In this paper, we demonstrate significant reduction in communication power by using a mobile observer to collect data from a wireless single-hop network of static sensors. The key challenge in using a mobile observer is that it remains within range of any sensor for a limited period, and inability to transfer data in this period causes data loss. This prompts us to choose the fraction of nodes successful in communicating data as our performance constraint as we try to minimize network power. First, we establish that the process of data collection by a mobile observer is analogous to a queue. The queuing-based data collection model is then used as a design tool to identify the combination of system parameters that satisfies the performance metric with minimum power. Second, we derive a sufficient condition on node placement for zero data loss in a mobile observer network. As our third contribution, we demonstrate that in a dense network, the data collection analysis is much simpler, which allows us to obtain closed expressions for the network power. Power comparisons with static observer networks show that power reduction by multiple orders of magnitude is typical. The scenarios chosen for power comparisons also provide guidelines on the choice of path, if such a choice is available. As an example, a disc shaped network is analyzed and among the set of concentric circular paths, the best path is identified.