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Delay/Disruption-Tolerant Networking (DTN) originated from research on Interplanetary Internet and still today space applications are the most important application field and research stimulus. This paper investigates DTN communications between the Earth and the far side of the Moon, by means of a lunar orbiter acting as relay. After an introductory part, the paper presents a comprehensive analysis of the DTN performance that can be achieved on the identified communication scenario. The focus is on the evaluation of the stateof-the-art ability of Interplanetary Overlay Network (ION), the NASA DTN implementation of Bundle Protocol (BP) and Contact Graph Routing (CGR), to meet the many challenges of the space communication scenario investigated (and more generally of a future interplaynetary Internet): intermittent links, network partitioning, scarce bandwidth, long delays, dynamic routing, handling of high priority and emergency traffic, interoperability issues. A study of security threats and Bundle Security Protocol (BSP) countermeasures complete the work. The many results provided, confirm the essential role of DTN in future space communications.