This paper studies the impact of mobility on the power consumption of wireless networks. With increasing mobility, we show that the network should dedicate a non negligible fraction of the useful rate to estimate the different degrees of freedom. In order to keep the rate constant, we quantify the increase of power required for several cases of interest. In the case of a point to point MIMO link, we calculate the minimum transmit power required for a target rate and outage probability as a function of the coherence time and the number of antennas. Interestingly, the results show that there is an optimal number of antennas to be used for a given coherence time and power consumption. This provides a lower bound limit on the minimum power required for maintaining a green network.