seasonal variations of $bar{C}$20. Then, through a least square process, we have jointly adjusted the rotation and $bar{C}$20 parameters from an a priori knowledge. Our results show that it is possible to decorrelate $bar{C}$20 from all rotation parameters. We obtain an accurate adjustment of the $bar{C}$20 variations and a precision at the level of a few milliarcseconds for the estimation of the rotation rate variations.