A gossip network is considered in which a source node updates its status while other nodes in the network aim at keeping track of it as it varies over time. Information gets disseminated by the source sending status updates to the nodes, and the nodes gossiping with each other. In addition, the nodes in the network are mobile, and can move to other nodes to get information, which we term contact mobility. The goal for the nodes is to remain as fresh as possible, i.e., to have the same information as the source's. To evaluate the freshness of information, we use the Version Age-of-Information (VAoI) metric, defined as the difference between the version of information available at a given node and that at the source. We analyze the effect of contact mobility on information dissemination in the gossip network using a Stochastic Hybrid System (SHS) framework for different topologies and mobility scalings with increasing number of nodes. It is shown that with the presence of contact mobility the freshness of the network improves in both ends of the network connectivity spectrum: disconnected and fully connected gossip networks. We mathematically analyze the average version age scalings and validate our theoretical results via simulations. Finally, we incorporate the cost of mobility for the network by formulating and solving an optimization problem that minimizes a weighted sum of version age and mobility cost. Our results show that contact mobility, with optimized mobility cost, improves the average version age in the network.