Challenged networks represent a class of networks characterized by widely varying network conditions such as intermittent connectivity, a heterogeneous mix of resource-constrained nodes, long and variable message communication time, bidirectional data-rate asymmetries and, high failure rate of nodes. In such deployment scenarios, connectivity is not well served either by the standard Internet architecture and protocols, or by traditional mobile ad hoc network (MANET) and wireless sensor network (WSN) routing schemes. Given that advances in hardware technology have been continuously improving the computing and storage capabilities of nodes in challenged networks, there is a huge untapped potential for embedding complex control and analytic services in such networks. In this paper, we propose a first-of-its-kind distributed computing framework called challenged computing for providing timely, secure and dependable in-network computational services for complex and diverse types of space missions. We introduce a novel Weighted Temporal Graph model to capture the realistic dynamic and adversarial network conditions in the envisioned space-based challenged networks. We then present a discussion of the key service components and their associated research challenges towards realizing our proposed challenged computing framework in the context of overlaying a distributed computing environment over a space-based challenged network.